diff --git "a/L1-1K.json" "b/L1-1K.json" new file mode 100644--- /dev/null +++ "b/L1-1K.json" @@ -0,0 +1,7003 @@ +[ + { + "id": 1, + "scenario_code": "3.1", + "instruction": " Chang'e-6 rover is performing exploration tasks at the lunar south pole, and its solar panel uses a two-dimensional tracking algorithm (azimuth + pitch angle). At the current moment, the solar elevation angle is 15°, and the azimuth angle is 30° (0° is due north, increasing clockwise). There is a lunar hill 100 meters ahead of the rover with a height of 20 meters. The maximum pitch angle of the solar panel is 90°, and the azimuth angle rotation range is ±180°. The solar radiation intensity on the lunar surface is 1360 W/m², the efficiency of the solar panel is 28%, and the effective area is 2 m².", + "question": "Calculate the theoretical maximum power generation of the solar panel under the current conditions (ignoring shading), and determine whether the azimuth angle needs to be adjusted to avoid shading by the lunar hill (the adjusted azimuth angle range should be provided)?", + "answer": "Theoretical maximum power generation = 1360 * 2 * 0.28 * cos(15°) = 735.6 W; Shading determination: Lunar hill elevation angle = arctan(20/100) = 11.3° < solar elevation angle 15°, so there is no shading at the current azimuth angle of 30°, and no adjustment is needed." + }, + { + "id": 2, + "scenario_code": "3.4", + "instruction": " Yutu-2 needs to perform three tasks simultaneously during the lunar day: ① Continuous operation of the X-ray spectrometer (35W power consumption) ② Sample collection by the robotic arm (instantaneous peak 120W, lasting 5 minutes) ③ Data transmission (75W power consumption, requiring a 10-minute window). The current available power limit of the power system is 150W, and the lithium-ion battery pack can provide an additional 50W of peak buffer power, with a duration not exceeding 8 minutes.", + "question": "Design a load scheduling plan that meets all task requirements, specifying the start sequence of each task and the timing of battery intervention.", + "answer": "Plan: ① The X-ray spectrometer remains on throughout (35W); ② Start the robotic arm sampling 5 minutes before data transmission begins (120W), at this time the total power consumption is 155W = 35 + 120, with the battery providing a 5W buffer; ③ Immediately start data transmission (75W) after sampling is completed, at this time the total power consumption is 110W = 35 + 75, and the battery stops supplying power." + }, + { + "id": 3, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the moon, located at coordinate point A(10°N, 120°E), and needs to travel to scientific target point B(12°N, 122°E). It is known that: 1) The straight-line distance between the two points is 30km, but the actual path requires detouring around 3 craters, increasing the total travel distance to 45km; 2) The energy consumption model of the lunar rover is E = 0.15*d + 2.5 (d is the travel distance, unit km, E is the power consumption, unit Wh); 3) The current remaining power is 80Wh; 4) The remaining time of the lunar day only allows continuous travel for 4 hours, and the average speed of the lunar rover is 0.3km/min.", + "question": "Please calculate the total power consumption for Yutu-2 to complete this movement task, and determine whether it can meet both the energy and time constraints under the current conditions.", + "answer": "Total power consumption E = 0.15*45 + 2.5 = 9.25Wh <80Wh; Required time t = 45/(0.3*60)=2.5h <4h. Conclusion: It can meet both the energy and time constraints simultaneously." + }, + { + "id": 4, + "scenario_code": "2.7", + "instruction": " The lunar rover encounters a solar proton event warning while driving near the terminator and needs to reach a permanently shadowed area within a 50-meter radius in 10 minutes. The current speed limit is 0.1 m/s, and the inertial navigation system shows a position error of ±3 meters per minute. The center of the safe area is located 40 meters away at an azimuth of 30°, but there is a 15-meter diameter impact crater in that direction.", + "question": "Provide the key parameters for a collision-avoidance path that meets the time and safety constraints: the maximum allowable detour angle, the minimum safe distance, and the theoretical reachability (yes/no). Hint: Consider the accumulation of position errors and the physical size of the obstacle.", + "answer": "Maximum detour angle = arcsin(15/(2*40)) = 11°, minimum safe distance = 15/2 + 3*10 = 25 meters (10 minutes error accumulation 30 meters), theoretical reachability = yes (since 40/cos11° ≈ 41 meters, time required 410 seconds < 600 seconds and avoidance distance 25 meters > 7.5 meters crater radius)." + }, + { + "id": 5, + "scenario_code": "2.10", + "instruction": " The probe needs to perform centimeter-level close-up observations on a 0.5-meter diameter basalt outcrop. Known: the visual navigation camera resolution is 2 mm/pixel (at a distance of 1 meter), the IMU angular velocity measurement error is ±0.01°/s, and the end-effector positioning accuracy of the robotic arm is ±1 cm. The approach phase uses a 'segmented deceleration' strategy: speed is 5 cm/s when >1 m from the target, and reduces to 1 cm/s when ≤1 m from the target.", + "question": "Calculate the minimum parking distance to ensure clear imaging (target occupies ≥100 pixels) and verify whether the positioning error of the robotic arm meets the total accuracy requirement of ±3 cm at this distance (including IMU drift effect, assuming an approach time of 30 seconds).", + "answer": "Minimum parking distance = 0.5 m / (100 pix * 2 mm/pix) = 1 m; total error = robotic arm error 1 cm + IMU drift error = 1 cm + 30 s * 0.01°/s * π/180 * 100 cm ≈ 1 cm + 0.52 cm = 1.52 cm < 3 cm, meeting the requirement." + }, + { + "id": 6, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the soil in this area are as follows: medium hardness (Mohs hardness 4-5), low viscosity, and high volatile content (about 2%). There are three sampling tools available: 1) A diamond-coated rotary drill (suitable for rocks with hardness >6); 2) A titanium alloy grab (suitable for loose lunar soil); 3) A scraper with heating function (suitable for samples containing volatiles). The force control parameters for each tool are different: the drill requires maintaining 500-800N axial pressure, the grab requires 200-300N clamping force, and the scraper requires a constant 150N pressure with 50°C heating.", + "question": "Based on the characteristics of the lunar soil and the parameters of the tools, which sampling tool should be chosen? Explain the basis for setting its force control parameters.", + "answer": "The scraper with heating function should be chosen. The setting basis is: 1) The hardness of the lunar soil (4-5) is lower than the standard for the drill; 2) The high volatile content (2%) requires heating to prevent volatilization; 3) The low viscosity does not require the high clamping force of the grab, and the 150N pressure of the scraper is sufficient to remove the lunar soil layer." + }, + { + "id": 7, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. The standard procedure requires: 1) Internal pressure of the container <10^-3Pa; 2) RFID tag signal strength ≥-60dBm; 3) Temperature recorder shows the entire process maintained at -50±5℃. Current inspection data: pressure 8*10^-4Pa, RFID signal -55dBm, temperature record shows a minimum of -52℃ and a maximum of -47℃. The handover time limit has 8 minutes remaining, and the time required for individual re-inspections are: pressure test 3 minutes, RFID test 1 minute, temperature data download 2 minutes.", + "question": "Determine whether the current sample container meets the handover standards? If re-inspection is needed, provide the most time-saving re-inspection plan.", + "answer": "Meets standards (pressure 8e-4Pa<1e-3Pa; RFID -55dBm≥-60dBm; temperature -52~-47℃ within the range of -50±5℃). No re-inspection needed." + }, + { + "id": 8, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing a patrol mission on the far side of the moon, located at coordinate point A(10,20), and needs to reach the scientific target point B(80,60). Terrain data indicates there are three selectable paths between the two points:\n1. Path 1: straight-line distance of 100 meters, average slope of 15°, loose lunar soil ratio of 40%;\n2. Path 2: zigzag distance of 120 meters, average slope of 8°, loose lunar soil ratio of 20%;\n3. Path 3: detour distance of 150 meters, average slope of 5°, loose lunar soil ratio of 10%.\nThe known energy consumption model is: E = 0.5*d*(1+0.02*slope) + 0.3*d*loose ratio (d is the path length, unit meters; E is the energy consumption, unit Wh). The current remaining energy is 180Wh.", + "question": "If only considering the energy consumption constraint and it is necessary to reach the target point, which path should Yutu-2 choose? Calculate the total energy consumption of each path and explain the basis for the choice.", + "answer": "Path 1 energy consumption = 0.5*100*(1+0.02*15) + 0.3*100*0.4 = 65 + 12 = 77Wh; Path 2 = 0.5*120*(1+0.02*8) + 0.3*120*0.2 = 69.6 + 7.2 = 76.8Wh; Path 3 = 0.5*150*(1+0.02*5) + 0.3*150*0.1 = 82.5 + 4.5 = 87Wh. Path 2 should be chosen, as its energy consumption of 76.8Wh is below the remaining energy and is the lowest of the three." + }, + { + "id": 9, + "scenario_code": "4.6", + "instruction": " The lunar sample sealed container uses a three-level purification system: a primary titanium alloy chamber (background contamination <0.1μg/m³), a secondary PTFE liner (organic permeation rate <1×10^-12g/cm²·s), and a tertiary nitrogen positive pressure protection (purity 99.9999%). It is known that the typical organic concentration in Earth laboratories is 500μg/m³. During a certain operation, the engineer needs to transfer the sample from the glove box to the sealed can within 15 seconds, with the interface area between the glove box and the sealed can being 20cm². During the operation, it was found that the oxygen sensor in the glove box suddenly rose to 100ppm (it should normally be <1ppm).", + "question": "Calculate the maximum possible organic contamination introduced during this operation and determine whether it exceeds the organic contamination limit for lunar soil samples (specified <1ng/g). Assume the sample mass is 100g.", + "answer": "Contamination = concentration * exposure area * time = 500μg/m³ * (20/10000)m² * (15/3600)h * 10^6 = 500*0.002*0.00417*10^6=4.17μg. Contamination per unit mass = 4.17μg/100g = 41.7ng/g. Conclusion: Exceeds by 41.7 times." + }, + { + "id": 10, + "scenario_code": "4.4", + "instruction": " Yutu-2 obtained the following data while conducting exploration in the Von Kármán crater: Point A (45.3°N, 176.2°E) spectral characteristics show a 85% probability of KREEP rock composition; Point B (45.1°N, 176.4°E) 3D point cloud shows the presence of a boulder outcrop with a diameter of 2m; Point C (45.0°N, 176.3°E) thermal infrared data shows an abnormally high temperature point. The rover has enough remaining power to move a total distance of no more than 500m, and it is currently located at the center of the three points (distances to each point: A=180m, B=220m, C=150m). The scientific priority ranking rule is: KREEP rock sampling weight 50%, boulder 30%, thermal anomaly 20%.", + "question": "According to the multi-objective optimization principle, please calculate the inspection path sequence that the rover should adopt and the theoretical maximum scientific benefit value (formula: scientific benefit = Σ(target weight * completion coefficient), completion coefficient=1-0.5*(travel distance/500)).", + "answer": "Optimal path sequence: C→A→B. Scientific benefit calculation: Completing point C benefit=20%*(1-0.5*150/500)=17%; Completing point A cumulative travel 330m, benefit=50%*(1-0.5*330/500)=33.5%; Completing point B cumulative travel 550m exceeds the limit, so the actual maximum scientific benefit is 17%+33.5%=50.5%." + }, + { + "id": 11, + "scenario_code": "5.10", + "instruction": " The ground control station uses pseudo-code ranging technology to track the orbit of the Chang'e-5 orbiter around the moon. Given a ranging code rate of 10 MHz, the measured round-trip signal delay is 2.567 ms. The speed of light is 3 * 10^8 m/s, and the average radius of the moon is 1737 km. Ranging formula: distance = (delay * speed of light) / 2 - ΔR (ΔR is a fixed equipment delay value of 50 km).", + "question": "Calculate the theoretical distance from the Chang'e-5 orbiter to the moon's center, and determine whether it is operating on the preset 200±15 km circular orbit.", + "answer": "Theoretical distance = (2.567e-3 * 3e8) / 2 - 50 = (770100) / 2 -50 ≈385050 -50=385000 m=385 km; Orbit height=385-1737≈-1352 km (invalid value), indicating that there may be an error in the Earth-Moon distance calculation or the relative position of the Earth and Moon needs to be considered." + }, + { + "id": 12, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin (SEL) on the far side of the moon, and needs to maintain communication with Earth through the Queqiao-2 relay satellite. Known: 1) The Queqiao-2 orbit is a large elliptical frozen orbit around the moon, with a perigee height of 300km and an apogee height of 8600km; 2) The maximum visible time window between the lander and Queqiao-2 is 4 hours per orbit; 3) The current orbital period T=12 hours; 4) The ground station can only see Queqiao-2 and the lander simultaneously for 8 hours per day. Now, the optimal communication window needs to be planned within 24 hours.", + "question": "If each communication session must last no less than 30 minutes and the interval must not exceed 6 hours, what is the maximum number of effective communications that can be arranged? Provide the calculation process.", + "answer": "A maximum of 4 times. Calculation process: 1) The maximum communication window per orbit is 4 hours, but it is limited by the ground station to 8 hours, so the actual available window is min(4*2 orbits, 8) = 8 hours; 2) Each communication session lasts 30 minutes, theoretically allowing for 16 sessions, but the interval must be ≤6 hours; 3) Divide the 8 hours into 4 segments (0h, 2h, 4h, 6h) to start communication, each session lasting 30 minutes, with a total duration of 2 hours, and intervals of 2h/2h/2h, meeting all constraints." + }, + { + "id": 13, + "scenario_code": "5.7", + "instruction": " The relay satellite of Chang'e-7 is equipped with a 512GB radiation-resistant SSD, using NAND flash chips (block size 128KB, lifespan 3000 write-erase cycles). The file system design must meet: 1) Daily write volume fluctuates between 20-50GB; 2) Critical telemetry data is written daily at a fixed 5GB (non-overwritable); 3) Science data retention period ≥30 days. The wear leveling algorithm uses a dynamic hot zone adjustment strategy.", + "question": "To ensure the SSD does not fail due to wear over a 5-year mission, calculate the daily average write limit (considering wear leveling efficiency of 90%) and provide recommendations for the allocation of storage blocks for critical telemetry data.", + "answer": "Daily limit 34.6GB. Calculation: 1) Total writable data=512GB*3000*90%=1382400GB; 2) Daily average limit=1382400/(5*365)≈757GB/day; 3) After deducting the fixed 5GB, it is 752GB. Recommendation: Allocate independent block groups for critical data (5GB/day corresponds to 40 128KB blocks), use append-only write mode to avoid repeated erasures." + }, + { + "id": 14, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth. The Queqiao relay satellite is positioned at the Earth-Moon L2 point, responsible for forwarding communication signals. It is known that the maximum communication distance between Queqiao and the lander is 80,000 km, and the maximum communication distance between Queqiao and Earth is 450,000 km. At this moment, the distance between Queqiao and the lander is 75,000 km, and the distance between Queqiao and Earth is 400,000 km. The communication link budget formula is: Received power = Transmission power + Transmission antenna gain + Reception antenna gain - Path loss - System loss. The path loss calculation formula is: 20 * log10(4 * π * d / λ), where d is the distance, and λ is the wavelength (0.1 m). The system loss is fixed at 3 dB.", + "question": "If the transmission power of the lander is 10 W (converted to dBm as 40 dBm), the transmission antenna gain is 15 dBi, and the reception antenna gain of Queqiao is 20 dBi, calculate the signal power received by Queqiao (dBm).", + "answer": "Received power = 40 dBm + 15 dBi + 20 dBi - (20 * log10(4 * π * 75000 / 0.1)) - 3 dB = 40 + 15 + 20 - 179.5 - 3 = -107.5 dBm" + }, + { + "id": 15, + "scenario_code": "5.4", + "instruction": " The Yutu-2 lunar rover is currently performing scientific exploration tasks when the communication link with the Queqiao relay satellite is suddenly interrupted due to lunar terrain blocking. The communication buffer inside Yutu-2 can store up to 2 hours of scientific data (data generation rate of 1 Mbps) and is equipped with two backup communication plans: Plan A uses a low-frequency band antenna (recovery time 5 minutes, bandwidth 500 kbps), and Plan B uses a high-frequency band antenna (recovery time 15 minutes, bandwidth 2 Mbps). The current buffer has already stored 30 minutes of data.", + "question": "To ensure that scientific data is not lost, which communication recovery plan should Yutu-2 choose? Please calculate the total time required for data transmission to complete under both plans (starting from the moment of interruption).", + "answer": "Remaining buffer capacity = (120 - 30) * 60 * 1 Mbps = 5400 Mb. Total time for Plan A = 5 minutes + (5400 / 500) seconds ≈ 5 + 648 seconds ≈ 15.8 minutes; Total time for Plan B = 15 minutes + (5400 / 2000) seconds = 15 + 162 seconds ≈ 17.7 minutes. Plan A should be chosen." + }, + { + "id": 16, + "scenario_code": "2.7", + "instruction": " When the Chang'e-7 lander is working at the edge of the Shackleton crater, it suddenly receives a solar proton event warning (lasting 4 hours). Currently located at coordinates (10°S, 90°E), it needs to urgently move to a permanent shadow area 3 kilometers away for safety. The maximum speed of the lunar rover is 0.1m/s, the IMU drift error is 0.5°/h, and the lighting conditions allow the use of visual navigation for only 20 minutes. It is known that the safety route has two 5-meter wide fissures that need to be detoured (each adding 50 meters to the journey).", + "question": "Calculate whether the safety can be completed before the visual navigation window closes. If not, what backup navigation mode should be used.", + "answer": "Total distance = 3000 + 2*50 = 3100m; Required time = 3100 / 0.1 = 31000 seconds > 1200 seconds window period. Need to switch to pure inertial navigation + periodic starlight correction mode." + }, + { + "id": 17, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the lunar soil in this area are as follows: medium hardness (Mohs hardness 4-5), low viscosity, and high volatile content (about 1200ppm). There are three sampling tools available: A-type rotary impact drill (suitable for rocks with hardness >6), B-type vibrating grab (suitable for loose lunar soil), and C-type scraper (suitable for lunar soil with medium hardness and volatile content). The working energy consumption of each tool is: A-type 18W/h, B-type 12W/h, C-type 15W/h. The mission requires that the total energy consumption during the sampling process does not exceed 50Wh, and it must ensure that the volatiles are not lost due to the heat generated by the tool (the surface temperature of the tool must be <100°C). It is known that the surface temperature of the A-type tool during operation is 150°C, B-type is 80°C, and C-type is 95°C.", + "question": "According to the above conditions, which sampling tool combination should be chosen to complete the sampling task while meeting the energy consumption and temperature limit requirements? Please explain the specific selection reasons.", + "answer": "Choose the C-type scraper. Reasons: 1) The lunar soil hardness is suitable for the C-type tool; 2) The surface temperature of the C-type tool, 95°C, meets the requirement for protecting volatiles; 3) The maximum working time of the C-type tool alone is 50/15 ≈ 3.33 hours, which meets the sampling requirements; 4) The temperature of the A-type tool exceeds the limit, while the B-type tool, although temperature-qualified, is not suitable for medium-hardness lunar soil." + }, + { + "id": 18, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. It is known that: 1) The designed pressure of the sealed cabin should be maintained at 1.2 ± 0.1 atm; 2) The success rate of RFID reading is related to distance as p = 1 - 0.2 * d (d in meters); 3) The positioning error of the handover robotic arm follows a normal distribution N(0, 0.05^2). Current telemetry shows a sealed pressure of 1.18 atm, RFID read/write distance of 0.8 meters, and the robotic arm has undergone three positioning calibrations (cumulative error formula: σ_total = σ_single * sqrt(n)). The handover process requires that the following conditions be met simultaneously: pressure within specifications, RFID read success rate ≥ 90%, and positioning error with 99.7% probability < 0.15m.", + "question": "Based on the current parameters, determine whether all handover conditions are met. If not, identify the parameters that need adjustment and their target values.", + "answer": "All conditions are met: 1) Pressure 1.18 atm is within the 1.1-1.3 atm range; 2) RFID success rate p = 1 - 0.2 * 0.8 = 84% < 90%, does not meet the requirement, need to adjust distance to ≤ 0.5 meters; 3) Total positioning error 3σ = 3 * 0.05 * sqrt(3) = 0.26m > 0.15m, need to increase the number of calibrations to n ≥ (0.15 / (3 * 0.05))^2 ≈ 4 times." + }, + { + "id": 19, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the Moon's south pole, it is necessary to power three devices simultaneously: a seismometer, a magnetometer, and a spectrometer. The current power grid provides a peak power of 120W. The basic power consumption of each device is as follows: seismometer 15W (requires continuous operation), magnetometer 20W (operates for 2 minutes every 10 minutes), and spectrometer with a peak power of 80W (operates for 5 minutes every 30 minutes). The energy management system uses a dynamic priority allocation strategy: seismometer > magnetometer > spectrometer. All devices share a bandwidth-limited data return link.", + "question": "During the 5 minutes when the spectrometer starts working, if the magnetometer also happens to enter its working cycle, can the system's remaining available power support both running simultaneously? Please calculate and explain.", + "answer": "No. At this time, the total power demand = seismometer 15W + magnetometer 20W + spectrometer 80W = 115W, although it does not exceed the peak of 120W, the insufficient data link bandwidth will cause the spectrometer to run at a reduced frequency (at least 15W margin must be reserved), so the actual available power = 120-15=105W < 115W." + }, + { + "id": 20, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the lunar soil in this area are as follows: medium hardness (Mohs hardness 4-5), low viscosity, and high content of volatiles (about 2%). There are three sampling tools available: 1) diamond-coated rotary drill bit (suitable for rocks with hardness >6); 2) titanium alloy grab (suitable for loose lunar soil); 3) scraper with heating function (suitable for lunar soil containing volatiles). The working energy consumption of each tool is: drill bit 50W/h, grab 20W/h, scraper 30W/h. The mission requires that the total energy consumption during the sampling process does not exceed 100W/h, and it must ensure that the volatiles do not escape.", + "question": "Based on the above conditions, which sampling tool combination (single or multiple) should be chosen to optimally complete the sampling task while meeting the energy consumption constraints and ensuring no loss of volatiles during the sampling process? ", + "answer": "Choose the scraper with heating function (30W/h), as it is specifically designed for lunar soil containing volatiles and meets the energy consumption constraints." + }, + { + "id": 21, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration near the Von Kármán crater. According to the interpretation of high-spectral data from the orbiter, there are three potential high-value targets in the area: Point A (70% probability of KREEP rock, 200 meters away), Point B (85% probability of volcanic glass, 350 meters away), and Point C (60% probability of breccia, 150 meters away). The rover's average daily travel capability is 300 meters, and scientific investigations require at least 30 minutes of in-situ analysis at each target point (15W per point). The remaining power can only support a total energy consumption of no more than 45W for movement and exploration activities.", + "question": "If the highest mineral probability target is prioritized, what exploration route should be planned to meet the constraints of total travel distance and scientific exploration both being satisfied within the constraints of the remaining power and travel capability of the rover per day？", + "answer": "Route: Base → Point B (350 meters) → Base. The total travel distance of 700 meters exceeds the daily travel capability, so it is not feasible; it needs to be changed to the nearest high-probability target, Point A (200 meters round trip) or Point C (150 meters round trip)." + }, + { + "id": 22, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, a temporary energy-sharing network needs to be established. There are currently 3 devices: A (drilling sampler, peak power 120W), B (spectrometer, peak power 80W), C (data transmission node, peak power 60W). The shared energy module has a maximum output power of 200W, using dynamic priority scheduling: during drilling operations, A must receive full power, and during non-drilling periods, the remaining power is allocated in the order of B>C>A. The remaining duration of the lunar day is measured to be 8 hours, with the drilling task lasting 3 hours.", + "question": "If all devices need to run throughout and power fluctuations are not considered, calculate whether the energy module can meet the demand? If not, what is the minimum additional power reserve required in watts (W)?", + "answer": "Yes. During the drilling period, the total power consumption is 120W (A exclusively), and during the non-drilling period, the total power consumption is 140W (B 80W + C 60W), both of which do not exceed the 200W limit." + }, + { + "id": 23, + "scenario_code": "1.5", + "instruction": " The Yutu-2 lunar rover needs to be remotely controlled to cross a lunar rille with a communication delay of 1.3 seconds. The vehicle's current speed is 0.15m/s, and there is a 1.8-meter-wide crack 20 meters ahead. After the ground control center sends a braking command, the vehicle continues to travel a buffer distance d=0.2*v^2 (v is the current speed). Safety rules require the stopping point to be at least 0.5 meters from the edge of the crack.", + "question": "Determine if the current command can ensure safe stopping? If not, calculate the maximum allowable speed (保留2位小数) (retain 2 decimal places).", + "answer": "No. The buffer distance = 0.2*0.15^2 = 0.0045m, the total braking distance 1.3*0.15+0.0045 = 0.1995m, the remaining distance 19.8005m > 1.8+0.5m; however, the problem description is contradictory, and the actual maximum allowable speed v should be calculated: 1.3v+0.2v^2 ≤ 20-1.8-0.5 → v ≤ 3.25m/s" + }, + { + "id": 24, + "scenario_code": "1.8", + "instruction": " When deploying a seismometer array, it was found that the local lunar soil bearing capacity is only 3kPa, lower than the expected 5kPa. Each instrument weighs 50kg, with a base area of 0.2m^2. Given the lunar surface gravitational acceleration is 1.62m/s^2, and the safety factor requires that the actual pressure does not exceed 70% of the bearing capacity.", + "question": "Determine if the current base design is safe? If not, calculate the minimum additional base area required (保留3位小数).", + "answer": "Not safe. Actual pressure=(50*1.62)/0.2=405Pa=0.405kPa>3*70%=2.1kPa; It needs to satisfy (50*1.62)/A≤2.1→A≥38.571cm^2 (the original 2000cm^2 is already sufficient, the data in the question is contradictory and should be adjusted)." + }, + { + "id": 25, + "scenario_code": "1.4", + "instruction": " In the permanently shadowed region of the lunar south pole, 3 scientific instruments have been deployed (A: Infrared spectrometer, peak power 120W; B: Neutron detector, peak power 80W; C: Laser ranging reflector, peak power 30W). The lunar surface power grid consists of a solar array (maximum output 200W) and a backup nuclear battery (constant output 50W). All devices share the same power bus and must meet: 1) Total instantaneous power does not exceed 250W; 2) The nuclear battery load must not be less than 20W to maintain its temperature. The current system is in the lunar night period and can only use the nuclear battery for power.", + "question": "If device A needs to operate continuously for 2 hours to collect key data, how should the operation of other devices be scheduled during this period to meet the power constraints? Please provide a specific power allocation plan.", + "answer": "Device A operates (120W), Device B is off (0W), Device C operates (30W). Total power=120+0+30=150W, nuclear battery load=50-150=-100W (must be limited to above 20W), so the actual total power consumption must be ≤30W. Therefore, only Device C (30W) can operate, and Devices A and B must be turned off. However, the question requires Device A to operate, so there is no feasible solution." + }, + { + "id": 26, + "scenario_code": "1.5", + "instruction": " When remotely operating a lunar rover from the ground control center for rock sampling, the one-way communication delay is 1.3 seconds. The current speed of the lunar rover is 0.2m/s, and there is an unforeseen loose lunar soil area 3 meters ahead (it needs to decelerate to 0.05m/s 1.5 seconds in advance to safely pass through). The control command generation takes 0.4 seconds, and the on-board control system response delay is 0.2 seconds.", + "question": "Calculate the total delay time from when the deceleration command is issued from the ground to when the lunar rover actually begins to decelerate, and determine whether it can avoid entering the hazardous area at the current speed.", + "answer": "Total delay = command uplink 1.3 seconds + generation 0.4 seconds + downlink 1.3 seconds + response 0.2 seconds = 3.2 seconds. Distance traveled by the vehicle during the delay period = 0.2m/s * 3.2s = 0.64m. Remaining distance = 3 - 0.64 = 2.36m, safe deceleration time required = 1.5s, distance traveled = 0.2 * 1.5 + 0.5 * (0.2 - 0.05) * 1.5 = 0.4125m < 2.36m, therefore it can avoid danger." + }, + { + "id": 27, + "scenario_code": "1.8", + "instruction": " When deploying a seismic array, it was found that the local lunar soil bearing capacity is only 60% of the expected value (the original design load-bearing standard is 500N/m²). The total mass of the existing four-legged support equipment is 42kg, and the area of each footpad is 50cm². The lunar surface gravitational acceleration is 1.62m/s².", + "question": "Verify whether the current support design meets the actual lunar soil bearing capacity requirements. If not, calculate the minimum area that needs to be added to each footpad (rounded to the nearest whole number cm²).", + "answer": "Total weight of the equipment = 42kg * 1.62m/s² = 68N; force on each foot = 68/4 = 17N; actual bearing capacity = 500 * 60% = 300N/m²; current footpad pressure = 17 / (50/10000) = 3400Pa > 30000Pa (not met). Minimum area required = 17 / 30000 ≈ 57cm², need to increase 7cm² per footpad." + }, + { + "id": 28, + "scenario_code": "4.4", + "instruction": " Yutu-2 is conducting exploration in the Von Kármán crater, obtaining data from three candidate sampling points: Point A (KREEP rock enrichment 85%, distance 1.2km), Point B (volcanic glass coverage 70%, distance 0.8km), Point C (breccia freshness index 90%, distance 1.5km). The rover's movement speed is 0.05m/s, and the scientific value weight formula is: priority score = mineral abundance * 0.6 + (1 - distance/2km) * 0.4. It can work 8 hours per day, and 2 hours need to be reserved for in-situ analysis.", + "question": "If it is necessary to complete sampling at the highest priority point within 1 working day, please calculate which point should be chosen? And verify whether the time is sufficient for round trip + sampling (sampling requires 1.5 hours).", + "answer": "Calculate priority: A = 85 * 0.6 + (1 - 1.2/2) * 0.4 = 51 + 0.16 = 51.16; B = 70 * 0.6 + (1 - 0.8/2) * 0.4 = 42 + 0.24 = 42.24; C = 90 * 0.6 + (1 - 1.5/2) * 0.4 = 54 + 0.1 = 54.1. Choose point C. Time verification: travel time = (1500m) / (0.05m/s) = 30000s = 8.33h, total time = 8.33 * 2 + 1.5 = 18.16h > 6h available working time, so in practice, point A should be chosen (round trip time = (1200/0.05) * 2 / 3600 = 13.33h) + 1.5h = 14.83h still exceeds the limit, ultimately no solution, the plan needs to be adjusted." + }, + { + "id": 29, + "scenario_code": "4.9", + "instruction": " Lunar sample return capsule design parameters: inner diameter of the sealed container 20cm, height 30cm, sample bag size 10×10×15cm. The ascent vehicle docking accuracy requires the deviation between the center of the container and the axis of the docking mechanism to be ≤5cm. The container is equipped with an RFID tag (read/write distance 3cm) and three temperature sensors (error ±0.5℃), and must transmit data to the ascent vehicle computer within the range of -20℃ to +30℃ (sampling rate 1Hz). The relative velocity during docking must be <0.1m/s.", + "question": "If the actual measured parameters at the moment of docking are: center deviation 3cm, temperature sensor readings -19℃/-21℃/-20℃, relative velocity 0.08m/s, RFID signal strength meets the standard but continuously loses (interrupts 4 times per second), please determine whether it meets the safe transfer conditions or not.", + "answer": "Does not meet. Reasons: ① The temperature sensor reading of -21℃ exceeds the lower limit (-20±0.5℃, the actual lower limit is -20.5℃); ② The RFID interruption frequency of 4Hz > the sampling rate of 1Hz leads to incomplete data; although the center deviation (3cm≤5cm) and relative velocity (0.08m/s<0.1m/s) meet the standards." + }, + { + "id": 30, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to conduct sampling in an area on the far side of the moon rich in KREEP rock. The hardness of the lunar regolith in this area is 3.5 on the Mohs scale, with medium viscosity and a high content of volatiles. There are three sampling tools available: A-type drill (suitable for rocks with hardness >4, power consumption 120W), B-type grab (suitable for loose lunar regolith with medium viscosity, power consumption 80W), C-type scraper (suitable for soft lunar regolith with high volatile content, power consumption 60W). The current remaining power of the probe is 1500Wh, and 300Wh must be reserved for return communication.", + "question": "To ensure the success of the sampling task without exceeding the power consumption budget, which sampling tool should be chosen? Please calculate the maximum allowable sampling duration.", + "answer": "Choose the C-type scraper. The maximum allowable sampling duration is (1500Wh - 300Wh) / 60W = 20 hours." + }, + { + "id": 31, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover has discovered three potential sampling points at the edge of a 100-meter diameter impact crater: Point 1 (KREEP rock probability 85%, 35 meters from the current position), Point 2 (breccia probability 70%, 50 meters away), Point 3 (volcanic glass probability 95%, 80 meters away). The rover's movement speed is 0.05m/s, energy consumption is 0.8Wh per meter, and the total available energy is 400Wh. The scientific priority weights are: KREEP rock 1.2, breccia 1.0, volcanic glass 1.5.", + "question": "Based on the principle of energy consumption constraints and maximizing scientific value, which point should be prioritized for investigation? Provide the calculation process for the decision-making basis.", + "answer": "Point 3 (volcanic glass) should be prioritized. Decision basis: Energy consumption for Point 1 = 35 * 0.8 = 28Wh, value = 85% * 1.2 = 1.02; Energy consumption for Point 2 = 50 * 0.8 = 40Wh, value = 70% * 1.0 = 0.7; Energy consumption for Point 3 = 80 * 0.8 = 64Wh < 400Wh, value = 95% * 1.5 = 1.425 (highest)." + }, + { + "id": 32, + "scenario_code": "4.9", + "instruction": " The automatic rendezvous and docking window for the ascent vehicle and the lander is ±15 minutes. The sample container weighs 2kg and needs to be heated from -50°C to 20°C for integrity checks, with a specific heat capacity of 800J/(kg·K). The heating system efficiency is 60%, the power supply voltage is 28V, and the maximum allowable current is 5A. The environmental heat loss rate is 10W. The remaining preparation time is currently 25 minutes.", + "question": "Calculate whether the heating system can complete the heating within the time limit? If it can be completed, find the actual required time (ignoring latent heat).", + "answer": "It can be completed. The required heat Q = 2kg * 800J/(kg·K) * 70K = 112000J; Effective power P = 28V * 5A * 60% = 84W; Net heating power = 84W - 10W = 74W; Time t = 112000J / 74W ≈ 1513 seconds ≈ 25.2 minutes < 25 minutes (the actual calculation should be that 25 minutes is sufficient)." + }, + { + "id": 33, + "scenario_code": "3.4", + "instruction": " Yutu-2 rover plans to execute three tasks simultaneously on the 3rd lunar day: 1) Upload data via X-band communication equipment (peak power consumption 45W, lasting 15 minutes); 2) Infrared imager operation (30W, requiring continuous power supply for 20 minutes); 3) Mechanical arm sampling (instantaneous impact current 120W, each lasting 5 seconds, repeated 10 times every 2 minutes). Power system constraints: Lithium-ion battery pack maximum discharge current 15A (nominal voltage 28V), current solar array output power 180W.", + "question": "Design a power supply sequence plan that meets all task requirements, specifying the start and stop times of each device and the rationale (starting from T=0)?", + "answer": "1) T0-T20min prioritize the infrared imager (30W); 2) The mechanical arm starts at T0, T2, ... T18min (each for 5 seconds), total average power consumption = 120*5*10/1200=5W; 3) X-band starts at T20-T35min (45W). The total peak power consumption throughout the process = 30+120=150W < 180W solar output, the battery only needs to supplement <15A*28V=420W of instantaneous difference." + }, + { + "id": 34, + "scenario_code": "3.6", + "instruction": " Chang'e-4 relay satellite needs to maintain the temperature of the critical equipment compartment at ≥-40°C during the lunar night (-180°C). Thermal insulation system parameters: 1) Compartment surface area 1.2m², thermal emissivity 0.85; 2) Equivalent thermal resistance of multi-layer insulation material 8K/W; 3) RTG isotope heat source rated heat output 50W; 4) Steady-state heat generation power of the equipment compartment 12W. Stefan-Boltzmann constant σ=5.67e-8 W/(m²·K⁴).", + "question": "Verify whether the existing thermal insulation plan meets the requirements? If not, how much additional electric heating power is needed at least to meet the requirements? ", + "answer": "Heat balance equation: Q_rtg + Q_elec + Q_device = Q_loss = (T_in^4 - T_out^4)*σ*A*ε + (T_in - T_out)/R_th. Substituting T_in=233K, T_out=93K yields Q_loss≈62.3W. Current heat supply = 50+12=62W ≈ 62.3W, which is in a critical state. It is recommended to add ≥1W of electric heating redundancy." + }, + { + "id": 35, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 lander is located on the edge of an impact crater at 23.5° East longitude and 12.8° North latitude on the lunar near side. Its solar panels operate in a two-dimensional tracking mode. According to the lunar almanac, the current solar elevation angle on the lunar surface is 15°, and the azimuth angle is 45° (with 0° being due north and increasing clockwise). The crater wall forms an obstruction in the azimuth range of 30°-60°, reducing the solar elevation angle by 10° in the shadowed area. Known conditions: 1) The solar panel output power P0 = 1200W without obstruction; 2) Power varies linearly with the sine of the solar elevation angle; 3) Two-dimensional tracking can maintain the angle between the wing normal and the sunlight ≤5°.", + "question": "Calculate the actual output power of the solar panels under the current conditions (round to the nearest integer).", + "answer": "600W" + }, + { + "id": 36, + "scenario_code": "3.6", + "instruction": " Before the Chang'e-7 lander enters the lunar night phase, it needs to maintain the temperature of key equipment: 1) Main control computer (heat generation 5W, operating temperature -40°C~+70°C); 2) Spectrometer (heat generation 2W, operating temperature -20°C~+50°C). Thermal insulation plan: a) Multi-layer thermal insulation material with a thermal resistance R=2K/W; b) Isotope heat source providing a constant 8W of heat; c) Electric heating as a backup (power consumption 12W/K). The lunar night environmental temperature is stable at -180°C, and the initial temperature of the equipment is -50°C. Thermal balance formula: Equipment temperature T_env + (total heat generation - heat loss)*R.", + "question": "Verify whether the main control computer can operate normally relying solely on the isotope heat source? If not, calculate the minimum power of the electric heating that needs to be activated (保留1位小数).", + "answer": "Not possible, need to activate 7.5W electric heating" + }, + { + "id": 37, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the Moon's south pole, a shared power grid consisting of 3 Mobile Energy Modules (MEMs) needs to be constructed. Each MEM has a maximum output power of 500W, but due to the extremely low temperatures during the lunar night, the actual available power must be calculated using the formula `P_available = P_max * (1 - 0.002 * (T_ambient + 150))` (T_ambient is the ambient temperature in °C). The current temperature in the area is -180°C. The scientific equipment includes: a seismometer (constant power consumption of 80W), a spectrometer (peak power consumption of 200W, duty cycle of 30%), and a robotic arm (instantaneous power consumption of 350W, each operation lasts for 5 minutes). All equipment must share the power through a time-triggered mechanism.", + "question": "If the spectrometer and the robotic arm cannot operate simultaneously, and the seismometer must be continuously powered, please calculate whether the power grid can support the normal operation of all equipment under the current environmental conditions.", + "answer": "It can support. Calculation steps: 1) Available power per MEM = 500 * (1 - 0.002 * (-180 + 150)) = 470W; 2) Total available power = 3 * 470 = 1410W; 3) Seismometer fixed consumption = 80W; 4) Average power consumption of the spectrometer = 200 * 0.3 = 60W; 5) Average power consumption of the robotic arm = 350 * (5/60) = 29.17W; 6) Maximum concurrent load = 80 + max(60, 29.17) = 140W << 1410W" + }, + { + "id": 38, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing exploration tasks at the edge of the Von Kármán crater, located at coordinate point A(10,20). It needs to reach the scientific target point B(45,60) within 3 hours, while avoiding a crater with a diameter of 15 meters (center coordinates (30,40)). The maximum climbing angle of the lunar rover is 15°, with an average moving speed of 0.05m/s, and energy consumption per unit distance on flat ground and uphill is 0.1Wh/m and 0.3Wh/m, respectively. The remaining battery energy is 180Wh, and the solar charging rate is 5W. The lunar surface has 4 hours of remaining sunlight.", + "question": "If the shortest path around the crater (the tangent path of the straight line AB at the edge of the crater) is chosen, calculate the total length of this path, total energy consumption, and the feasibility of the mission (considering energy and time constraints). The formula for the distance between two points is d = sqrt((x2-x1)^2 + (y2-y1)^2), and the detour distance added by the tangent path is the radius of the crater.", + "answer": "The straight-line distance AB = sqrt((45-10)^2+(60-20)^2) = 50m; the detour distance added = 15m; the total path = 65m. Time required = 65/0.05 = 1300s ≈ 0.36h < 3h; energy consumption on flat sections = 50*0.1 = 5Wh, energy consumption on sloping sections = 15*0.3 = 4.5Wh; total energy consumption = 9.5Wh < 180Wh. Feasible." + }, + { + "id": 39, + "scenario_code": "1.4", + "instruction": " The lunar surface energy grid needs to allocate peak power to 3 devices: a seismometer (continuous demand of 30W), a spectrometer (intermittent peak demand of 50W per 10-minute cycle), and a rover charging station (demand of 80W but can be delayed). The grid has a maximum output of 100W, and the spectrometer must trigger a working cycle every 30 minutes. At this moment, the spectrometer has just completed a working cycle.", + "question": "Design a power distribution plan for the next 30 minutes to ensure all device demands are met without exceeding the grid capacity.", + "answer": "Plan: 0-10 minutes, spectrometer 50W + seismometer 30W = 80W; 10-20 minutes, charging station 80W + seismometer 30W = 110W → over capacity, changed to charging station 70W + seismometer 30W = 100W; 20-30 minutes, spectrometer 50W + seismometer 30W = 80W. The remaining 10W for rover charging is delayed to the next cycle." + }, + { + "id": 40, + "scenario_code": "1.8", + "instruction": " When deploying a lunar seismometer array, the bearing capacity of the lunar soil at point A was measured to be 8kPa, and at point B to be 5kPa (minimum safe value). The mass distribution of the instruments is: main unit 40kg (must be placed at a point with higher bearing capacity), auxiliary units 20kg x 2. The contact area is: main unit 0.05m², auxiliary units 0.02m². The lunar gravitational acceleration is 1.62m/s².", + "question": "Verify whether the current deployment plan (main unit at point A, auxiliary units at points A and B) meets the bearing capacity requirements? If not, how should it be adjusted? ", + "answer": "Verification: Main unit pressure = (40*1.62)/0.05 = 1296Pa = 1.296kPa < 8kPa; Auxiliary unit pressure at point A = (20*1.62)/0.02 = 1620Pa = 1.62kPa < 8kPa; Auxiliary unit pressure at point B = 1.62kPa < 5kPa. The plan meets the requirements and no adjustment is needed." + }, + { + "id": 41, + "scenario_code": "3.1", + "instruction": " The Chang'e-5 lander is located near the Rümker Mountains at 43.06°N, 51.92°W on the near side of the Moon. During the lunar day, the solar elevation angle in this area varies from 5° to 35°, and terrain blocking reduces the effective sunlight hours by 20% compared to the theoretical value. The lander is equipped with two triple-junction gallium arsenide solar wings, each with a nominal power of 350W (AM0 condition, 25°C), and a two-dimensional drive mechanism can achieve ±90° azimuth adjustment and 0°-90° pitch angle adjustment. It is currently the 3rd day of the lunar day at noon, with a solar azimuth of 182�� and an elevation angle of 28°. The right solar wing has a 15% efficiency reduction due to lunar dust coverage.", + "question": "If at this time the left solar wing is optimally oriented (facing the sun directly), and the right wing is limited to its default deployed position (azimuth 0°, pitch 60°) due to a mechanism failure, calculate the total power generation of both wings at this moment (ignoring temperature effects). It is known that the power correction formula for triple-junction gallium arsenide cells under non-perpendicular incidence is P_actual = P_nominal * cos(θ), where θ is the angle of incidence of sunlight.", + "answer": "Left power: 350W * cos(0°) = 350W; Right incidence angle calculation: cos(θ) = sin(28°)*sin(60°) + cos(28°)*cos(60°)*cos(182°) ≈ 0.469 * 0.866 + 0.883 * 0.5 * (-0.999) ≈ -0.078 → take 0 (negative value is considered no sunlight), so right power = 350W * 0.85 * 0 = 0W; Total power = 350W + 0W = 350W" + }, + { + "id": 42, + "scenario_code": "3.6", + "instruction": " The Chang'e-4 lander is about to enter the lunar night phase, and it needs to maintain the temperature of key equipment within the range of -20°C to +30°C. The thermal control system is configured as follows: ① The radioisotope heat source (RHU) can provide a constant 15W of thermal power; ② The electric heater has a maximum power of 30W (divided into three levels: 10/20/30W); ③ The equivalent thermal resistance of the multi-layer insulation material R=2 K/W. The lunar night environmental temperature is -180°C, the heat generated by the equipment inside the cabin is 5W, and the initial temperature is +25°C. Given that the heat capacity of the equipment C=1000 J/K, the temperature change rate formula is ΔT/Δt = (Q_in - Q_out)/(C), where Q_out = (T_in - T_env)/R.", + "question": "Calculate the expected time for the cabin temperature to drop to -20°C when only the RHU is turned on, and propose the lowest combination of electric heater settings to maintain the temperature no lower than -20°C.", + "answer": "① When only the RHU is on, the net heat flow: Q_net = (15+5) - (25-(-180))/2 = 20 - 102.5 = -82.5W; cooling time Δt = C*ΔT/Q_net = 1000*(25-(-20))/82.5 ≈ 545 seconds ≈ 9.1 minutes; ② To maintain balance, Q_in ≥ Q_out → (15+5+P_heater) ≥ (-20-(-180))/2 → P_heater ≥ 80 - 20 = 60W, but the maximum electric heating is only 30W, so it cannot be maintained alone, and other measures need to be combined." + }, + { + "id": 43, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. The characteristics of the lunar soil in this area are: average hardness of 3.5 on the Mohs scale (similar to feldspar), moderate viscosity, and a volatile content of about 120 ppm. There are three sampling tools available: ① A diamond-coated rotary impact drill bit (suitable for hardness >4, power consumption 35W); ② A titanium alloy grab (suitable for hardness <3, power consumption 15W); ③ A tungsten carbide scraper (suitable for hardness 2-4, power consumption 25W). The total power budget for the sampling system is 60W, and it must ensure both sampling success and power consumption does not exceed the limit.", + "question": "Based on the characteristics of the lunar soil and the parameters of the tools, select the optimal combination of two tools and explain the reasons.", + "answer": "Choose the combination of the rotary impact drill bit and the tungsten carbide scraper. Reasons: ① The hardness of the lunar soil is 3.5 on the Mohs scale, which falls within the overlapping suitable range for both the drill bit (>4) and the scraper (2-4); ② The total power consumption of the two tools, 35W + 25W = 60W, just meets the budget; ③ The drill bit can handle areas of higher hardness, while the scraper is suitable for large-scale collection." + }, + { + "id": 44, + "scenario_code": "3.4", + "instruction": " The rover simultaneously performs three tasks: ① Drilling and sampling (peak power consumption 120W, lasting 30 minutes); ② Data transmission (peak power consumption 80W, lasting 20 minutes); ③ Spectral analysis (steady-state power consumption 60W, lasting 40 minutes). The current available capacity of the lithium-ion battery pack is 200Wh, and the power management system adopts the constraint condition of 'instantaneous power consumption not exceeding 100W'. The priority of each task is: drilling > data transmission > spectral analysis.", + "question": "Design a task scheduling plan that meets the energy constraints and calculate the remaining power after all tasks are executed.", + "answer": "Scheduling plan: First, execute drilling (120W) alone for 30 minutes, consuming 60Wh; then data transmission (80W) and spectral analysis (60W) run in parallel for 20 minutes, consuming 46.67Wh; finally, spectral analysis runs alone for 20 minutes, consuming 20Wh. Total consumption = 60 + 46.67 + 20 = 126.67Wh, remaining power = 200 - 126.67 = 73.33Wh" + }, + { + "id": 45, + "scenario_code": "3.1", + "instruction": " In the Chang'e-4 mission, the lander is located in the South Pole-Aitken Basin on the far side of the moon, and its solar wings use a two-dimensional tracking algorithm. It is known that the current lunar surface time is noon 12:00 (solar elevation angle 90 degrees), and the theoretical maximum power generation of the solar wings is 200W. Due to the遮挡 of nearby craters, the actual received solar radiation intensity is reduced by 30%. The solar wing tracking system has a pointing error of 5 degrees. Assuming that the power generation is proportional to the solar radiation intensity and proportional to cos(pointing error angle).", + "question": "Calculate the actual power generation of the solar wings at this time (保留 two decimal places).", + "answer": "133.60W" + }, + { + "id": 46, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the Moon's south pole, the mission team needs to coordinate the energy usage of multiple devices. The current lunar surface power grid consists of 3 solar power units (each with a peak power of 500W) and 2 radioisotope thermoelectric generators (each providing a continuous output of 200W). The equipment includes: 1 drilling machine (peak power consumption 800W, working duration 2 hours), 2 spectrometers (each with a continuous power consumption of 50W), and 1 communication relay system (base power consumption 100W, additional consumption of 300W during data transmission). The communication window opens for 1 hour every 8 hours. All equipment must complete their assigned tasks within 24 hours.", + "question": "If the drilling operation is required to completely overlap with the data transmission during the communication window, and the spectrometers need to operate throughout, please calculate whether the power grid can meet the requirements? If not, how many additional radioisotope thermoelectric generators are at least needed at minimum? ", + "answer": "Total power demand = Drilling machine 800W + Spectrometers 50W*2 + Communication relay system (100W+300W) = 1300W; Available peak power = Solar 500W*3 + Radioisotope 200W*2 = 1900W. Since 1300W < 1900W, the current configuration can meet the demand, and no additional radioisotope thermoelectric generators are needed." + }, + { + "id": 47, + "scenario_code": "3.8", + "instruction": " The mission profile for a certain lunar rover requires: 1) Movement phase: speed 0.1m/s, power consumption 50W, lasting 2 hours; 2) Exploration phase: X-ray fluorescence instrument operating power consumption 80W, collecting data for 3 minutes every 10 minutes; 3) Communication phase: directional antenna transmission power consumption 100W, each transmission lasting 15 minutes. The energy budget allocation is: no more than 30% for movement, no more than 20% for communication, and the rest for exploration. The total battery capacity is 5000Wh.", + "question": "Calculate how many complete communication transmissions the mission profile can perform at most while meeting the energy allocation constraints.", + "answer": "6 times" + }, + { + "id": 48, + "scenario_code": "3.8", + "instruction": " The Chang'e-7 relay satellite needs to support the following during its operation in lunar orbit: ① Two 30-minute X-band communications with the ground station each day (transmission power 40W); ② 10 minutes of payload operation per orbit (average power consumption 25W); ③ Continuous consumption of 15W for satellite management. The orbital period is 120 minutes, the lithium-ion battery pack capacity is 200Wh, and the depth of discharge is limited to 80%. The solar panels can provide an average of 150W of power during the illumination period.", + "question": "Calculate whether this power configuration can meet the needs of a complete orbital cycle? List the key decision-making steps.", + "answer": "1. Power supply during illumination period: 150*(120/2) = 9000Wh;\n2. Total power consumption: 40*1 + 25*(10/60)*12 +15*2 = 40+50+30=120Wh;\n3. Battery requirement max(0,120-90)=30Wh <200*0.8=160Wh;\n4. Conclusion: meets the requirement" + }, + { + "id": 49, + "scenario_code": "3.1", + "instruction": " Chang'e-6 lander is located in the South Pole-Aitken Basin on the far side of the Moon (latitude 85°S). Its solar panels use a two-dimensional tracking system (azimuth + elevation angle). According to the lunar calendar, it is currently the 5th day of the lunar day, and the solar elevation angle changes over time according to h(t) = 30 * sin(π*t/300), where t is in minutes (0≤t≤300). Terrain shadow analysis shows: there is a permanent shadow area at an azimuth of 180°, and at 90° and 270°, there is temporary shading when h(t)<15°. The maximum output power of the solar panels P_max = 200W, and the actual power P = P_max * cos(θ), where θ is the angle between the direction of the incident sunlight and the normal to the panel.", + "question": "If the solar panels are adjusted to an elevation angle of 25° and an azimuth of 135° at t=100 minutes, what is the actual output power at that time? (Hint: First calculate the current solar elevation angle and the optimal orientation.)", + "answer": "The solar elevation angle h(100) = 30 * sin(π*100/300) = 30 * sin(π/3) ≈ 25.98°. The optimal elevation angle should equal h(t), which is 25.98°. The current setting of 25° results in an incident angle θ=0.98°. Azimuth error: The optimal azimuth should be 0° (directly facing the sun), the current 135° deviates by 45°, the total incident angle θ_total = sqrt(0.98^2 + 45^2) ≈45°. P = 200 * cos(45°) ≈141.42W" + }, + { + "id": 50, + "scenario_code": "3.4", + "instruction": " The Yutu-2 rover plans to perform three tasks simultaneously: ① X-ray spectrometer (peak power consumption 80W, lasting 20 minutes); ② Panoramic camera shooting (peak 120W, lasting 5 minutes); ③ Data transmission (peak 150W, lasting 8 minutes). The energy system limits the total instantaneous power consumption to no more than 200W. The current remaining battery capacity is 1800Wh, and the remaining lunar day time is 4 hours. The task priority is ③＞①＞②.", + "question": "Please design a task scheduling plan that meets all constraints and calculate the remaining power after executing all tasks (base power consumption is 10W).", + "answer": "Scheduling plan: First execute ③ (150W) for 8 minutes → execute ① (80W) for 20 minutes (staggered with ②: the first 5 minutes ①+②=200W just reaches the limit, the next 15 minutes only ①) → finally execute ② for the remaining 3 minutes. Total energy consumption: (150*8 + 200*5 + 80*15 + 120*3)/60 ≈ 76.67Wh; base consumption 10*4=40Wh; remaining power=1800-76.67-40=1683.33Wh" + }, + { + "id": 51, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover experienced an X-band communication interruption during the lunar day, diagnosed as caused by a solar conjunction leading to signal attenuation exceeding the threshold. The rover's internal cache can store 8 hours of scientific data (generation rate 50MB/h), and the backup UHF band (400MHz) link has a maximum transmission rate of only 2Mbps but is not affected by the solar conjunction. At the time of the interruption, the cache was 30% full.", + "question": "Calculate the shortest time required to complete the emergency transmission of cached data after switching to the UHF link, and determine whether it can be completed before the end of the lunar day (9 hours remaining)?", + "answer": "1. Data to be transmitted = 8h * 50MB/h * 30% = 120MB\n2. UHF link transmission time = 120MB / (2Mbps / 8) = 480 seconds = 0.133 hours\n3. 0.133h < 9h, it can be completed" + }, + { + "id": 52, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover conducts exploration in the Von Kármán crater, obtaining the following regional data: (1) Orbital hyperspectral data show that there is a KREEP rock characteristic absorption peak at coordinates (12.3°S, 135.7°E) (reflectance <0.2 at 950nm wavelength); (2) LiDAR measurements indicate a slope of 8° at this point, with surface roughness RMS = 4cm; (3) The current remaining power is 800Wh, the energy consumption model for movement is E=0.5*d+20 (d is in kilometers), and the fixed energy consumption for scientific exploration is 50Wh per session. The rover's current position is 300 meters in a straight line from the target point, and the actual path to detour around obstacles is 450 meters.", + "question": "Determine whether the rover's current power is sufficient to complete the sampling and exploration task at this point, and calculate the remaining power after completing the task.", + "answer": "Total path energy consumption = 0.5*0.45+20 = 20.225Wh; Total energy consumption = 20.225+50 = 70.225Wh; Remaining power = 800-70.225 = 729.775Wh. Sufficient to complete the task" + }, + { + "id": 53, + "scenario_code": "1.8", + "instruction": " When deploying a network of magnetometers on the lunar surface, a local magnetic anomaly area (intensity fluctuation ±200nT) was discovered, which may affect the accuracy of the instruments. It is known that the calibration of a single magnetometer requires a stable environment for 30 consecutive minutes (fluctuation <50nT), and the current area's magnetic stability period conforms to an exponential decay model: fluctuation value ΔB(t) = 200*e^(-t/20) (t in minutes). The fluctuation values of the deployment point measured in the last three instances are ΔB=152nT at t=5min, ΔB=121nT at t=10min, and ΔB=98nT at t=15min.", + "question": "Verify the model parameters based on the actual measurement data, and calculate the earliest time point from the current moment when calibration can begin (requirement to predict the start time when the fluctuation is <50nT).", + "answer": "Model verification is correct (actual values 152≈200*e^(-5/20)=152, 121≈124, 98≈100); the fastest calibration time t satisfies 200*e^(-t/20)<50 → t>-20*ln(50/200)≈27.7 minutes, meaning calibration can start 28 minutes later." + }, + { + "id": 54, + "scenario_code": "3.1", + "instruction": " The Chang'e-5 lander performs sampling tasks in the area at 43.06°N, 51.92°W on the near side of the Moon. During the lunar day, the solar elevation angle in this area varies from 5° to 35°, and the solar panels use a two-dimensional tracking mode (azimuth + elevation). It is known that: 1) the maximum power P_max of a single solar panel under standard test conditions (AM0, 25°C) is 150W; 2) the actual power generation efficiency is affected by temperature with a coefficient of -0.45%/°C; 3) the average temperature on the lunar surface during the day is 100°C; 4) terrain blocking reduces the effective sunlight hours by 30%.", + "question": "If the current solar elevation angle is 20° and the azimuth tracking error is ±5°, calculate the actual output power of a single solar panel at this time (considering the temperature effect and a 15% power loss due to tracking error).", + "answer": "Actual power P = P_max * (1 - 0.0045*(100-25)) * (1-0.15) = 150 * 0.6625 * 0.85 ≈ 84.47W" + }, + { + "id": 55, + "scenario_code": "3.8", + "instruction": " The Chang'e-6 relay satellite performs an energy budget in lunar orbit: 1) Orbital period 2 hours, sunlight exposure rate 68%; 2) Payload peak power consumption 120W (operates for 45 minutes daily); 3) Platform base power consumption 80W; 4) Battery pack charge-discharge efficiency η=92%; 5) Average daily power generation of the solar array 1.8kWh.", + "question": "Verify whether the energy system can meet the survival needs of a continuous 7-day no-light period (entering the lunar shadow area), and explain the key calculation steps.", + "answer": "Total energy consumption for 7 days E_consume = (120*0.75 +80)*24*7 = 19320Wh; Available energy in the battery E_bat = (1.8*0.68 - (120*0.75 +80)*2/24)*7*0.92 ≈ -231Wh → Not sufficient" + }, + { + "id": 56, + "scenario_code": "2.7", + "instruction": " When the lunar rover is operating near the terminator and receives a solar proton event warning, it needs to reach the nearest safe point within a 500-meter radius within 30 minutes. The current position and data for three candidate points are as follows: Point A is 300 meters away but requires crossing a 10° slope; Point B is 450 meters away with loose lunar dust; Point C is 500 meters away in a flat basaltic area. It is known that the maximum climbing ability in an emergency is 8°, the lunar dust layer reduces speed to 30% of normal, and the safe moving speed limit is 0.1m/s.", + "question": "Determine which of the candidate points can be reached on time? Explain the basis for your choice.", + "answer": "Only Point C is reachable. Basis: The slope of Point A exceeds the limit; the time required for Point B = 450 / (0.1 * 0.3) = 15000 seconds > 1800 seconds; the time for Point C = 500 / 0.1 = 5000 seconds < 1800 seconds" + }, + { + "id": 57, + "scenario_code": "1.4", + "instruction": " A lunar surface energy grid needs to allocate power to drilling equipment (peak power 300W) and a communication relay station (peak power 200W). The total output limit of the grid is 400W, and a dynamic priority strategy is adopted: during drilling operations, the communication bandwidth can be reduced to 50%, at which point the relay station's power consumption drops to 100W. If both operate at full load simultaneously, it will trigger an overload protection shutdown. Currently, the drilling equipment is in continuous operation mode, and the communication relay needs to maintain real-time data transmission.", + "question": "Calculate whether the current system will overload? If so, how should the priority strategy be adjusted to keep the total power consumption within 400W? ", + "answer": "Current total power consumption = 300W (drilling) + 200W (communication) = 500W > 400W, it will overload. Solution: activate the communication frequency reduction strategy, after adjustment, the total power consumption = 300W + 100W = 400W ≤ limit." + }, + { + "id": 58, + "scenario_code": "1.5", + "instruction": " When remotely operating a lunar rover for rock sampling from the ground control center, the one-way communication delay between Earth and the Moon is 1.3 seconds. The rover is currently moving towards the target at a speed of 0.1m/s, and the control system uses a predictive algorithm to compensate for the delay: it sends movement commands for the next 2.6 seconds (2 times the delay) in advance. The target rock is 0.5 meters away from the initial position, and the rover's braking distance is 0.05 meters.", + "question": "Calculate the distance deviation between the final stop point set by the predictive command and the target, and explain whether this deviation is within the allowable tolerance range (assuming a tolerance of ±0.1 meters).", + "answer": "Distance moved during prediction = 0.1m/s * 2.6s = 0.26m; distance from the target to the stop point = |0.5m - (0.26m + 0.05m)| = 0.19m > ±0.1m tolerance, does not meet the requirement." + }, + { + "id": 59, + "scenario_code": "5.10", + "instruction": " The ground station determines the position of Chang'e-5 orbiter through pseudo-range measurement, with a ranging code rate of 10 MHz, and the measured pseudo-range observation value is 384402.137 km. It is known that the ionospheric delay correction is +2.3m, the tropospheric delay correction is -1.7m, and the equipment delay calibration value is +0.5ns (speed of light c=299792458m/s). The clock bias calculation formula is δt = (pseudo-range observation value - true distance - Σcorrections)/c.", + "question": "If the true orbital radius of the orbiter is 384400km, calculate the receiver clock bias (including sign) in this measurement? ", + "answer": "Total correction = ionosphere (+2.3m) + troposphere (-1.7m) + equipment delay (0.5ns*c≈0.15m) = 0.7m; Clock bias δt = (384402137m - 384400000m - 0.7m) / 299792458 ≈ (2137 - 0.7) / 299792458 ≈ 7.126μs (positive for receiver clock being faster)." + }, + { + "id": 60, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S), and needs to establish a communication link through the Queqiao-2 relay satellite. It is known that Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, with an orbital period of 14 days and a maximum lunar viewing angle of 8°. At this moment, the geometric distance between the relay satellite and the lander is 44,800 km, the downlink frequency of the X-band is 8.4 GHz, the transmission power is 20 W, and the antenna gain is 38 dBi. The free space path loss formula is L = 92.4 + 20*lg(f) + 20*lg(d), where f is the frequency (GHz) and d is the distance (km).", + "question": "Calculate the free space path loss value (dB) of the current link, and determine whether this value meets the minimum receiving sensitivity requirement of -120 dBm (ignoring other loss factors)?", + "answer": "Free space path loss L = 92.4 + 20*lg(8.4) + 20*lg(44800) ≈ 92.4 + 18.5 + 93 ≈ 203.9 dB; Received power P = Transmission power (20W → 43 dBm) + Antenna gain (38 dBi) - L (203.9 dB) = -122.9 dBm < -120 dBm, does not meet the requirement." + }, + { + "id": 61, + "scenario_code": "2.10", + "instruction": " The lunar rover needs to perform centimeter-accurate close-up observations of a special rock outcrop with a diameter of 2 meters. Currently, it is 10 meters directly in front of the rock, with a visual navigation system positioning error of ±5cm (3σ) and IMU angular velocity measurement noise of 0.01°/s (1σ). The approach process requires a final position error ≤10cm and attitude angle error ≤1°. Given: each forward 1 meter takes 20 seconds and the positioning error accumulates by 3cm; each stop for calibration takes 60 seconds and can reset the positioning error to ±5cm.", + "question": "Design a segmented approach strategy (including the number of stops for calibration and the maximum distance per segment) to ensure the final accuracy requirements are met and the total time is minimized.", + "answer": "The error increment per segment should be ≤ (10cm - 5cm) = 5cm → the maximum distance per segment = 5cm / (3cm/m) = 1.67m; choose the segmented plan: 6m + 3m + 1m (each segment ≤ 1.67m requires calibration twice). Total time = (6 + 3 + 1) * 20 + 2 * 60 = 200 + 120 = 320 seconds." + }, + { + "id": 62, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the moon, located at coordinate point A (0,0), and needs to reach scientific target point B (1000,500) (unit: meters). Terrain data indicates there are three optional paths between the two points: Path 1 is a straight-line distance of 1200 meters with an average slope of 5 degrees; Path 2 is a detour distance of 1500 meters with an average slope of 2 degrees; Path 3 is a zigzag distance of 1300 meters with an average slope of 3 degrees. The motor efficiency model of the lunar rover shows: the energy consumption per unit distance when driving on a flat surface is 0.1Wh/m, and the additional energy consumption for climbing is 0.05Wh/m* slope (degrees). The remaining battery power is only 180Wh, and it needs to reach the target point before the power is exhausted.", + "question": "Calculate the total energy consumption of the three paths and determine which path can ensure that Yutu-2 safely reaches target point B within the remaining power.", + "answer": "Energy consumption of Path 1 = 1200*(0.1 + 0.05*5) = 210Wh; Energy consumption of Path 2 = 1500*(0.1 + 0.05*2) = 180Wh; Energy consumption of Path 3 = 1300*(0.1 + 0.05*3) = 175Wh. Only Path 2 and Path 3 meet the energy consumption ≤180Wh, among which Path 3 has the lowest energy consumption." + }, + { + "id": 63, + "scenario_code": "2.7", + "instruction": " When the Chang'e-7 lander was working at the edge of the Shackleton crater, it suddenly received a solar proton event warning (lasting 4 hours). The current lander is located at the boundary of the permanent shadow area (coordinate X) and needs to be transferred to a backup safe area Y 500 meters away within 30 minutes. There are two optional routes: Route A is a 300-meter straight-line crossing of the illuminated area (radiation dose rate 8Gy/h), and Route B is a 600-meter detour through the permanent shadow area (radiation dose rate 1Gy/h). The maximum moving speed of the lander is 20 meters/minute, and the radiation tolerance limit is 50Gy.", + "question": "Analyze the total radiation dose and time consumption of the two routes to determine the transfer plan that meets safety requirements.", + "answer": "Time for Route A = 300/20 = 15 minutes <30 minutes, radiation dose = 8*(15/60) = 2Gy <50Gy; Time for Route B = 600/20 = 30 minutes ≤30 minutes, radiation dose = 1*(30/60) = 0.5Gy <50Gy. Both routes meet the requirements, and Route B with lower radiation should be prioritized." + }, + { + "id": 64, + "scenario_code": "2.2", + "instruction": " The Chang'e-7 lander is conducting exploration at the edge of the Shackleton crater in the permanently shadowed area. The navigation system uses multi-sensor fusion: the position error of the visual odometry (VO) accumulates over time as e_vo = 0.1% * d (d is the travel distance), the IMU attitude error is e_imu = 0.5°/h, and the absolute positioning error of the LiDAR SLAM is fixed at ±3cm. The current mission has lasted 2 hours, with a travel distance of 15m, and the VO failed due to lunar dust interference for 10 minutes (during which it relied solely on the IMU).", + "question": "Calculate the maximum possible position error of the current system (without considering SLAM correction)?", + "answer": "VO error during normal operation = 0.1% * (15m - v*t), first calculate the travel distance during the failure period: typical speed v=15m/120min=0.125m/min, failure segment distance=0.125*10=1.25m; VO effective segment error=0.1%*(15-1.25)=0.01375m; IMU failure segment angle error=0.5°/h*(10/60)h≈0.083°, displacement error≈1.25m*tan(0.083°)≈0.0018m; total error=0.01375+0.0018+SLAM fixed error±3cm→maximum possible error=1.375+0.18+3≈4.555cm" + }, + { + "id": 65, + "scenario_code": "2.7", + "instruction": " The lunar rover encounters a solar proton event warning near the terminator and needs to urgently take shelter in a 500m radius shadow area within 30 minutes. Known: 1) Current communication is interrupted, and it can only rely on autonomous navigation; 2) Terrain data shows that there is a permanent shadow area 300m to the exact north, but it requires crossing a 20° slope; 3) There is a temporary shadow area (lasting 4 hours) 450m to the northeast, with a flat path; 4) The lunar rover's maximum slope climbing ability is 25°, with a safe speed of 0.1m/s (on slopes) or 0.3m/s (on flat ground).", + "question": "From the perspectives of timeliness and safety, which shelter path should be prioritized? Provide quantitative analysis as evidence.", + "answer": "Northern path: Time = 300 / (0.1 * cos20°) ≈ 319 seconds ≈ 5.3 minutes (reachable); Northeastern path: Time = 450 / 0.3 = 150 seconds = 2.5 minutes (reachable). Although the northeastern path is faster and does not require climbing, the shadow duration (4 hours) may not be sufficient to cover the entire proton event (usually >6 hours), so the northern permanent shadow area path should be chosen." + }, + { + "id": 66, + "scenario_code": "1.5", + "instruction": " In the Chang'e-7 mission, the ground control center needs to remotely control the lunar rover to precisely dock with the scientific payload interface within a 10-meter distance (tolerance ±2cm). Given: the one-way communication delay between Earth and Moon is 1.28 seconds, the maximum movement speed of the lunar rover is 0.1m/s, and the control system uses a predictive algorithm to compensate for the delay, with the position prediction error increasing over time as e(t) = 0.01*t^2 cm (t is the prediction duration in seconds). The docking operation requires the total positioning error to not exceed ±1.5cm.", + "question": "Calculate the shortest time interval t_min from issuing the movement command to stopping the command, so that the prediction error + movement error does not exceed the tolerance? (Movement error is calculated as uniform linear motion.)", + "answer": "Movement time t = 10m / 0.1m/s = 100s; prediction error e(100) = 0.01*100^2 = 100cm >> tolerance. Segmental operation is required: if the single segment movement time is t, then the total error 0.01*t^2 + 0.1*t*1.28 ≤ 1.5cm → t_max ≈ 3.16 seconds (rounded to 3 seconds)." + }, + { + "id": 67, + "scenario_code": "1.8", + "instruction": " When the lander deployed the magnetometer on the lunar surface, it found that the local magnetic field strength reached 200nT (expected <50nT). It was verified that this was due to the backup lithium battery pack 10 meters away not being fully shielded. Given: the magnetometer sensitivity is 0.1nT, and the measurement environment background noise requirement is <5nT; the magnetic field strength of the battery decays with distance according to the formula B(r) = B0*(r0/r)^3, where B0 = 200nT @ r0 = 10m. There is movable lunar regolith (density 1.8g/cm³) between the deployment point and the battery.", + "question": "If the noise requirement is to be met, how thick a barrier of lunar regolith needs to be constructed between the equipment and the battery? (The magnetic permeability of lunar regolith μ ≈ 1.)", + "answer": "Target B(r) ≤ 5nT → 200*(10/r)^3 ≤ 5 → r ≥ (200/5)^(1/3)*10 ≈ 29.24m; the additional thickness required = 29.24 - 10 = 19.24 meters." + }, + { + "id": 68, + "scenario_code": "3.3", + "instruction": " The Yutu-2 rover is about to enter the lunar night hibernation mode. The current battery state of charge (SOC) is 65%, with a remaining available capacity of 1800Wh. It is known that: 1) The lunar night lasts 14 Earth days; 2) The basic maintenance power consumption (clock, memory, etc.) requires a continuous power supply of 5W; 3) The electric heater needs to operate periodically to maintain a safe temperature of -20°C, with an average power consumption of 12W; 4) After waking up, 300Wh must be reserved for the startup of scientific instruments.", + "question": "Determine whether the current energy reserve meets the survival needs of the lunar night (the total energy consumption calculation process must be listed).", + "answer": "Total energy consumption = (5 + 12) * 24 * 14 + 300 = 6012Wh > 1800Wh, energy is insufficient" + }, + { + "id": 69, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the lunar soil in this area are as follows: average hardness of 3.5 Mohs (similar to feldspar), viscosity coefficient of 0.8 Pa·s, and volatile content of about 120 ppm. There are three sampling tool parameters: ① Rotary impact drill (suitable for hardness >4 Mohs, power consumption 35W/min); ② Electric grab (suitable for viscosity <1.2 Pa·s, power consumption 20W/min); ③ Ultrasonic scraper (suitable for volatile content >100 ppm, power consumption 25W/min). The mission requires prioritizing the preservation of volatile integrity, followed by minimizing power consumption.", + "question": "Based on the above conditions, which sampling tool should be selected? Provide the calculation process for the specific selection criteria.", + "answer": "Choose the ultrasonic scraper. Justification: 1) The volatile content of 120 ppm >100 ppm meets the primary condition; 2) The viscosity of 0.8 Pa·s <1.2 Pa·s also meets the condition for the electric grab, but the grab does not ensure the preservation of volatiles; 3) The hardness requirement for the rotary drill is not met (3.5 <4 Mohs). Power consumption ranking: scraper (25W) is between the drill (35W) and the grab (20W), but it meets the primary scientific objective." + }, + { + "id": 70, + "scenario_code": "4.5", + "instruction": " Implement a 2-meter deep drilling task in the Oceanus Procellarum region on the near side of the Moon. Known: the lunar regolith from 0-0.5 meters is a loose layer (drilling speed 5 cm/min), 0.5-1.5 meters is a compact layer (speed 2 cm/min), and below 1.5 meters is a water-ice mixed layer (speed 1 cm/min). The drill's rated power is 300W, with a base power consumption of 150W, and the actual power consumption formula is P = 150 + 30*v (v is the drilling speed in cm/min). The maximum continuous operation time allowed for the task is 30 minutes.", + "question": "Calculate the total energy consumption and time required to complete the 2-meter drilling. If it is not feasible, suggest how to adjust the operation strategy.", + "answer": "Total time required = (50cm/5) + (100cm/2) + (50cm/1) = 10 + 50 + 50 = 110 minutes > 30 minutes, which is not feasible. Adjustment strategy: segmental operation, the maximum depth of a single operation = 30 / (10/5 + x/2 + y/1), which must satisfy x + y = 150 and 10 + x + y <= 300 (power limit), the optimal solution is to complete the loose layer first and then go into sleep mode." + }, + { + "id": 71, + "scenario_code": "4.9", + "instruction": " Design parameters for the lunar sample return capsule: the inner diameter of the sealed container is 20cm, and the sample tubes with an outer diameter of 4cm are arranged in a tight hexagonal pattern. The container must maintain an internal pressure <0.1Pa, with a temperature control range of -50℃ to +10℃. The docking window of the ascent vehicle lasts only 100 seconds, and during the handover, the following must be met simultaneously: ① the distance from the center of the sample tube to the wall of the capsule ≥ 3cm; ② the distance between adjacent sample tubes ≥ 1cm; ③ the total mass ≤ 5kg (the mass of a single tube is 80g).", + "question": "Calculate the maximum number of sample tubes that the container can load and the corresponding number of layers (Hint: the formula for hexagonal arrangement is the number of tubes per layer = 3*n*(n+1)+1, where n is the number of layers).", + "answer": "Effective loading radius = (20/2) - 3 - (4/2) = 7 - 2 = 5cm. By iterating the hexagonal formula: when n=1, the radius ≈ 4*0.577 ≈ 2.31cm; when n=2, ≈ 4*1.155 ≈ 4.62cm; when n=3, ≈ 6.93cm > 5cm. Therefore, the maximum n=2 layers, the number of tubes = 3*2*3 + 1 = 19 tubes. Verify the mass: 19*80g = 1520g < 5000g, which meets the requirements." + }, + { + "id": 72, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. According to preliminary remote sensing data analysis, the target area has two typical types of lunar soil: Area A is loose and dry fine-grained lunar soil (average particle size 50 microns, internal friction angle 28 degrees), and Area B is cohesive lunar soil containing trace amounts of water ice (moisture content 0.6%, shear strength 15kPa). The engineering team has prepared three sampling tools: ① Rotary impact drill (suitable for rocks with hardness > 5MPa), ② Electric shovel (suitable for loose to moderately compact lunar soil), ③ Spiral sampler (suitable for cohesive soil). It is known that the sampling depth requirement is 0.5 meters, and the stratification structure of the samples must be maintained intact.", + "question": "For the lunar soil characteristics of Area A and Area B, which sampling tool should be selected respectively? Please explain the basis for your selection.", + "answer": "For Area A, the electric shovel is chosen because it is suitable for loose fine-grained lunar soil and can maintain the stratification structure; For Area B, the spiral sampler is chosen because it is specifically designed for cohesive soil and can effectively collect water-containing samples." + }, + { + "id": 73, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the moon, located at point A (0,0), and needs to reach the scientific target point B (100,50) (unit: meters). Terrain data indicates that there are three optional paths between the two points: Path 1 is a flat area with a straight-line distance of 120 meters, Path 2 is a slope segment with a total length of 110 meters and a 30° incline (length 40 meters), and Path 3 is a route with a total length of 105 meters that requires bypassing a small impact crater. It is known that the rover consumes E_flat=0.1Wh/m when traveling on flat ground, and an additional E_slope=0.05Wh/m*inclination angle (degrees) when climbing a slope, with a motor system efficiency of η=85%. The current remaining battery energy is 15Wh.", + "question": "To ensure that there is at least 3Wh of emergency power left after reaching target point B, which path should be chosen? Please calculate the total energy consumption for each path and provide the basis for your choice.", + "answer": "Energy consumption for Path 1 = 120*0.1/0.85 = 14.12Wh; Energy consumption for Path 2 = (70*0.1 + 40*(0.1 + 0.05*30))/0.85 = (7 + 10)/0.85 = 20Wh; Energy consumption for Path 3 = 105*0.1/0.85 = 12.35Wh. Maximum allowable consumption = 15 - 3 = 12Wh, only Path 3 meets the requirement." + }, + { + "id": 74, + "scenario_code": "2.2", + "instruction": " The Chang'e-7 lander is conducting exploration at the edge of the Shackleton crater in a permanently shadowed area. The navigation system uses a combination of visual odometry (VO) and IMU, where the VO position error accumulates over time as e_VO=0.1%*travel distance, and the IMU speed error is e_IMU=0.5cm/s. After the lander travels at a constant speed of 5cm/s for 200 seconds, the star sensor measures an 8cm deviation between the actual position and the position calculated by the combined navigation system.", + "question": " ", + "answer": "VO error = 200*5*0.1% = 1cm; IMU error = 200*0.5 = 100cm; Theoretical maximum error = sqrt(1^2 + 100^2) = 100.005cm. The 8cm deviation is less than the threshold of 10cm, so no correction is needed for now." + }, + { + "id": 75, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover, while conducting exploration in the Von Kármán crater, obtained the following prior data: 1) Orbital spectrometry shows three KREEP rock anomaly zones (X: 12% iron content, Y: 8 ppm thorium content, Z: 3% titanium content); 2) Topographic data indicates that point X is located on a 5° gentle slope, point Y is on an 8° slope with 10 cm of loose soil, and point Z is on a 15° steep slope; 3) The remaining energy can support a total travel distance of 200 meters or a stay at 3 scientific points. The rover's movement power consumption model is: 0.8 Wh/m on flat ground, with an increase of 0.1 Wh/m for each additional degree of slope.", + "question": "If the priority is to sample the KREEP rock with the highest thorium content, how should the path be planned to maximize the remaining energy? Calculate the total energy consumption of the optimal path.", + "answer": "Priority should be given to going to point Y (highest thorium content). The path should choose the 5° gentle slope route to point X (energy consumption = 0.8 + 5 * 0.1 = 1.3 Wh/m) and then to point Y (an additional 3° slope increment, energy consumption = 1.6 Wh/m segment). The total distance is 150 meters (100 meters from the starting point to X, 50 meters from X to Y), total energy consumption = 100 * 1.3 + 50 * 1.6 = 130 + 80 = 210 Wh (exceeding the budget, it needs to be adjusted to a direct single trip to Y: direct 8° slope route energy consumption = 0.8 + 8 * 0.1 = 1.6 Wh/m, total consumption for 100 meters is 160 Wh)." + }, + { + "id": 76, + "scenario_code": "4.9", + "instruction": " The design parameters for the lunar sample return capsule require: ① Sealed chamber leakage rate <1×10^-9 Pa·m³/s; ② Temperature recording interval ≤10 minutes; ③ Impact acceleration during docking with the ascent vehicle <5g. During a certain mission, the following data were measured: Container A - leakage rate 5×10^-10 Pa·m³/s, temperature recording interval 8 minutes, docking impact 4.2g; Container B - leakage rate 2×10^-9 Pa·m³/s, temperature recording interval 5 minutes, docking impact 5.8g; Container C - leakage rate 3×10^-10 Pa·m³/s, temperature recording interval 12 minutes, docking impact 3.9g.", + "question": "According to the design specifications, which sample containers meet all the requirements? List the specific items that meet and do not meet the standards.", + "answer": "Only container A fully meets the requirements: leakage rate meets the standard (5×10^-10), temperature interval meets the standard (8min), and impact meets the standard (4.2g). Container B exceeds the standard for leakage rate (2×10^-9) and impact (5.8g); Container C exceeds the standard for temperature interval (12min)." + }, + { + "id": 77, + "scenario_code": "2.7", + "instruction": " The lunar rover receives a solar proton event warning while patrolling near the terminator and needs to return to the safety cabin located 500 meters northwest within 30 minutes. The current environmental temperature has suddenly dropped to -150°C, causing a 40% decrease in power of the right drive motor. Under normal conditions, the maximum speed is 5 cm/s, and the energy consumption for turning is 1.5 times that of moving straight. There is a crater with a diameter of 200 meters blocking the direct path 300 meters ahead.", + "question": "Calculate whether it is possible to return to the safety cabin on time under the current constraints. If not, propose a feasible emergency plan (specific parameters must be provided).", + "answer": "Normal time required = 500/5 = 10000s > 1800s; The shortest detour around the crater = 300 + π*100 ≈ 614 meters, time required 614/(5*0.6) ≈ 2047s still exceeds the limit. Emergency plan: Discard non-essential payload to reduce weight by 20%, increasing speed to 6 cm/s, detour time required 614/6 ≈ 1023s < 1800s." + }, + { + "id": 78, + "scenario_code": "3.8", + "instruction": " Chang'e-7 lander mission profile requires: 8 hours of scientific exploration during the lunar day (average power consumption 120W), 2 hours of data transmission (peak power consumption 300W), and the rest of the time in hibernation (20W); during the lunar night, it remains in hibernation (15W) throughout. Energy system configuration: average daily power generation from solar arrays is 1.8kWh, battery pack capacity is 2kWh (charge-discharge efficiency 92%), and initial SOC is 80%.", + "question": "Determine whether this energy configuration can support 3 complete lunar day-night cycles (each cycle lasts 336 hours)? List the key calculation steps.", + "answer": "Single cycle energy consumption: lunar day = (120*8 + 300*2 + 20*14) * 24 / 336 = 1584Wh; lunar night = 15 * 336 / 2 = 2520Wh; total demand = (1584 + 2520) * 3 = 12312Wh; available energy = (1800 * 3 + 2000 * 0.8 * 0.92) = 5400 + 1472 = 6872Wh < 12312Wh → cannot support" + }, + { + "id": 79, + "scenario_code": "3.1", + "instruction": " Chang'e-6 rover is conducting exploration tasks in the South Pole-Aitken Basin of the Moon, where the terrain is complex with multiple highlands causing obstructions. The rover is equipped with dual-axis adjustable solar panels, with a maximum power generation capacity of 180W (under standard lighting conditions). According to orbital data, the current solar elevation angle during the lunar day is 15 degrees, and the azimuth angle is 30 degrees (with north as 0 degrees). Terrain analysis shows that there is a 20-degree highland in the due east direction causing partial obstruction to the solar panels, with an obstruction ratio of 40%. It is known that the actual output power formula for the solar panels without obstruction is: P = P_max * cos(θ) * cos(φ), where θ is the solar elevation angle, and φ is the horizontal angle between the solar rays and the normal to the solar panel.", + "question": "If the rover maintains its current attitude (solar panels placed horizontally), calculate the actual output power of the solar panels at this time (unit: W)?", + "answer": "77.76" + }, + { + "id": 80, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, energy supply becomes a critical constraint. In the current mission, a mobile power module (output power 500W) needs to simultaneously power the following devices: 1) Seismometer (continuous power consumption 80W, high priority); 2) Infrared spectrometer (operating cycle 10 minutes/hour, peak power consumption 300W); 3) Data relay node (continuous power consumption 50W, medium priority). The battery capacity of the power module is 2000Wh, with a current remaining charge of 1200Wh. There are 8 hours of lunar daylight remaining, during which there is no opportunity to recharge.", + "question": "To ensure all devices continue to operate until the end of the lunar day, how should the operating cycle of the infrared spectrometer be adjusted? Assume that each start-up of the spectrometer requires an additional 20Wh of transient energy.", + "answer": "Adjust the operating cycle of the infrared spectrometer to work for 10 minutes every 2 hours. Calculation process: 1) Base energy consumption = (80W +50W)*8h =1040Wh; 2) Remaining available energy=1200Wh-1040Wh=160Wh; 3) Total energy consumption per operation of the spectrometer=300W*(10/60)h +20Wh=70Wh; 4) Maximum allowable start-up times=160Wh/70Wh≈2 times; 5) 2 start-ups within 8 hours correspond to once every 4 hours, but at least 2 measurements must be guaranteed, so it is adjusted to work for 10 minutes every 2 hours (actual 4 start-ups consume 280Wh>160Wh not feasible), therefore the optimal solution is to work for 10 minutes every 2 hours (total 3 start-ups consume 210Wh still exceeds the limit), ultimately only the option to work for 10 minutes every 4 hours (total 2 start-ups consume 140Wh<160Wh) can be chosen." + }, + { + "id": 81, + "scenario_code": "1.5", + "instruction": " When controlling the lunar rover to perform rock sampling, there is a fixed delay of 1.3 seconds in the instructions sent from the ground control center. The current speed of the lunar rover is 0.2m/s, and there is a target rock 3 meters ahead. The response delay of the braking system is 0.5 seconds (from the issuance of the command to the start of deceleration), with a maximum deceleration of 0.15m/s^2. To ensure that the relative speed between the sampling arm and the rock does not exceed 0.05m/s when they make contact.", + "question": "Calculate the latest distance from the target rock at which the braking command should be issued? Consider the combined effect of communication delay and system response delay.", + "answer": "The braking command should be issued when the distance to the target rock is 4.138 meters. Calculation steps: 1) Total delay = communication delay + response delay = 1.3s + 0.5s = 1.8s; 2) Distance traveled during delay = 0.2m/s * 1.8s = 0.36m; 3) Braking time required = (initial speed - final speed) / deceleration = (0.2 - 0.05) / 0.15 = 1s; 4) Braking distance = initial speed * t - 0.5 * a * t^2 = 0.2 * 1 - 0.5 * 0.15 * 1^2 = 0.125m; 5) Total stopping distance = delay distance + braking distance = 0.36m + 0.125m = 0.485m; 6) Actual required lead = 3m + 0.485m = 3.485m (this step corrects the error). The correct solution should be: Let the distance when the command is issued be D, then D = v * (t_delay) + [v * t_brake - 0.5 * a * t_brake^2] + d_final → D = 0.2 * 1.8 + [0.2 * 1 - 0.5 * 0.15 * 1^2] + 3 = 3 + 0.36 + (0.2 - 0.075) = 3 + 0.36 + 0.125 = 3.485m" + }, + { + "id": 82, + "scenario_code": "5.7", + "instruction": " The 128TB NAND flash memory carried by the Queqiao-2 relay satellite has been operating continuously for 3 years, using a dynamic wear-leveling algorithm. Monitoring shows: the average number of erase/write cycles for storage blocks is distributed as follows: Area A (12,000 times), Area B (8,000 times), Area C (15,000 times). The rated endurance of the NAND chip is 30,000 erase/write cycles. Currently, a batch of continuously updated engineering telemetry data (50GB written daily, retention period 7 days) needs to be stored.", + "question": "According to the wear-leveling strategy, which area should the new data be written to first? If the wear difference between areas needs to be controlled within ±10%, calculate the theoretical allocation ratio for each area (rounded to the nearest integer percentage).", + "answer": "Data should be written to Area B first (the least worn); theoretical allocation ratio: Area A=(1-0.8/1.25)*100≈36%, Area B=(1-0.8/1)*100=20%, Area C=(1-0.8/1.5)*100≈44% (total 100%)." + }, + { + "id": 83, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 lander is located on the edge of an impact crater at 45° North latitude on the near side of the Moon. Its solar panels use a two-dimensional tracking algorithm (azimuth + pitch). According to the lunar ephemeris, the current solar elevation angle is 15°, and the azimuth angle is 30° (0° is due north, increasing clockwise). Terrain shadow analysis shows that the western crater will cause shadow obstruction when the solar azimuth angle is between 180° and 270°. The initial installation angle of the solar panels at this moment is: azimuth 0°, pitch 0° (parallel to the lunar surface). It is known that: 1) the ideal power generation per unit area P_max=300W/m²; 2) the actual power generation efficiency η=cos(α)*cos(β), where α is the horizontal angle between the sunlight and the panel normal, and β is the vertical angle.", + "question": "Please calculate the optimal azimuth and pitch angle combination for the solar panels at this moment, and estimate the actual power generation efficiency η (to two decimal places).", + "answer": "Optimal azimuth=30° (tracking the sun's azimuth), pitch=15° (tracking the sun's elevation); η=cos(0°)*cos(0°)=1.00" + }, + { + "id": 84, + "scenario_code": "1.4", + "instruction": " When deploying scientific payloads in the permanently shadowed regions of the lunar south pole, it is necessary to allocate shared energy to three devices (seismometer, infrared spectrometer, neutron detector). The system uses a hybrid solar-battery power supply, with a peak power limit of 120W. The power consumption of the devices is as follows: the seismometer consumes 5W in standby/30W in operation (operates for 4 hours daily), the spectrometer consumes 8W in standby/45W in operation (operates for 2 hours daily), and the neutron detector consumes 10W in standby/60W in operation (operates continuously). During the lunar day, solar power can provide 80W of stable electricity, and during the lunar night, it is completely dependent on the battery.", + "question": "If all devices are required to maintain at least 18 hours of standby during the lunar night, and the battery capacity is 2000Wh, please calculate whether the system can meet the energy requirements for three consecutive lunar day-night cycles.", + "answer": "No. Calculation steps: 1) Total energy consumption during the lunar day = (30*4 + 45*2 + 60*12) + 5*20 + 8*22 + 10*12 = 1118Wh; 2) Energy consumption during the lunar night = (5+8+10)*18 = 414Wh; 3) Total demand per cycle = (1118+414)*3 = 4596Wh > Battery capacity 2000Wh" + }, + { + "id": 85, + "scenario_code": "1.8", + "instruction": " The lunar rover plans to deploy 4 seismometers on the rim of an impact crater with a diameter of 5 kilometers. It is known that the bearing capacity of the lunar soil in this area is 15kPa, the rover's own weight is 120kg (including payload), and the contact area is 0.12m². When deploying the instruments, the supports need to contact the lunar surface, with a single support contact area of 25cm², and the safety factor must be ≥2. The deployment point selection must simultaneously meet: ① The ground pressure of the rover during travel < 50% of the bearing capacity; ② The pressure of the instrument support < 80% of the bearing capacity.", + "question": "Calculate how many seismometers the rover can carry at most for safe deployment? (Take the gravitational acceleration as 1.62m/s²).", + "answer": "3 units. Calculation steps: 1) Maximum mass of the rover = 15kPa * 50% * 0.12m² / 1.62 = 555kg; 2) Upper limit of the mass of a single instrument = 15kPa * 80% * 0.0025m² / 1.62 = 18.5kg; 3) (555-120) / 18.5 ≈ 23.5, but limited by the total number of supports, only 3 can be carried." + }, + { + "id": 86, + "scenario_code": "1.2", + "instruction": " When deploying an integrated drilling and sampling device in the permanently shadowed region of the lunar south pole, the geometric constraints of equipment installation sequence must be considered. The maximum extension radius of the main robotic arm is 2.5 meters, and the docking accuracy requirement for the end effector and the drill module is ±5mm. The base of the device is already fixed on the lunar surface, but due to the terrain, the robotic arm must install components in the following order: 1) Power module (mass 20kg, dimensions 0.4×0.3×0.2m); 2) Sample cache (mass 15kg, 0.5m diameter cylinder); 3) Drill module (mass 30kg, length 1.2m). It is known that the positioning error of the robotic arm will expand to ±8mm when fully loaded (≥25kg).", + "question": "To ensure the docking accuracy of the drill module meets the requirements, how should the installation sequence be adjusted? Please explain the specific adjustment plan and the reasons.", + "answer": "The installation sequence of the drill module should be moved up to the second position. Because the mass of the drill module, 30kg, exceeds the 25kg threshold, if it is installed in the original third position, the positioning error will exceed the ±5mm requirement. The adjusted sequence is: 1) Power module; 2) Drill module (at this point, the robotic arm load is 20+30=50kg > 25kg, but the docking has been completed); 3) Sample cache (load 50+15=65kg, only affects non-precision operations)." + }, + { + "id": 87, + "scenario_code": "1.4", + "instruction": " A lunar base energy grid is powered by 3 Radioisotope Thermoelectric Generators (RTGs), each continuously outputting 100W with a peak of 150W (sustainable ≤10 minutes). The current mission requires the simultaneous operation of: 1) a lunar soil analyzer (steady power consumption 80W, start-up peak 120W/5 seconds); 2) a robotic arm control system (base power consumption 20W, additional 40W during movement); 3) a data transmitter (200W for each 3-minute transmission). The system priority is set as: data transmission > robotic arm movement > lunar soil analysis. All devices share the same power bus, with an overload threshold of 450W.", + "question": "If it is necessary to start the lunar soil analyzer and trigger data transmission during the continuous movement of the robotic arm, please calculate whether the power scheduling plan is safe? If not, how should it be adjusted? ", + "answer": "Not safe. Total power consumption = RTG peak 150*3 = 450W; demand = robotic arm (20+40) + lunar soil analysis (120) + data transmission (200) = 380W. However, the instantaneous start-up of the lunar soil analysis at 120W and data transmission at 200W adds up to 320W, plus the robotic arm at 60W totals 380W < 450W. The issue is that during data transmission, the three RTGs need to maintain an output of 150*3 = 450W for more than 10 minutes, exceeding the limit. Solution: stagger the data transmission and the start-up of the lunar soil analysis by ≥10 minutes." + }, + { + "id": 88, + "scenario_code": "1.8", + "instruction": " When deploying a magnetometer in the Oceanus Procellarum region, the lunar regolith bearing capacity was measured to be 8kPa. The contact area of each leg of the magnetometer's triangular stand is 0.02m², and the total mass of the instrument is 50kg. It is known that the safety factor must be ≥2, and the lunar surface gravitational acceleration is 1.62m/s². The stand design allows for two configurations: A) all three legs in contact with the lunar surface; B) only two legs in contact (the third leg is suspended for leveling).", + "question": "Calculate and verify whether the two configurations meet the bearing capacity requirements? If configuration B does not meet the requirements, what parameters can be improved? (Formula: pressure P=F/A; F=mass*gravitational acceleration*safety factor).", + "answer": "Configuration A: P=(50*1.62*2)/(3*0.02)=2700Pa=2.7kPa<8kPa; Configuration B: P=(50*1.62*2)/(2*0.02)=4050Pa=4.05kPa<8kPa. Both configurations meet the requirements. No improvement needed." + }, + { + "id": 89, + "scenario_code": "5.7", + "instruction": " The Chang'e-7 orbiter SSD storage system uses NAND flash memory, with the following parameters:\n1. Total capacity 1TB, block size 256KB, page size 8KB\n2. Each block can be erased and written 10^5 times\n3. Daily write volume fluctuation: 20GB/day during lunar day, 5GB/day during lunar night\n4. Wear-leveling algorithm uses dynamic cold-hot partitioning + garbage collection", + "question": "If the SSD's lifespan is required to be ≥5 years, please verify whether the current design meets the requirement? Provide the formula for calculating the critical value of the annual average write amplification factor (WA).", + "answer": "It meets the requirement. Calculation process:\n1. Total write volume over five years = (20*14+5*14)*12*5 = 21000GB = 21TB\n2. SSD endurance = 1TB*(10^5)/1000 = 100TB\n3. Critical value of WA = 100/21 ≈ 4.76\nFormula: WA_max = (Block erase/write cycles * Total capacity) / (Annual average write volume * Years of use)." + }, + { + "id": 90, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to sample an area on the far side of the Moon rich in KREEP rock. The characteristics of the regolith in this area are as follows: average hardness 3.5 Mohs (between calcite and fluorite), viscosity coefficient 0.8 kPa·s, volatile content 1200 ppm. There are three sampling tool parameters: ① Rotary impact drill (suitable for hardness ≤4, maximum torque 8 Nm, power consumption 15 W/min); ② Electric grab (suitable for viscosity ≤1.2 kPa·s, gripping force 200 N, power consumption 8 W/min); ③ Scraper (suitable for volatile content ≤1500 ppm, digging depth 5 cm, power consumption 5 W/min). The remaining working time during the lunar day is 40 minutes, and the current solar panel output power is stable at 25 W.", + "question": "To ensure sampling is completed before the power runs out and the tool is suitable for the geological characteristics, which sampling tool should be chosen? Please list the key parameter comparison process for the selection.", + "answer": "Choose the electric grab. Basis: ① Hardness suitability: Lunar regolith hardness 3.5 < drill upper limit 4, but the total energy consumption of the drill 15*40=600W > available energy 25*40=1000W; ② Viscosity suitability: Lunar regolith viscosity 0.8 < grab upper limit 1.2; ③ Volatile content suitability: Although the scraper meets the volatile content requirement, its scientific value is lower; ④ Energy consumption comparison: Total energy consumption of the grab 8*40=320W < 1000W and meets all constraint conditions." + }, + { + "id": 91, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin (SEL) on the far side of the Moon, and needs to communicate with the ground station via the Queqiao-2 relay satellite. It is known that:\n1. Queqiao-2 operates in a halo orbit around the Earth-Moon L2 point, about 65,000 kilometers from the Moon's center\n2. The maximum communication elevation angle between the lander and Queqiao-2 is 25 degrees\n3. The Moon's radius is 1,737 kilometers\n4. At the current moment, the angle between the line connecting Queqiao-2 to the Moon's center and the line connecting the lander to the Moon's center is 50 degrees\n5. The average distance between the Earth and the Moon is 380,000 kilometers", + "question": "Please calculate whether an effective communication link can be established between the ground station, Queqiao-2, and the lander at the current moment? The conditions to be met are:\n1. Queqiao is not blocked by the Moon when communicating with the Earth or the Moon\n2. The elevation angle of the lander to Queqiao is ≥15 degrees", + "answer": "Invalid. Calculation steps:\n1. The surface distance d from the lander to Queqiao = Moon's radius * sin(50°) ≈ 1330km\n2. Communication elevation angle θ = arctan((65000 - 1737*cos(50°)) / (1737*sin(50°))) ≈ 18.7° >15° (satisfied)\n3. But at this time, the angle α between Queqiao, the Moon's center, and the Earth = arcsin(Moon's radius / Earth-Moon distance) ≈ 0.26°, while the actual angle 50° >> α, indicating that Queqiao is blocked by the Moon and cannot communicate with the Earth" + }, + { + "id": 92, + "scenario_code": "3.1", + "instruction": " Chang'e-7 lander is located near the lunar south pole (latitude 85°S), and its solar panels use a two-dimensional tracking algorithm. According to the lunar almanac, the current solar elevation angle is 5°, and the azimuth angle is 45° (0° is due north, increasing clockwise). Terrain obstruction analysis shows: there is a permanent shadow area (obstruction angle 10°) within 30° of due east, with no obstructions in other directions. The maximum output power of the solar panel P_max = 300W (when vertically incident), and the actual output power P_actual = P_max * cos(θ), where θ is the angle between the sunlight and the normal of the solar panel.", + "question": "If the solar panel is adjusted to align its normal with the sun, what is the actual output power at this time? If it needs to adjust the azimuth to avoid terrain obstructions, which direction should it adjust to？", + "answer": "The actual power when aligned with the sun is 300W * cos(0°) = 300W; to avoid terrain obstructions, the azimuth should be adjusted westward (away from the eastern obstruction area)." + }, + { + "id": 93, + "scenario_code": "3.3", + "instruction": " Yutu-2 rover is about to enter the lunar night, with the current state of charge (SOC) of the lithium-ion battery pack at 65%, and the lunar night lasts for 14 Earth days. It is known that: the total battery capacity is 20Ah, the base load (heating + clock control) current during the lunar night is 0.2A, and the peak current when the scientific instruments are awakened for detection is 2A (each lasting 1 hour, up to 3 times). The thermal control system requires that the SOC must not fall below 20%.", + "question": "Calculate how many times the scientific instruments can be awakened for detection during the lunar night without charging.", + "answer": "Usable power = (65%-20%) * 20Ah = 9Ah; base consumption = 0.2A * 14 * 24h = 67.2Ah; exceeding the limit, so no wake-up detection can be performed." + }, + { + "id": 94, + "scenario_code": "3.6", + "instruction": " Chang'e-6 lander uses an electric heating + multi-layer insulation combined thermal maintenance scheme during the lunar night. The critical equipment compartment requires maintaining a temperature above -40°C. Given: the cabin surface area is 2m², the equivalent thermal conductivity of the insulation layer is 0.05W/(m·K), and the lunar night environment is -180°C. The electric heater power can be adjusted between 10-50W, with a heating efficiency η=85%. The thermal balance formula: heating power*η = thermal conductivity*area*(T_in - T_out).", + "question": "Calculate the minimum electric heating power required to maintain the equipment compartment at -40°C (round to the nearest integer) and the total energy consumption of the system (assuming the lunar night lasts 336 hours).", + "answer": "Minimum power=0.05*2*(40-(-180))/0.85≈26W; total energy consumption=26W*336h=8736Wh≈8.7kWh" + }, + { + "id": 95, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 lander is located on the edge of an impact crater at 23.5° North latitude on the near side of the Moon. Its solar panels use a two-dimensional tracking algorithm (azimuth + pitch). According to the lunar almanac, the current solar elevation angle during the lunar day is 15°, and the azimuth is 30° south of due east. The crater wall will block sunlight from the west within a 30° range in the morning. The theoretical maximum output power of the solar panels is 200W/m², and the actual output power is proportional to the cosine of the solar incidence angle.", + "question": "If the solar panels are currently facing due east (azimuth 90°) and the pitch angle is adjusted to 15°, calculate the actual output power per unit area at this time (保留两位小数)？", + "answer": "193.19W/m²" + }, + { + "id": 96, + "scenario_code": "3.6", + "instruction": " Chang'e-7 polar lander needs to maintain key equipment at -180°C during the lunar night. The insulation system includes: ① a 10mm aerogel layer (thermal conductivity 0.02W/mK) ② an isotope heat source (constant output of 8W) ③ an electric heating backup system (can supplement up to 20W). The normal operating temperature range for the equipment is -40°C to +50°C, with a casing surface area of 0.5m². When the temperature difference with the environment ΔT=130°C, the natural heat dissipation power Q=ΔT*0.04* surface area.", + "question": "Calculate whether the internal equipment can maintain above -40°C relying solely on the aerogel and isotope heat source. If not, how many watts of electric heating are required at minimum to maintain the temperature above -40°C.", + "answer": "It cannot maintain; at least 4W of electric heating is required." + }, + { + "id": 97, + "scenario_code": "1.4", + "instruction": " When deploying scientific payloads in the permanently shadowed regions of the lunar south pole, a temporary energy sharing network needs to be established. Currently, there are 3 devices: a drill (peak power 120W), a spectrometer (80W), and a robotic arm (60W), all powered by a shared solar-battery system. The system's maximum output power is 200W, and the current battery energy storage is 500Wh. The operation priority of the devices is: drill > spectrometer > robotic arm. All devices need to work continuously for 2 hours to complete the critical mission phase.", + "question": "If the spectrometer needs an additional 30 minutes of high-precision mode (+20W power consumption), calculate whether the system can support this adjustment without interrupting the drill. How much battery energy will remain after the adjustment.", + "answer": "The system can support the adjustment, with 140Wh of energy remaining. Calculation process: base total power consumption = 120 + 80 + 60 = 260W > 200W, after closing the robotic arm according to priority, the power consumption = 200W, which just meets the requirement. After the adjustment, the additional power consumption of the spectrometer = 20W * 0.5h = 10Wh, total power consumption = 200W * 2h + 10Wh = 410Wh, remaining = 500 - 410 = 90Wh (the original answer was incorrect, it should be 90Wh)." + }, + { + "id": 98, + "scenario_code": "1.5", + "instruction": " The Yutu-2 rover needs to be remotely controlled to cross a lunar crater with a 1.3-second communication delay. The crater is 2 meters wide, the rover's maximum speed is 0.2 m/s, and the braking distance is 0.15 meters. After the ground control center sends a movement command, it must wait for image feedback to confirm before sending the next command. The rover is equipped with a predictive control system that can autonomously fine-tune the path based on terrain data.", + "question": "If there is a ±5cm positioning error at the edge of the crater, what is the minimum lead time that the ground should set in the command to ensure safe crossing of the crater? (Consider braking distance + error compensation).", + "answer": "11.75 seconds. Calculation process: Crossing time = crater width / (speed - safety margin) = (2m + 0.15m + 0.05m) / 0.2m/s = 11s, plus communication delay 1.3s * 2 (round trip) = 2.6s, total 11 + 0.75 (error compensation) = 11.75s" + }, + { + "id": 99, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 lunar far-side sample return mission, direct communication between the lander and the ground station is blocked by the Moon. At this time, communication links need to be established through the Queqiao-2 relay satellite. Known:\n1. Queqiao-2 is located in the Halo orbit at the Earth-Moon L2 point, with an average altitude of about 45,000 kilometers above the lunar surface.\n2. The lander's transmission power is 10W, and the relay satellite's receiving antenna gain is 40dB.\n3. Free space path loss formula: L = 20 * log10(4 * π * d / λ), where d is the distance and λ is the wavelength (using S-band 2.2GHz).\n4. The system requires a minimum received power of -120dBm.", + "question": "Calculate whether the uplink from the lander to the relay satellite meets the communication requirements? (Step-by-step calculation of path loss and received power is required.)", + "answer": "1. Calculate the wavelength λ = c / f = 3e8 / 2.2e9 ≈ 0.136m\n2. Path loss L = 20 * log10(4 * π * 4.5e7 / 0.136) ≈ 207.6dB\n3. Received power Pr = Pt + Gt - L = 10log10(10) + 40 - 207.6 ≈ -157.6dBm < -120dBm → Not satisfied" + }, + { + "id": 100, + "scenario_code": "5.8", + "instruction": " The intelligent data processing system carried by the Chang'e-7 orbiter has the following characteristics:\n1. AI model can identify the spectral characteristics of lunar surface minerals (accuracy 95%)\n2. RAW format original data volume 10GB/orbit, reduced to 200MB after feature extraction\n3. X-band downlink bandwidth 20Mbps\n4. Ground station visibility duration per orbit 8 minutes", + "question": "Calculate how many more orbits of scientific data can be transmitted using AI screening compared to the original data transmission.", + "answer": "1. Original data transmission volume: 20Mbps * 480s ≈ 1.2GB/orbit → can only transmit 1 orbit\n2. AI processed transmission volume: 200MB < bandwidth capacity → can transmit all data\n3: ∴ Additional number of orbits that can be transmitted = total number of orbits - 1" + }, + { + "id": 101, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander suddenly receives a solar proton event warning while exploring in a permanently shadowed area and needs to transfer to an emergency safety point 500 meters away within 15 minutes. Known: the lander's maximum speed is 0.05m/s (limited by the characteristics of lunar soil), the average slope of the current area is 5°, the IMU drift error is 0.1°/min, and in emergency mode, only LiDAR SLAM navigation (positioning accuracy ±0.3m) can be used. The safety point is located at an azimuth of 120°, and the lighting conditions allow continuous operation for 10 minutes.", + "question": "Determine whether the lander can safely reach the target point within the warning time limit and explain the key constraints.", + "answer": "It cannot arrive. Calculation of required time: 500m / 0.05m/s = 10000 seconds ≈166.67 minutes, far exceeding the 15-minute warning time limit. Key constraints include: too low movement speed, insufficient time, and continuous operation time of only 10 minutes cannot support the entire movement." + }, + { + "id": 102, + "scenario_code": "2.9", + "instruction": " When the Lunar Navigation Satellite System (LBNSS-1) is 200km away from the rover, it sends navigation signals with a frequency of 2GHz, transmission power of 20W, and antenna gain of 26dB. The receiver sensitivity of the rover is -110dBm, and the antenna gain is 18dB. Given the free space path loss formula: Lfs=32.45+20log10(d_km)+20log10(f_MHz), the system margin requirement is ≥6dB.", + "question": "Calculate whether the margin of this communication link meets the requirements (the complete calculation process must be listed).", + "answer": "Calculation steps: 1) Lfs=32.45+20log10(200)+20log10(2000)=32.45+46.02+66.02=144.49dB; 2) Received power Pr=Pt+Gt+Gr-Lfs=20dBm+26dB+18dB-144.49=-80.49dBm; 3) Margin=Pr-sensitivity=-80.49-(-110)=29.51dB＞6dB, meeting the requirement." + }, + { + "id": 103, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover experienced a sudden communication interruption during the lunar day, and the diagnosis found:\n1. The main X-band transmitter's power amplifier failed due to a solar flare;\n2. The backup S-band system is available but has only 1/3 the bandwidth of the X-band;\n3. The SSD cache currently stores 50GB of untransmitted scientific data, with 30GB of remaining capacity;\n4. The next communication window is 12 hours later and lasts for 4 hours;\n5. The maximum transmission rate of the S-band is 2Mbps, and the X-band is 6Mbps.", + "question": "To ensure the complete return of key data, how should the data compression strategy be adjusted? (Assuming the original data compression rate can be adjusted between 50%~90%)", + "answer": "Available transmission volume: S-band 4h*3600s*2Mbps=28.8Gb=3.6GB <<50GB. Compression must be enabled and at least achieve a compression ratio of 50GB*0.9=45GB→3.6GB (92%). However, the maximum compression rate is only 90%, so high-value data must be prioritized, and some low-priority data must be discarded. Final strategy: Implement 90% compression on core data (leaving 5GB), and then select 3.6GB for transmission." + }, + { + "id": 104, + "scenario_code": "5.7", + "instruction": " The Chang'e-7 orbiter SSD uses NAND flash memory, with the following characteristics:\n1. Total capacity 1TB, using 256 4GB chips in parallel access;\n2. Each block can be erased and written 3000 times, with an average wear level of 800 times currently;\n3. The file system uses a dynamic wear leveling algorithm, distributing write requests to the N most idle chips;\n4. Average daily write volume is 20GB, with a peak of 50GB.", + "question": "If the SSD's lifespan is required to be ≥5 years, what is the minimum value of N in the current wear leveling algorithm? ", + "answer": "Total remaining erase/write cycles: (3000-800)*256=563,200 times. Total write volume over five years: 5*365*20GB=36,500GB=142.6GB per chip. Each GB requires 1 erase/write cycle (4GB chip), thus 142.6 cycles per chip are needed. The minimum N must satisfy 563,200/(142.6*256)≈15.4→rounding to the nearest integer N=16" + }, + { + "id": 105, + "scenario_code": "2.10", + "instruction": " To study a suspected water ice-rich area, the lunar rover needs to approach a 30 cm diameter rock outcrop for microscopic imaging. The visual system identifies the target center coordinates as (5.2m, 3.7m) (in the rover's coordinate system), with a stereo camera ranging accuracy of ±1cm. The control system requires the final parking position to be 50±5cm from the target, and the solar panel normal vector deviation from the sun's azimuth must be <10° (current deviation is 8°). It is known that the minimum turning angle of the wheels is 5°, and the movement positioning accuracy is ±3cm.", + "question": "Design a two-stage control strategy (coarse approach + fine adjustment) from the current position (0,0) to the target point, explaining the action parameters and tolerance requirements for each stage.", + "answer": "Stage 1: Coarse approach to (5m, 3.5m), allowing ±10cm error; Stage 2: Fine adjustment in two steps: first rotate arctan(0.2/0.5) = 21.8° (rounded to 20°) to align with the target, then advance sqrt(0.2^2 + 0.5^2) = 53cm (compensating for 3cm positioning error), the final distance of 49-53cm meets the requirement." + }, + { + "id": 106, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. Analysis of the soil characteristics in this area shows: the surface layer 0-30cm is loose fine particles (shear strength <5kPa), 30-60cm is a medium-hard layer containing breccia (shear strength 15-20kPa), and below 60cm there is a high-titanium basalt layer (shear strength >50kPa). The parameters of the existing sampling tools are as follows: scraper (maximum force 10N, suitable for <10kPa), rotary drill A type (maximum torque 3Nm, suitable for 10-25kPa), rotary drill B type (maximum torque 8Nm, suitable for 25-60kPa). The sampling process must ensure that the tool load does not exceed 80% of the maximum capacity.", + "question": "If it is necessary to completely collect a 0-80cm depth profile sample, please design a layered sampling tool combination and corresponding depth intervals, and explain the basis for the selection.", + "answer": "0-30cm use the scraper (loose layer load safety margin 100%), 30-60cm use the rotary drill A type (medium layer load 67%-80%), 60-80cm use the rotary drill B type (hard layer load 62.5%)" + }, + { + "id": 107, + "scenario_code": "1.2", + "instruction": " When deploying an integrated drilling and sampling device on the edge of a crater at the lunar south pole, the geometric constraints of the equipment installation sequence must be considered. The maximum extension radius of the main robotic arm is 2.5 meters, and the total mass of the sampling device is 50kg (including the lunar soil container). The positioning accuracy of the end effector of the robotic arm and the drill head interface must be better than ±3cm. The installation process requires: 1) First, fix the base (15 minutes); 2) Unfold the solar panels (8 minutes, requiring the base to be 90% fixed); 3) Calibrate the drill head azimuth (5 minutes, requiring the solar panels to be fully unfolded). The current lander is located on a 10° slope at the edge of the crater, with a lunar surface static friction coefficient μ=0.6.", + "question": "If the deployment is required to be completed within 1 hour, and the robotic arm must operate within 2 meters of a support point below the slope to ensure stability, please calculate the theoretically allowable maximum straight-line distance from the farthest sampling point to the center of the base (lunar gravity acceleration g_moon=1.62m/s²).", + "answer": "2.21 meters. Derivation steps: 1) Maximum static friction force F_max=μ*m*g_moon*cos10°=0.6*50*1.62*0.985≈47.7N; 2) Downhill force F_parallel=m*g_moon*sin10°≈14.1N; 3) Safety margin requirement F_max≥1.5*F_parallel→actual maximum allowable F_parallel=47.7/1.5≈31.8N→corresponding maximum inclination angle α=arcsin(31.8/(50*1.62))≈23°; 4) Geometric constraint: farthest distance d=2.5*cos23°≈2.21 meters" + }, + { + "id": 108, + "scenario_code": "5.4", + "instruction": " Yutu-2 rover experienced an X-band communication interruption during the lunar day, with fault diagnosis indicating that a solar flare had damaged the RF front end. The remaining energy can support the core system for 4 hours, and there are 2GB of untransmitted exploration data in the cache. The system has the following emergency capabilities: ① Switch to UHF band to communicate with a relay node 20km away, at a rate of 50kbps; ② Enable ZIP lossless compression (compression ratio 1.5:1); ③ Use selective transmission mode (transmit only data with priority ≥3, accounting for 60% of the total).", + "question": "Calculate the shortest time required to rescue and transmit all high-priority data after enabling all emergency measures (including 15 minutes for system switching).", + "answer": "82 minutes" + }, + { + "id": 109, + "scenario_code": "5.7", + "instruction": " The 128GB on-board SSD of Chang'e-7 orbiter uses a NAND flash architecture, with a block size of 4MB and an average write/erase life of 3000 cycles. Currently, 78GB of valid data (evenly distributed) has been written, with 1.2GB of new data added daily. The wear-leveling algorithm uses a dynamic hot spot migration strategy, triggering a balancing operation when the difference in write/erase cycles between blocks reaches ≥500. The SSD controller reserves 15% of the OP space.", + "question": "Calculate the theoretical maximum continuous operating time of the SSD without triggering wear leveling (in Earth days).", + "answer": "1022 days" + }, + { + "id": 110, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (longitude 180°E, latitude 45°S), and needs to communicate with the ground station through the Queqiao-2 relay satellite. It is known that Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, at a height of about 80,000 kilometers above the lunar surface. At the current moment, the elevation angle of the ground station (110°E) to Queqiao is 25°, and the elevation angle of the lander to Queqiao is 40°. The Earth's rotational angular velocity is 15°/hour, and the Moon's rotational angular velocity is 0.55°/hour. The communication system requires a link elevation angle ≥10° and a duration ≥30 minutes to establish a stable connection.", + "question": "If the current time is 12:00 UTC, calculate the start time of the next communication window that meets the dual elevation angle conditions (ignoring orbital perturbations and antenna adjustment times).", + "answer": "14:18 UTC" + }, + { + "id": 111, + "scenario_code": "1.5", + "instruction": " The Yutu-2 rover needs to operate its robotic arm to grab rock samples with a communication delay of 1.3 seconds. The maximum movement speed of the robotic arm's end effector is 0.1m/s, and it is currently 0.25 meters away from the target position. After the ground control center sends a movement command, it must wait for a position confirmation signal before sending the next command. The rock sampling window is only 8 seconds remaining.", + "question": "Calculate the shortest theoretical time from sending the first movement command to completing the grab (ignoring acceleration/deceleration of the robotic arm), and determine whether the task can be completed within the window.", + "answer": "One-way communication delay 1.3 seconds * 2 + Movement time 0.25m / 0.1m/s = 2.6 + 2.5 = 5.1 seconds < 8 seconds, it can be completed." + }, + { + "id": 112, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 rover is conducting exploration tasks in the lunar south pole region, which has complex terrain with multiple permanently shadowed craters. The rover is equipped with a two-dimensional adjustable solar panel, with a maximum tracking efficiency of 92%. During the current lunar day, the solar elevation angle is 15 degrees, and the azimuth angle change rate is 0.25 degrees/minute. According to the three-dimensional terrain model analysis, it will enter a 300-meter diameter impact crater area in 2 hours ahead, where the crater walls will block 50% of the direct sunlight for 90 minutes. The standard operating condition power generation of the solar panel is 200W (when unobstructed).", + "question": "If the current azimuth tracking strategy remains unchanged, calculate the total power generation over the next 3 hours (considering the impact of terrain blocking)?", + "answer": "Power generation for the first 2 hours = 200W * 92% * 2h = 368Wh; Power generation during the blocking period = 200W * 50% * 92% * 1.5h = 138Wh; Total power generation = 368 + 138 = 506Wh" + }, + { + "id": 113, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 probe plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. The characteristics of the soil in this area are as follows: medium hardness (Mohs hardness 4-5), low viscosity, and high volatile content (about 3%). There are three sampling tools available: 1) a diamond-coated rotary drill (suitable for rocks with hardness >6); 2) a titanium alloy scoop (suitable for loose lunar soil); 3) a scraper with heating function (suitable for sticky materials with high volatile content). The maximum output torque of the probe's robotic arm is 10 Nm, and the sampling time window is 15 minutes.", + "question": "Based on the characteristics of the lunar soil and the parameters of the tools, which sampling tool should be chosen? Please explain the basis for your choice and calculate the theoretical sampling depth of the tool under maximum torque (assuming the average density of the lunar soil is 1.5 g/cm³ and the contact area of the tool is 5 cm²).", + "answer": "The scraper with heating function should be chosen. Justification: 1) The lunar soil has medium hardness but contains volatiles, and the heating function of the scraper can prevent the loss of volatiles; 2) The low viscosity does not require a high-torque drill. Theoretical sampling depth calculation: Pressure P = Torque / (Contact Area * Lever Arm) = 10 / (0.0005 m² * 0.1 m) = 200 kPa; Depth h = P / (Density * g) = 200000 / (1500 * 1.62) ≈ 82 cm" + }, + { + "id": 114, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform rock sampling, the one-way communication delay between Earth and the Moon is 1.3 seconds. The motion control of the lunar rover uses a predictive compensation algorithm: actual position = command position + v * Δt * k (v is the command speed 0.1m/s, Δt is the delay time, k=0.8 is the ground-measured friction coefficient compensation value). The current command requires the lunar rover to move in a straight line along the X-axis from coordinates (0,0), sending a movement command at t=0 seconds, and a stop command at t=5 seconds.", + "question": "Calculate the theoretical X coordinate value when the lunar rover finally stops (ignoring other error factors).", + "answer": "X = v * (t_stop - t_start - Δt) + v * Δt * k = 0.1*(5-1.3) + 0.1*1.3*0.8 = 0.37 + 0.104 = 0.474m" + }, + { + "id": 115, + "scenario_code": "1.8", + "instruction": " When deploying the lunar-based telescope, it was found that the bearing capacity of the regolith at the designated location is only 3kPa, which is lower than the 5kPa required by the support design. The support uses a three-legged structure, with a single leg contact area of 0.02m², and the total mass of the telescope is 120kg (lunar surface gravitational acceleration 1.62m/s²). Engineers propose two solutions: ① Increase the pad area to 0.03m²; ② Reduce the support mass to 80% of the original design.", + "question": "Calculate the adjusted pressure per leg for both solutions and indicate which solutions meet the bearing capacity requirement.", + "answer": "Solution ① pressure = (120*1.62/3)/0.03 = 2160Pa=2.16kPa; Solution ② pressure = (120*0.8*1.62/3)/0.02 = 2592Pa=2.59kPa; both solutions meet the <3kPa requirement." + }, + { + "id": 116, + "scenario_code": "5.7", + "instruction": " The 128TB solid-state storage on the lunar orbiter has experienced an abnormal increase in the bad block rate. Technical parameters: 1) NAND flash block size 256KB; 2) The current number of bad blocks has reached 0.1% of the total number of blocks; 3) The storage controller uses a dynamic wear-leveling algorithm, with an average write/erase cycle of 2000 times; 4) The file system is log-structured, with frequent metadata updates.", + "question": "Calculate whether the current number of bad blocks exceeds the design tolerance (design allows a bad block rate of 0.15%), and analyze the most likely cause of the increase in the bad block rate.", + "answer": "1) Total number of blocks = 128TB / 256KB = 128 * 1024^2 / 256 = 524288 blocks; current number of bad blocks = 524288 * 0.1% = 524 blocks; design tolerance value = 524288 * 0.15% = 786 blocks. Not exceeded but close to the threshold. 2) The most likely cause: Frequent metadata updates lead to specific blocks being written and erased far more often than the average, causing localized wear to intensify. It is recommended to optimize the file system's log writing strategy." + }, + { + "id": 117, + "scenario_code": "5.1", + "instruction": " The Chang'e-6 probe is executing a sample return mission on the far side of the Moon, and needs to establish a communication link with the ground station through the Queqiao-2 relay satellite. Known: 1) Queqiao-2 operates in the Earth-Moon L2 Halo orbit, with an average altitude of 45,000 km above the lunar surface; 2) The probe's maximum transmission power is 20W, with an antenna gain of 10dBi; 3) The receiving system quality factor G/T of the relay satellite is 10dB/K; 4) The operating frequency is 2.4GHz, and the free space loss formula is Lfs=92.45+20lg(d)+20lg(f), where d is the distance (km), and f is the frequency (GHz); 5) The required minimum received signal-to-noise ratio Eb/N0 is 12dB.", + "question": "Calculate the uplink margin from the probe to the relay satellite (considering only free space loss), and determine whether it meets the communication requirements (a 3dB margin must be reserved).", + "answer": "1) Calculate the distance d=45,000 km, frequency f=2.4GHz; free space loss Lfs=92.45+20lg(45000)+20lg(2.4)=92.45+93.06+7.6=193.11dB; 2) The equivalent isotropic radiated power EIRP at the transmitting end=10lg(20)+10=13+10=23dBW; 3) The received C/N0 at the receiving end=EIRP-Lfs+G/T-228.6=23-193.11+10-228.6=-388.71dBHz; 4) Eb/N0=C/N0-10lg(data rate), assuming the minimum data rate is 1kbps, then Eb/N0=-388.71-30=-418.71dB << 12dB requirement. Conclusion: Does not meet communication requirements (power or antenna gain needs to be increased)." + }, + { + "id": 118, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 rover is conducting exploration tasks in the South Pole-Aitken Basin on the Moon, an area with complex terrain and multiple craters that can obstruct the view. The rover is equipped with a dual-axis adjustable solar panel, with a maximum tracking efficiency of 92%. According to the lunar calendar, the current solar elevation angle during the lunar day is 15°, and the azimuth angle change rate is 0.25°/min. At a certain moment, there is a 1.5-meter-high rock 2 meters ahead, and the solar panel is 0.8 meters above the ground. It is known that the theoretical power generation without obstruction is 180W.", + "question": "Calculate the actual power generation of the solar panel under the current conditions (considering terrain obstruction and tracking efficiency loss).", + "answer": "Actual power generation = 180W * (1 - 1.5m / (2m * tan15°)) * 92% = 180 * (1 - 2.8) * 0.92 → If the obstruction rate exceeds 100%, it is calculated as 0, the final output is 0W." + }, + { + "id": 119, + "scenario_code": "5.7", + "instruction": " The Chang'e-5 return capsule's onboard SSD uses NAND Flash storage with a total capacity of 1TB and a block size of 128KB. The write amplification factor is 1.2, and on average, each block can withstand 3000 program/erase cycles. 50GB of new data is generated and evenly written to all blocks every day.", + "question": "Calculate the theoretical lifespan (in years) of this storage under ideal wear-leveling conditions, rounding to two decimal places.", + "answer": "Daily write volume = 50GB * 1.2 = 60GB; Daily program/erase block count = 60GB / 128KB ≈ 468750; Total block count = 1TB / 128KB = 8,388,608; Theoretical lifespan = (8,388,608 * 3000) / 468750 / 365 ≈ 146.88 years" + }, + { + "id": 120, + "scenario_code": "1.8", + "instruction": " When deploying a magnetometer on the lunar surface, it was found that local magnetic field interference reached ±200nT (design requirement <50nT). After surveying, the source of interference was found to be a 3-meter diameter lunar rock located 8 meters northwest, with a magnetic moment of 180A·m^2. It is known that the magnetic induction strength is inversely proportional to the cube of the distance: B = (μ0/4π) * (3(m��r)r - m)/r^5, where μ0/4π=1e-7 Tm/A, and r is the direction vector.", + "question": "If the magnetometer is moved southeast to a position where interference <50nT, how far at least should it be moved? (Simplified calculation takes the maximum value relationship: B_max ≈ 2*(μ0/4π)*m/r^3).", + "answer": "From B_max = 2*1e-7*180/r^3 ≤ 50e-9 → r^3 ≥ (2*1e-7*180)/(50e-9)=720 → r ≥ 720^(1/3)≈8.96m. Originally 8 meters from the interference source, the new position's line to the interference source must be ≥8.96 meters. Moving southeast means the new position forms a right triangle with the original position and the interference source: (8+x)^2 + x^2 ≥ 8.96^2 → x≥0.83 meters (taking x=0.85 meters satisfies 64+16x+x^2≥80.28)." + }, + { + "id": 121, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth, and must relay data through the Queqiao relay satellite. It is known that Queqiao operates in a Halo orbit around the Earth-Moon L2 point, approximately 65,000 km from the lunar surface. The X-band transmission power of the lander is 20W, with an antenna gain of 36dBi; the equivalent noise temperature of the Queqiao receiving system is 120K, and the bandwidth is 10MHz. It is required that the bit error rate (BER) be less than 1e-6, which necessitates an Eb/N0 of 13dB (including a 3dB margin).", + "question": "Calculate the maximum allowable path loss (including margin) for this communication link, given that the Boltzmann constant k=1.38e-23 J/K, and 1dB=10*lg(ratio).", + "answer": "The maximum allowable path loss = transmitted EIRP - receiving sensitivity + antenna gain difference. EIRP=20W + 36dBi=56dBm; receiving sensitivity=10*lg(k*T*B) + Eb/N0=10*lg(1.38e-23*120*10e6) + 13=-158.2+13=-145.2dBm; assuming the antenna gain difference is 0 (already included in EIRP). Therefore, the maximum path loss=56-(-145.2)=201.2dB" + }, + { + "id": 122, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover needs to transmit 500MB of scientific data daily through the Queqiao relay satellite during the lunar day. One day, due to a solar flare, the X-band link was interrupted for 3 hours, and the remaining storage capacity of the rover was only 600MB. The current compression algorithm has a compression ratio of 1:0.7 (original data:compressed), and the retransmission efficiency using the ARQ protocol is 80%.", + "question": "To ensure no data loss, how should the compression parameters be adjusted? Provide the specific compression ratio required and the calculation process.", + "answer": "The data volume to be transmitted=500MB/24h*21h=437.5MB; remaining storage capacity=600MB-437.5MB*0.7/0.8=600-382.8=217.2MB, which is insufficient. The new compression ratio x should satisfy: 437.5*x/0.8≤600 → x≤600*0.8/437.5≈1:1.1 (i.e., the compressed data does not exceed 90% of the original data)." + }, + { + "id": 123, + "scenario_code": "4.4", + "instruction": " Yutu-2 is conducting exploration in the Von Kármán crater, obtaining the following remote sensing data: ① 10m resolution multispectral images show a silicate anomaly at coordinates (12.3E, 45.2S); ② LiDAR elevation data indicate that this point is on a 3° slope; ③ The neutron detector shows that the hydrogen content at 1m underground reaches 150ppm. Scientific priority rules: signs of water ice (weight 0.4) > mineral diversity (0.3) > terrain safety (0.2) > communication convenience (0.1). The weighted scores of the other two candidate points B and C are 72 and 65 points, respectively.", + "question": "Based on the given data, calculate the scientific priority score of the current target point, and determine whether the path should be adjusted to prioritize exploration of this point. (Note: Silicate anomaly is counted as the full score of mineral diversity 100; slope < 5° gets the full score for terrain safety; hydrogen content > 100ppm gets the full score for signs of water ice.)", + "answer": "Target point score = signs of water ice (100*0.4) + mineral diversity (100*0.3) + terrain safety (100*0.2) + communication convenience (assuming default 60*0.1) = 40 + 30 + 20 + 6 = 96 points. Since 96 > 72 > 65, this point should be prioritized for exploration." + }, + { + "id": 124, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (longitude 177.6°E, latitude 45.5°S) and needs to communicate with the ground station via the Queqiao-2 relay satellite. It is known that Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, with an average altitude of 8000km above the lunar surface. The lander uses an X-band (8GHz) directional antenna (gain 20dBi) to communicate with the relay satellite, with a transmission power of 10W. The gain of the relay satellite's receiving antenna is 25dBi, the system noise temperature is 300K, and the minimum required received signal-to-noise ratio (SNR) is 10dB. The free space path loss formula is: L = 32.45 + 20*log10(f) + 20*log10(d), where f is the frequency (MHz), and d is the distance (km).", + "question": "Calculate whether the actual SNR at the relay satellite's receiver meets the requirement when the lander and Queqiao-2 are at the farthest visible communication distance. If not, to what power in watts must the transmission power be increased at least to meet the requirement? ", + "answer": "1. Calculate the path loss: L = 32.45 + 20*log10(8000) + 20*log10(8000) ≈ 220.5dB; 2. Received power Pr = Pt + Gt + Gr - L = 10dBW + 20dBi + 25dBi - 220.5dB = -165.5dBW; 3. Noise power Pn = -228.6 + 10*log10(300) + 10*log10(assumed bandwidth 1Hz) ≈ -204.8dBW/Hz; 4. SNR = Pr - Pn = -165.5 - (-204.8) = 39.3dB >> 10dB requirement, so no power increase is needed." + }, + { + "id": 125, + "scenario_code": "1.4", + "instruction": " The lunar rover and the fixed power station form a shared power network. The power station has a maximum output power of 300W, and the lunar rover has a peak power consumption of 180W during operations. When the lunar rover performs drilling tasks, it requires an additional 120W of power, at which time the power station must reserve at least 80W of redundant power for life support systems. The communication relay consumes a fixed 50W of power and has a higher priority than scientific instruments.", + "question": "If the lunar rover suddenly starts a drilling task, what is the maximum allowable power consumption of the current scientific instrument set? ", + "answer": "50W" + }, + { + "id": 126, + "scenario_code": "3.6", + "instruction": " The relay satellite of Chang'e-4 is about to enter the lunar night phase, and key equipment needs to be kept warm. The X-band transponder requires a working temperature ≥ -20°C, with a basic thermal consumption of 8W in sleep mode; the lithium-ion battery pack allows a working temperature range of -30°C~50°C, with a self-discharge heat rate of 5W during the lunar night. The thermal insulation system uses 10mm thick multi-layer insulation material (overall thermal conductivity 0.0005W/(m·K)) to wrap the equipment compartment (surface area 2.4m^2), and is equipped with 6 surface mount heaters rated at 10W each. The lunar night environmental temperature will stabilize at -180°C, and the initial temperature of the equipment compartment is 15°C.", + "question": "Calculate whether the internal temperature of the equipment compartment at steady state without using heaters meets the requirements of the X-band transponder? The steady-state thermal balance formula is known: Q_out = k*A*(T_in - T_env)/d, where k is the thermal conductivity, A is the surface area, and d is the thickness.", + "answer": "At steady state, the heat loss Q_out = (8+5) = 13W; from 13 = 0.0005*2.4*(T_in + 180)/0.01, we get T_in = (13*0.01)/(0.0005*2.4) - 180 = -42°C < -20°C, which does not meet the requirement." + }, + { + "id": 127, + "scenario_code": "3.1", + "instruction": " The Chang'e-5 lander is located near the Rümker Mountains at 43.06°N, 51.92°W on the near side of the Moon. During the lunar day, the solar elevation angle in this area varies between 5° and 35°, and terrain blocking reduces the actual sunlight exposure time by about 2 hours compared to the theoretical value. The lander is equipped with two 1.5m^2 triple-junction gallium arsenide solar panels, which have a conversion efficiency of 30% under standard conditions (AM0, 25°C), and a two-dimensional drive mechanism that can adjust the azimuth angle by ±180° and the tilt angle from 0° to 90°. At noon on the 3rd day of the current lunar day (local time), the solar azimuth angle is 215°, and the elevation angle is 28°, and the terrain blocking analysis shows that there will be no shadow impact in the next 2 hours.", + "question": "If the solar panels are optimally oriented (normal to the sun) at this time, and the battery pack is fully charged and does not need to be charged, calculate the maximum net power output under the current conditions (considering a PCU conversion efficiency of 95%). It is known that the solar radiation intensity under AM0 conditions is 1368W/m^2, the battery temperature is maintained at 45°C through thermal control, and the temperature coefficient is -0.002/°C.", + "answer": "Maximum net power output = 1368 * (1 - 0.002*(45-25)) * 1.5 * 2 * 0.3 * 0.95 = 1368 * 0.96 * 3 * 0.3 * 0.95 = 1123.6W" + }, + { + "id": 128, + "scenario_code": "3.4", + "instruction": " The Yutu-2 rover plans to perform three tasks simultaneously on the 5th day of the lunar day: ① Continuous X-ray spectrometer detection (peak power consumption 85W, lasting 40 minutes); ② Panoramic camera panoramic shooting (instantaneous power consumption 120W, each trigger lasts 5 seconds, a total of 12 directions need to be shot); ③ Transmit 500MB of scientific data to Earth through a directional antenna (transmission power 20W, needs to last 25 minutes). The energy system currently has 1800Wh of available power, and the solar panels can provide a stable charging power of 60W under the current lighting conditions. All tasks must be completed within 3 hours, and it must be ensured that the remaining power after the task is not less than 300Wh.", + "question": "Design a task scheduling plan that meets all the constraints, requiring the start time of each task (with the start time of the 5th day of the lunar day as T=0) to be given, and verify whether the total energy consumption meets the requirements.", + "answer": "Scheduling plan: ① T=0-40min (X-ray detection); ② T=40-65min (data transmission); ③ T=65-125min to perform panoramic shooting (triggered every 5 seconds, actual energy consumption 120*12*5/3600=2Wh). Total energy consumption=(85*40/60)+(20*25/60)+2=56.67+8.33+2=67Wh; Charging amount=60*3=180Wh; Final power=1800-67+180=1913Wh>300Wh, meets the requirements." + }, + { + "id": 129, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S) and needs to establish a communication link through the Queqiao-2 relay satellite. It is known that Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, with an average altitude of about 8000km above the lunar surface. At the current time, the visible arc segment between the ground station (Beijing station) and Queqiao-2 is UTC+8 from 09:00-15:00, and the lunar rotation period is 27.3 days. The lander is equipped with a directional antenna with a half-power angle of ±12°, X-band transmission power of 20W, and antenna gain of 38dBi.", + "question": "If the mission requires a minimum of 4 hours of effective communication window per day, please calculate whether the orbit height of Queqiao-2 needs to be adjusted under the current orbit configuration (assuming the link budget meets the minimum SNR requirements)? What are the key constraints to consider? ", + "answer": "Adjustment is required. Key constraints include: 1) Under the current configuration, the maximum theoretical communication window per day is 15:00-09:00=6 hours, but the actual effective window is shorter due to lunar obstruction; 2) It must be ensured that the elevation angle of the lander's antenna pointing to the relay satellite remains continuously greater than 12°; 3) Increasing the orbit height can extend the duration of each pass but will reduce the signal strength." + }, + { + "id": 130, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover experienced an X-band communication interruption during the lunar day, diagnosed as caused by solar flares leading to ionospheric disturbances. The rover is equipped with a dual-mode communication system (direct-to-Earth link + relay link), with remaining power to support continuous operation for 8 hours. Current status: the relay link signal-to-noise ratio has dropped by 15dB, the direct link requires waiting 2 hours to enter the ground station's visible window, and the solid-state storage has cached 12GB of untransmitted data (maximum compression rate of 50% in emergency mode).", + "question": "Please formulate the optimal communication recovery strategy, prioritizing which data to transmit first. Provide the rationale for your choice and the expected transmission time (assuming a compressed data transmission rate of 2Mbps).", + "answer": "Strategy: 1) Immediately switch to the direct link and wait for the ground station window; 2) Prioritize the transmission of engineering telemetry data (approximately 1GB) and key scientific data (approximately 3GB). Rationale: Engineering data is crucial for equipment safety, and key scientific data has time sensitivity. Expected time = (1+3)*1024MB/(2Mbps*60s) ≈ 34 minutes." + }, + { + "id": 131, + "scenario_code": "5.7", + "instruction": " The Chang'e-5 orbiter's SSD storage module uses NAND Flash chips, with a total capacity of 1TB and a block size of 4MB. The wear-leveling algorithm must meet the following requirements:\n1. Each block can be erased and written up to 10,000 times\n2. Average daily write volume is 20GB\n3. Design life is 8 years (including 2 years of redundancy)\n4. Write Amplification Factor (WA) = 1.5", + "question": "Verify whether the design meets the lifespan requirement (key calculation steps must be listed)?", + "answer": "Total write volume = 20GB * 365 * (8 + 2) * 1.5 ≈ 1095TB; Total write endurance = 1TB / 4MB * 10000 * 4MB = 10000TB; 1095TB < 10000TB, thus the requirement is met. Key steps: Compare the actual total write volume (including WA) with the theoretical endurance of the NAND." + }, + { + "id": 132, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing a patrol mission on the far side of the moon, located at point A (10°N, 120°E). The mission center has planned two scientific target points: Point B (12°N, 122°E) has a basalt outcrop that needs to be sampled, and Point C (11°N, 123°E) has a permanently shadowed area that needs to be explored. It is known that: the slope of the AB path is 5°, with a distance of 2km; the slope of the AC path is 8°, with a distance of 1.5km. The energy consumption model of the lunar rover is: E = 0.15*d + 2*θ (where d is the distance in kilometers, and θ is the absolute value of the slope). The remaining battery power can only support 5.5 units of energy consumption, and the exploration must be completed within 2 hours (the constant driving speed is 0.4km/h).", + "question": "If the mission requires that at least one target point must be explored, which path should Yutu-2 prioritize? Please explain the decision-making basis through calculations.", + "answer": "Choose the AB path. Calculation process: AB energy consumption = 0.15*2 + 2*5 = 10.3 units (exceeds power); AC energy consumption = 0.15*1.5 + 2*8 = 16.225 units (exceeds power). However, the travel time for AB = 2/0.4 = 5 hours (overtime), and the travel time for AC = 1.5/0.4 = 3.75 hours (overtime). Since neither meets the constraints, a new path needs to be planned or the rover needs to wait for recharging." + }, + { + "id": 133, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth, and must communicate through the Queqiao relay satellite. Queqiao operates in a Halo orbit around the Earth-Moon L2 point, about 65,000 kilometers from the Moon. Given:\n1. The communication elevation angle between a certain area on the far side of the Moon and Queqiao must be ≥10° to establish a stable link\n2. The Moon's rotation period is 27.3 days, and the landing site's longitude is 177.6° East\n3. The current time in UTC+8 is 2024-06-15 14:00:00, and Queqiao's orbital period is 14 days\n4. The average Earth-Moon distance is 380,000 kilometers, and the speed of light is 3×10^5 km/s", + "question": "Calculate the one-way communication delay (in seconds) between the lander and Queqiao at the current time, and determine whether the elevation angle is ≥10° for communication (explain the basis for your judgment)?", + "answer": "One-way delay = distance / speed of light = 65000 / 300000 ≈ 0.217 seconds; the condition is not met, as the far side of the Moon always faces away from Earth, and the landing site's longitude of 177.6° is close to the exact far side (180°). At this time, Queqiao is near the Earth-Moon line, and the elevation angle to the far side is close to 0°." + }, + { + "id": 134, + "scenario_code": "1.2", + "instruction": " When deploying an integrated drilling and sampling device in the permanently shadowed regions of the lunar south pole, the geometric constraints of the equipment installation sequence must be considered. The main drill tower is 2.1 meters high and, after deployment, must maintain a 0.5-meter safety distance from the spectrometer 3 meters away; the auxiliary robotic arm has a deployment radius of 1.8 meters and must not overlap with the lunar surface power module (coordinates X=1.2,Y=0). All equipment bases are circular with a diameter of 0.6 meters, and the lunar surface coordinate system is centered at the center of the drill tower base (0,0).", + "question": "If the spectrometer is deployed in the positive X-axis direction, what is the minimum X value of its base center coordinates to meet all constraint conditions? ", + "answer": "3.3" + }, + { + "id": 135, + "scenario_code": "1.4", + "instruction": " The lunar surface power grid must simultaneously power the lunar rover (peak power 200W), the seismometer array (150W), and the communication relay station (300W). The solar array has a maximum output power of 500W, and the storage battery can provide an additional 200W of continuous power but will accelerate aging. The current mission phase requires the communication relay station to operate at full power, and the seismometer array has a higher priority than the lunar rover.", + "question": "When the lunar rover needs an additional 180W of power for an emergency sampling task, how should the system adjust the power distribution? (Provide the final power values received by each device) ", + "answer": "Communication relay station 300W, seismometer array 150W, lunar rover 50W" + }, + { + "id": 136, + "scenario_code": "1.4", + "instruction": " Three scientific instruments (A/B/C) have been deployed in the permanent shadow region of the lunar south pole, sharing a lunar surface power grid. Instrument A (seismometer) needs to operate continuously with a peak power of 20W; Instrument B (spectrometer) operates for 15 minutes every 2 hours with a peak power of 50W; Instrument C (drill) operates three times a day, each for 10 minutes, with a peak power of 150W. The power grid consists of solar arrays and batteries, with a maximum continuous power supply of 100W, and the battery can store 500Wh of energy. The battery can be fully charged during the 10-hour daylight period and relies solely on the battery for power during the 14-hour night. It is currently the 3rd hour of the lunar day, and the battery has 400Wh of remaining power.", + "question": "If all instruments start according to the planned schedule and no other losses are considered, calculate whether there will be a power shortage in the next full day and night cycle (24 hours). If so, when will the first shortage occur during which time period of the night or day cycle? ", + "answer": "There will be a power shortage, and the first shortage will occur at the 11th hour (1st hour of the night). Calculation process: Total power supply during the day = 100W * 10h = 1000Wh; Total power supply at night = 500Wh (battery capacity). Total energy consumption during the day: A = 20W * 10h = 200Wh; B = 50W * (15min * 5 times) = 62.5Wh; C = 150W * (10min * 3 times) = 75Wh; Total 337.5Wh. Total energy consumption at night: A = 20W * 14h = 280Wh; B = 50W * (15min * 7 times) = 87.5Wh; Total 367.5Wh. Total demand 705Wh < 1500Wh supply, but the power consumption in the first hour of the night: A = 20W + B = 50W = 70W > the battery's continuous power supply capability 60W (500Wh / 14h ≈ 35.7W + remaining daytime power conversion), so there will actually be a shortage at the beginning of the night." + }, + { + "id": 137, + "scenario_code": "1.5", + "instruction": " The lunar rover is remotely operated from the ground control center to collect rock samples, with a one-way communication delay of 1.3 seconds. The current speed of the lunar rover is 0.2m/s, and a target rock has been detected 8 meters ahead. The control system uses a predictive algorithm to compensate for the delay: if the predicted position error at the time of command generation t0 exceeds 0.15 meters, an emergency brake is triggered. The known motion model of the lunar rover is x(t) = x0 + v*t + 0.5*a*t^2, with a maximum braking deceleration of 0.1m/s^2.", + "question": "When the operator issues a command to continue moving forward at t=0 seconds, if the command is not updated and obstacles are not considered, calculate whether an emergency brake will be triggered. If so, what is the ground station clock time when the brake is triggered? ", + "answer": "An emergency brake will be triggered, and the trigger time will be at the ground station clock t=6.5 seconds. Calculation process: When the command takes effect, the lunar rover has actually moved for t1=1.3 seconds, with a displacement of x1=0.2*1.3+0.5*0*1.3^2=0.26m; The predicted position is x_predicted=8-0.2*t; The actual position is x_real=8-0.26-0.2*(t-1.3). When |x_predicted - x_real|>0.15, the brake is triggered: |(8-0.2t)-(7.74-0.2t+0.26)|=|0|=0<0.15 is always not true. However, considering that the brake takes effect after another 1.3 seconds of propagation delay, the actual latest braking time when the position exceeds the limit should be calculated: Let t' be the moment when the lunar rover exceeds the limit locally, (8-0.2(t'+1.3))-(7.74-0.2t')>0.15 → t'<4.9s → The braking command is issued at the ground station clock t=t'+1.3=6.2s, and takes effect at 6.2+1.3=7.5s." + }, + { + "id": 138, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration near the Von Kármán crater. Pre-acquired orbital remote sensing data shows three candidate sampling points: Point 1 (coordinates X=12.3, Y=45.6) with 70% KREEP rock abundance, Point 2 (X=13.5, Y=44.8) with 60% breccia coverage, and Point 3 (X=11.9, Y=46.2) with 85% volcanic glass content. The rover is currently located at coordinates X=10.0, Y=40.0, with a movement speed of 0.05m/s, and the scientific priority weights are: KREEP rock > volcanic glass > breccia. At least 2 hours are required to stay at each sampling point for analysis.", + "question": "If the remaining operational time is 8 hours, please calculate the optimal sampling path and the time allocation for staying at each point.", + "answer": "Path order: Point 3 → Point 1; Time allocation: Stay at Point 3 for 4 hours (including 1.33 hours for movement), and stay at Point 1 for 3.67 hours (including 1.67 hours for movement)." + }, + { + "id": 139, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. The container weighs 2kg, with a maximum allowable acceleration of 5m/s^2; the maximum gripping force of the robotic arm's end effector is 15N, and the friction coefficient μ=0.8 at the contact surface; the gravitational acceleration on the lunar surface during handover is 1.62m/s^2. The container is equipped with an RFID tag, which requires a reading distance of <10cm and no metal obstruction. The docking ring of the ascent vehicle has a positioning accuracy of ±2cm.", + "question": "What is the minimum gripping force that the robotic arm should apply to ensure safe handover? Where should the RFID reading device be installed for optimal performance during the handover process? ", + "answer": "The minimum gripping force is 4.05N (2kg*1.62m/s^2/0.8), and the RFID reading device should be installed at a position <10cm away from the container surface and avoiding metal components in a non-contact manner." + }, + { + "id": 140, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 lander is located on the edge of an impact crater on the near side of the Moon at 23.5 degrees north latitude and 12.8 degrees east longitude. Its solar panels operate in a two-dimensional tracking mode (azimuth + elevation). According to the lunar calendar, it is currently the 5th day of the lunar day, with a solar elevation angle of 32 degrees. The crater wall casts a trapezoidal shadow on the solar panels during the morning, reducing the effective illuminated area by 40%. It is known that under standard conditions, the output power of a single solar panel is 120W/m², with a total area of 2.5m².", + "question": "If the current solar azimuth coincides with the direction of the shadow, calculate the actual power generation (considering the two-dimensional tracking maximum power point tracking function is enabled)?", + "answer": "180W" + }, + { + "id": 141, + "scenario_code": "3.4", + "instruction": " The Yutu-2 rover plans to perform three tasks simultaneously on the 3rd day of the lunar day: ① Continuous operation of the X-ray spectrometer for 2 hours (peak power consumption 45W) ② Sampling operation by the robotic arm for 20 minutes (instantaneous power consumption 120W) ③ High-speed data transmission for 1.5 hours (peak power consumption 60W). The power system uses a lithium-ion battery pack (available capacity 300Wh), with a current state of charge (SOC) of 80%, and the solar input power is stable at 80W. All tasks must be completed 4 hours before sunset.", + "question": "Determine whether the task sequence needs to be adjusted to meet the energy safety margin (require SOC ≥ 30% after task completion)? If so, provide the latest start time for the robotic arm operation.", + "answer": "Adjustment needed, the latest start time for the robotic arm operation is 3.2 hours after the task begins" + }, + { + "id": 142, + "scenario_code": "3.8", + "instruction": " The daily task profile of a rover includes: moving (power consumption 80W for 2h), drilling (peak 200W for 0.5h), data transmission (120W for 1h), and hibernation (5W). The available capacity of the lithium-ion battery pack is 500Wh, and the solar charging power curve is: linearly increasing from 0 to 150W from 08:00 to 16:00, and linearly decreasing to 0 from 16:00 to 20:00.", + "question": "Plan the execution time periods for each task (specify the exact time), ensuring that the battery is not depleted and solar charging is fully utilized.", + "answer": "Charging period from 08:00 to 16:00 can charge = integral (150/8*t) dt from 0 to 8 = 600Wh; from 16:00 to 20:00 charging = 300Wh. Total charging 900Wh > total consumption 80*2 + 200*0.5 + 120*1 + 5*(24-3.5) = 371Wh. It is recommended to schedule: drilling from 09:00 to 09:30 (high power consumption matches high charging power), moving from 10:30 to 12:30, transmission from 14:00 to 15:00, and hibernation for the rest of the time." + }, + { + "id": 143, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover needs to transmit 1GB of scientific data to Earth via the Queqiao relay satellite during the lunar day. The current link bandwidth is 1Mbps, but it is expected that 30 minutes later, it will enter the lunar night, causing a 12-hour communication interruption. Given:\n- DTN protocol header overhead 10%\n- Current link bit error rate 0.001%, retransmission efficiency 90%\n- SSD remaining capacity 50GB, equipment sleep power consumption during the lunar night 5W (battery remaining 200Wh).", + "question": "Determine whether the transmission can be completed before the communication interruption. If not, propose two feasible engineering solutions.", + "answer": "1. Effective transmission rate=1Mbps*90%*(1-10%)=0.81Mbps\n2. Data to be transmitted=1GB*8/0.81≈9876 seconds > 1800 seconds → cannot complete\nSolutions:\n① Enable compression algorithm (e.g., compress data to less than 300MB)\n② Switch to a higher bandwidth relay link (e.g., adjust the Queqiao beamforming)." + }, + { + "id": 144, + "scenario_code": "3.6", + "instruction": " Chang'e-7 lander enters the lunar night phase, and it needs to maintain the core cabin temperature no lower than -40°C. Given: 1) The cabin heat loss power Q_loss=12*(T_inner-T_outer) W (T_outer=-180°C); 2) The isotope heat source provides a constant 8W of heat; 3) The electric heater has a maximum power of 20W but the total power available during the lunar night is only 300Wh. The battery capacity is 500Wh, with an initial SOC=60%.", + "question": "Calculate the minimum constant power P_heater (round to the nearest integer) that needs to be set for the electric heater, so that it can maintain the temperature without exceeding the energy budget (Hint: Establish the thermal balance equation Q_loss=8+P_heater).", + "answer": "At -40°C, Q_loss=12*(-40+180)=1680W>8W, thus P_heater=1680-8=1672W. However, 20W<<1672W cannot meet the requirement, the conditions of the problem are contradictory. Correct understanding: Q_loss should be 12*(T_inner-T_outer)=12*(-40+180)=1680J/h≈0.467W, hence P_heater=0.467-8<0, only the isotope heat source is needed." + }, + { + "id": 145, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover needs to transmit at least 500MB of scientific data daily via the 'Queqiao' relay satellite during the lunar day. During a communication session, a sudden solar proton event caused the X-band link to fail, leaving only 30 minutes of usable lunar day time. The rover's local storage has 1GB of remaining capacity, and the current cache data is 600MB (priority: 100MB of engineering data > 200MB of spectral data > 300MB of image data). It is known that in emergency mode, the backup S-band link can be activated, but the transmission rate drops to 2Mbps (including protocol overhead).", + "question": "To ensure the complete transmission of core data without overflowing the storage, what transmission strategy should be formulated? Please explain the basis for your choice and the specific operational steps.", + "answer": "1) Calculate the S-band transmission capability: 30 minutes * 60 seconds * 2Mbps / 8 = 450MB\n2) Priority transmission order: 100MB of engineering data (must be transmitted) > 200MB of spectral data > 150MB of image data (450 - 100 - 200 = 150)\n3) Operational steps:\n a) Immediately switch to the S-band link\n b) Transmit data in order of priority until the 450MB limit is reached\n c) Discard the 150MB of untransmitted image data\nBasis: Ensure the complete transmission of core engineering data and that the total transmission volume does not exceed the link capacity and storage limits." + }, + { + "id": 146, + "scenario_code": "5.7", + "instruction": " The 'Chang'e-5' orbiter's solid-state storage uses a NAND Flash array design with a total capacity of 1TB, and employs a wear-leveling algorithm to extend its lifespan. It is known that the storage contains 1024 erase blocks (block), each of which can withstand 10,000 erase-write cycles. The current file system records show: Area A has 500 blocks with an average of 8000 erase-write cycles, and Area B has 524 blocks with an average of 2000 erase-write cycles. The storage controller needs to perform dynamic data migration to balance wear.", + "question": "If future missions require the continuous writing of a total of 300GB of new data (each write triggers an erase operation), calculate the expected final average erase-write cycles for each area before and after the implementation of the migration strategy. Assume that write requests are evenly distributed across all blocks.", + "answer": "1) Number of blocks involved in each write = 300GB / (1TB / 1024) = 307 blocks\n2) Without migration:\n Final cycles in Area A = 8000 + 307 * 500 / 1024 ≈ 8000 + 150 ≈ 8150 times\n Final cycles in Area B = 2000 + 307 * 524 / 1024 ≈ 2000 + 157 ≈ 2157 times\n3) After migration and balancing:\n Total erase-write cycles = (500 * 8000 + 524 * 2000) + 307 ≈ 5,048,000 times\n New average = (5,048,000 + 307) / 1024 ≈ 4929 times" + }, + { + "id": 147, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the Moon's south pole, a shared power grid needs to be established using 3 Mobile Energy Modules (MEMs). Each MEM has a maximum output power of 500W, but the actual available power is affected by temperature: when the local temperature is below -150°C, the output power decreases by 30%. The current temperatures at deployment points A, B, and C are -170°C, -160°C, and -140°C, respectively. The peak power consumption of the three scientific instruments D1, D2, and D3 are 400W, 350W, and 300W, respectively, and they must all be started simultaneously for 10 minutes for initialization.", + "question": "If an average distribution strategy is adopted, how many devices should each MEM power? Please verify whether this plan meets the peak power consumption requirements of all devices.", + "answer": "Each MEM should power 1 device. The plan does not meet the requirements: the actual power of the MEM at point A = 500*0.7=350W (<400W, unable to support D1), at point B = 500*0.7=350W (=350W, barely supports D2), and at point C = 500W (>300W, can support D3)." + }, + { + "id": 148, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform rock sampling tasks, the one-way communication delay between Earth and the Moon is 1.25 seconds. The current speed of the lunar rover is 0.2m/s, and a target rock is detected 3 meters ahead. The total system delay (including transmission, decoding, and execution) for control commands from issuance to execution is 2.8 seconds. The emergency braking distance formula is: d = v * t + 0.5 * a * t^2, where a=0.4m/s² is the braking acceleration, and t is the braking time.", + "question": "If a stop command is sent immediately, calculate the minimum distance margin between the predicted position of the lunar rover when it comes to a complete stop and the target rock.", + "answer": "Braking time t=v/a=0.2/0.4=0.5 seconds; braking distance d=0.2*0.5+0.5*0.4*0.5^2=0.15 meters; total movement distance=0.2*(1.25+2.8)+0.15=0.96 meters; margin=3-0.96=2.04 meters." + }, + { + "id": 149, + "scenario_code": "1.8", + "instruction": " When deploying a seismometer array, uneven bearing capacity of the lunar regolith was discovered: Area A has a bearing capacity of 8kPa (safe threshold), while Area B has 5kPa (below the 6kPa safety threshold). The seismometer weighs 50kg, and the base contact area is 0.2m². Given the pressure formula P=F/A, where F=mass*acceleration due to lunar gravity (1.62m/s²). There are two adjustment options: ① Use a spare base with 50% larger area in Area B; ② Move the instrument 30cm towards Area A so that 70% of its weight is on Area A.", + "question": "Calculate the pressure on Area B under both options, and indicate which option meets the safety threshold.", + "answer": "Option ①: New area=0.2*1.5=0.3m²; P=(50*1.62)/0.3=270Pa=0.27kPa (safe). Option ②: Area B bears 30% of the weight; P=(50*1.62*0.3)/0.2=121.5Pa≈0.12kPa (safe). Both options meet the requirements." + }, + { + "id": 150, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing a patrol mission on the far side of the moon, located at coordinate point A (177.6°E, 45.5°S), and needs to reach scientific target point B (177.8°E, 45.3°S). It is known that: 1) The straight-line distance between the two points is 1.2km, but there are several small impact craters along the path that need to be bypassed; 2) The average moving speed of the lunar rover is 0.05m/s; 3) The wheel-soil mechanics model shows that the energy consumption coefficient k=0.15*d (d is the tangent value of the slope angle) when driving on a slope; 4) The average slope in the current area is 8°; 5) The remaining battery energy is 1200Wh, and the basic power consumption is 20W.", + "question": "If the shortest detour path (actual travel distance 1.5km) is chosen, calculate the remaining battery power of the lunar rover after completing this section of travel (保留两位小数). Hint: Total energy consumption E=basic power consumption*time + k*distance, where time=distance/speed.", + "answer": "First, calculate the travel time: 1.5km / 0.05m/s = 30000 seconds ≈ 8.33 hours. Basic power consumption: 20W * 8.33h = 166.6Wh. Slope energy consumption coefficient k=0.15*tan(8°)≈0.021, movement energy consumption=0.021*1500m=31.5Wh. Total energy consumption=166.6+31.5=198.1Wh. Remaining power=1200-198.1=1001.90Wh" + }, + { + "id": 151, + "scenario_code": "3.1", + "instruction": " The Chang'e-7 lander is located near the lunar south pole (latitude 85°S), and its solar wings use a two-dimensional tracking algorithm. According to the lunar ephemeris, the current solar elevation angle is 5°, and the azimuth angle is 120°. Terrain shadow analysis shows: there is a permanently shadowed area within 30° of due east, and the maximum pitch angle limit for the solar wings is ±60°. It is known that: the standard power of a single solar panel P_std=200W (when vertically illuminated), the actual output power P=P_std*cos(θ), where θ is the angle of incidence of sunlight.", + "question": "If the current solar wings are oriented at an azimuth of 90° and a pitch of 30°, calculate the actual power generation (保留两位小数) at this time? ", + "answer": "100.00W" + }, + { + "id": 152, + "scenario_code": "1.5", + "instruction": " When controlling the lunar rover to perform rock sampling tasks, the ground control center must wait 1.3 seconds for feedback after sending a movement command. The current speed of the lunar rover is 0.2m/s, with a maximum braking deceleration of 0.1m/s^2. The control system uses a predictive control algorithm, with the position prediction model being: predicted position = current position + v*t_delay + 0.5*a*t_delay^2, where t_delay is the delay time, and a is the current acceleration (negative value during braking).", + "question": "If the ground command is issued when the lunar rover is 3 meters away from the target rock and it immediately starts braking, determine according to the prediction model whether it will overshoot the target position. Calculate the final predicted stopping position and the deviation from the target.", + "answer": "It will overshoot the target position. Predicted braking distance = 0.2*1.3 + 0.5*(-0.1)*1.3^2 = 0.26 - 0.0845 = 0.1755m; actual braking distance required = v^2/(2*a) = 0.2^2/(2*0.1) = 0.2m. Since the initial distance of 3m > 0.2m, the vehicle will stop before reaching the target. Deviation = 3 - (0.2*1.3 - 0.5*0.1*1.3^2 + 0.2) = 3 - (0.26 - 0.0845 + 0.2) = 2.6245m" + }, + { + "id": 153, + "scenario_code": "5.1", + "instruction": " The Chang'e-6 lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 45°S, 170°E), and plans to communicate with Earth via the Queqiao-2 relay satellite. Given: Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, with an average altitude of 80,000 km above the lunar surface; the lander's transmission power is 10W, with an antenna gain of 5dBi; the relay satellite's receiving antenna gain is 40dBi, and the system noise temperature is 150K; the operating frequency is 2.4GHz (wavelength 0.125m), and the required minimum signal-to-noise ratio (SNR) is 10dB. The current lunar surface temperature is -100℃, and the equipment operating bandwidth is 1MHz.", + "question": "Calculate the maximum theoretical data transmission rate of the Earth-Moon relay link under the current conditions (using Shannon's formula C = B * log2(1+SNR), ignoring atmospheric loss and polarization mismatch, and retaining two decimal places).", + "answer": "1.00 Mbps" + }, + { + "id": 154, + "scenario_code": "3.4", + "instruction": " Yutu-2 rover needs to perform the following tasks during the lunar day: ① X-ray spectrometer (peak power consumption 50W/10 minutes) ② Laser ranging (instantaneous 120W/30 seconds) ③ Data transmission (continuous 20W). Energy system constraints: instantaneous total power consumption must not exceed 150W, average power consumption must be ≤80W. Task priority: ②>③>①. Current battery SOC=65%, remaining available energy 500Wh.", + "question": "Design a load scheduling plan that meets the constraints and calculate the remaining SOC after executing all tasks (assuming 100% conversion efficiency)?", + "answer": "Scheduling plan: First, execute ② laser ranging (120W), then execute ③ data transmission (20W+50W=70W≤150W), and finally execute ① X-ray spectrometer; remaining SOC=65% - (120*0.00833 +20*0.333 +50*0.1667)/500*100%=62.08%." + }, + { + "id": 155, + "scenario_code": "3.8", + "instruction": " Chang'e-6 relay satellite has an orbital period of 6 hours, with the following energy consumption profile: ① Telemetry and communication (40W/1.5 hours) ② Payload operation (25W/2 hours) ③ Attitude maintenance (15W continuous). The solar panel can provide stable power of 120W during the illumination period, and relies on battery power during the shadow period. During a lunar eclipse, the shadow period is extended to 2.2 hours, with a battery capacity of 300Wh and an initial SOC=90%.", + "question": "Verify if the current energy configuration can support the complete cycle operation? If not, to what minimum capacity in Wh must the battery be increased to support the operation during the lunar eclipse period (assuming 100% conversion efficiency)?", + "answer": "Cannot support. Total energy consumption=40*1.5 +25*2 +15*6=230Wh, power required during the shadow period=15*2.2=33Wh, battery must provide 230-120*(6-2.2)= -226Wh→ capacity must be ≥226/0.9≈251.11Wh." + }, + { + "id": 156, + "scenario_code": "5.4", + "instruction": " During the lunar day, the Yutu-2 rover continuously transmits exploration data to the Queqiao relay satellite when it suddenly encounters a solar conjunction causing a communication interruption. It is known that: before the interruption, 85% of the data packets (total size 50GB) had been transmitted, and the remaining data needs to be transmitted within 8 hours before the end of the lunar day; the current alternative solutions are: (A) wait for the solar conjunction to end and resume the original link (expected wait time 3 hours), (B) switch to a low-gain antenna to communicate directly with Earth (rate reduced to 30% of the original link). The original link rate is 10Mbps, and the solid-state storage write speed limit is 5MB/s.", + "question": "Choose the optimal recovery strategy and calculate its theoretical completion time, considering the storage write speed limit.", + "answer": "Remaining data volume = 50GB * 15% = 7.5GB. Total time for option A = 3h + (7.5GB / (10Mbps / 8)) = 3h + 6000s ≈ 4.67h; for option B, the effective rate = 10Mbps * 30% = 3Mbps, limited by the storage speed of 5MB/s (40Mbps) which is not a bottleneck, total time = 7.5GB / (3Mbps / 8) = 20000s ≈ 5.56h. Therefore, option A is selected." + }, + { + "id": 157, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. Analysis of the characteristics of the lunar soil in this area shows: the top layer 0-30cm is loose fine particles (viscosity index 0.3, Mohs hardness 2), 30-50cm has a cemented layer (viscosity index 1.2, Mohs hardness 4), and below 50cm is basaltic debris (Mohs hardness 6). The probe is equipped with three sampling tools: A-type scraper (suitable for hardness ≤3), B-type vibrating drill (suitable for viscosity ≤1.5 and hardness ≤5), and C-type impact drill (suitable for hardness ≤7 but consumes three times the energy of the B-type). The sampling depth needs to reach 60cm to obtain fresh material.", + "question": "If both sampling success rate and energy efficiency are required, how should the above tools be combined to complete sampling? Provide the specific tool usage sequence and corresponding sampling depth intervals.", + "answer": "First, use the A-type scraper to collect the loose layer from 0-30cm, then use the B-type vibrating drill to penetrate the cemented layer from 30-50cm, and finally use the C-type impact drill to collect the basaltic layer from 50-60cm." + }, + { + "id": 158, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover obtained the following data while conducting exploration in the Von Kármán crater: 1) High-resolution images from the Gaofen-2 satellite show the presence of KREEP rock spectral characteristics at coordinates (12.34°S, 123.56°E); 2) The laser radar measured a slope of 8° at that point; 3) The current position of the rover is 320 meters in a straight line from the target point, but there is a 15-meter diameter crater in between that requires detouring. It is known that the average travel speed of the rover is 0.05m/s, the detour path increase factor is 1.8, and the remaining window period for scientific investigation is 2 hours.", + "question": "Determine whether the rover can complete the exploration task at this sampling point within the window period? List the calculation process.", + "answer": "Actual path distance = 320 * 1.8 = 576 meters; required time = 576 / 0.05 = 11520 seconds = 3.2 hours > 2-hour window period, therefore it cannot be completed." + }, + { + "id": 159, + "scenario_code": "4.4", + "instruction": " Yutu-2 obtained the following remote sensing data while patrolling the Von Kármán crater: 1) KREEP rock outcrop (coordinates X12/Y34, with distinct spectral characteristics but a slope of 15°); 2) Breccia-rich area (coordinates X18/Y29, with a slope of 8° but requires a detour of 300 meters); 3) Suspected volcanic glass area (coordinates X05/Y40, with a slope of 5° but indistinct spectral characteristics). The rover's maximum climbing ability is 12°, and the remaining power supports a total travel distance of 500 meters. The scientific priority order is: KREEP rock > breccia > volcanic glass.", + "question": "Which sampling point should be chosen according to the constraints? Provide a calculation to explain the choice.", + "answer": "Choose the breccia-rich area. The KREEP rock's slope exceeds the limit (15°>12°), and the evidence for volcanic glass is insufficient; the breccia meets the slope requirement (8°<12°), and after the detour, the total travel distance is 300m<500m, with a higher priority than volcanic glass." + }, + { + "id": 160, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration near the Von Kármán crater, obtaining the following remote sensing data: 1) Probability map of KREEP rock distribution (87% probability at coordinates X12Y34); 2) Thermal infrared characteristics of breccia (abnormal at coordinates X15Y32); 3) Navigation camera shows that the path from X12Y34 to X15Y32 has 3 slopes with a gradient >15°. The rover's movement power consumption formula is: P=5+0.3*gradient(°), and the remaining power can supply 300W·h. Scientific priority weights: KREEP rock=3, breccia=2.", + "question": "Calculate whether the rover can complete sampling at both locations along the X12Y34→X15Y32 route? Which type of rock should be prioritized for sampling? (Assuming a single point sampling takes 30 minutes, and static power consumption is 10W).", + "answer": "Total energy consumption for the route = (5+0.3*15)*3 segments*distance factor 1 + (10W*1h) = 43.5W·h < 300W·h, it can be completed. KREEP rock should be prioritized for sampling (higher weight)." + }, + { + "id": 161, + "scenario_code": "4.9", + "instruction": " The sample container transfer window between the ascender and the lander is 10 minutes. Container integrity check takes 2 minutes (requires continuous power of 25W), environmental parameter download takes 3 minutes (data transfer rate 2MB/s, power consumption 15W). The energy consumption formula for the transfer manipulator operation is: E=5+0.1*t (t is the operation time in seconds). The system currently has a remaining power of 50W·h, and the uplink bandwidth is limited to executing only one data transfer or mechanical operation at a time.", + "question": "Design the optimal operation sequence to achieve a 100% success rate, and verify whether the total energy consumption meets the constraints. (Note: The integrity check must be completed first before starting other operations.)", + "answer": "Operation sequence: 1) Integrity check (2min, 25W) → 2) Manipulator transfer (calculated at a maximum of 7min = 420s, E=5+0.1*420=47W) → 3) Parameter download (1min, 15W). Total energy consumption = (25*2/60) + (47) + (15*1/60) = 49.17W·h < 50W·h" + }, + { + "id": 162, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. Analysis of the soil characteristics in this area shows: the surface layer 0-30cm is loose fine particles (shear strength <5kPa), 30-50cm has a cemented layer (shear strength 15-20kPa), and below 50cm is basaltic debris (Mohs hardness 5-6). There are three sampling tools available: A-type scraper (maximum force 50N, suitable for hardness ≤4), B-type rotary drill (maximum torque 3Nm, suitable for hardness ≤6), and C-type vibrating core tube (frequency 10Hz, suitable for cemented layers). The end effector of the probe's robotic arm can provide a maximum thrust of 100N and a torque of 5Nm.", + "question": "If it is necessary to obtain a complete 0-60cm profile sample without damaging the tools, how should the sampling tools be combined for use? Provide the specific depth intervals and the basis for tool selection.", + "answer": "0-30cm use the A-type scraper (loose layer does not require a high-hardness tool), 30-50cm use the C-type vibrating core tube (cemented layer requires vibration to break), 50-60cm use the B-type rotary drill (basalt requires a hardness-matched tool). Basis: the parameters of each tool match the soil layer characteristics, and the output capabilities of the robotic arm meet the requirements." + }, + { + "id": 163, + "scenario_code": "4.4", + "instruction": " Yutu-2 obtained data from three candidate sampling points while patrolling the Von Kármán crater: Point 1 shows a spectrum characteristic of KREEP rock (8% KREEP component), 120 meters from the current position; Point 2 shows a high dielectric anomaly at a depth of 2 meters (possibly water ice) on radar, 80 meters from the current position but requires crossing a 10° slope; Point 3 detected 25% ilmenite content (highest of the entire mission) by XRF, 200 meters away in a flat area. The remaining power of the rover supports a total travel distance ≤300 meters, with the energy consumption coefficient for climbing being 1.8 times that of flat movement.", + "question": "If the scientific priority is: water ice > KREEP rock > ilmenite, please calculate the highest priority point that can be safely accessed and explain the path selection.", + "answer": "Choose Point 2. Total path energy consumption = 80 * 1.8 = 144 distance units < 300, meeting the power constraint. Basis: Water ice has the highest priority, and the combination of 80 * 1.8 + 120 = 264 < 300 cannot cover Point 1 simultaneously." + }, + { + "id": 164, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently conducting a patrol mission on the far side of the Moon, located at coordinate point A (10°N, 120°E), and needs to travel to scientific target point B (12°N, 122°E). Given: 1) The straight-line distance formula between two points on the lunar surface is d = R * arccos(sinφ1*sinφ2 + cosφ1*cosφ2*cosΔλ), where R=1737km is the lunar radius, φ is latitude, and Δλ is the difference in longitude; 2) The total energy consumption model for the path is E = 0.15*d + 5*(average slope)^2 (unit: Wh); 3) The average slope of the AB path measured by stereo imagery is 8°, and there is a crater with a diameter of 20m that needs to be bypassed, adding 50m to the journey.", + "question": "If Yutu-2 currently has 200Wh of remaining power, can it safely reach point B without recharging? Please provide specific calculation steps.", + "answer": "1) Calculate the straight-line distance AB: Δφ=2°=0.0349rad, Δλ=2°=0.0349rad → d=1737*arccos(sin10°*sin12°+cos10°*cos12°*cos2°)≈61.3km; 2) Actual path length=61.3km+0.05km=61.35km; 3) Calculate energy consumption: E=0.15*61.35+5*(8)^2=9.2025+320=329.2025Wh; 4) Compare: 329.2025Wh > 200Wh → It cannot reach safely." + }, + { + "id": 165, + "scenario_code": "3.6", + "instruction": " The Yutu-2 rover is about to enter the lunar night hibernation phase, with a battery capacity of 4000mAh and a working voltage of 28V. The lunar night lasts 14 Earth days, during which it needs to maintain a basic power consumption of 0.5W for electronic devices and a heating power consumption of 2W for scientific instruments. The effective discharge capacity of the battery at -180°C decreases to 70% of the nominal value, and the depth of discharge must not exceed 40%. The isotope heat source can provide a constant thermal power of 1W.", + "question": "Verify whether the current energy configuration can safely survive the lunar night (calculate the total energy consumption and available energy, and consider the capacity reduction due to temperature and the depth of discharge limit).", + "answer": "Total energy consumption = (0.5W + 2W - 1W) * 14*24h = 1.5W * 336h = 504Wh; Available energy = 4000mAh * 28V * 0.7 * 0.4 /1000 = 31.36Wh; Conclusion: 504Wh > 31.36Wh, configuration is insufficient" + }, + { + "id": 166, + "scenario_code": "3.8", + "instruction": " The relay satellite of the Chang'e-4 mission has a 24-hour task cycle, which includes the following power consumption phases: ① Orbit maintenance engine ignition twice (each at 15A@100V, lasting 30 seconds); ② Scientific payload operation for 8 hours (average power consumption 50W); ③ Communication system transmission window 4 times daily (each 20 minutes, peak power consumption 120W); ④ Platform equipment continuous power consumption 25W. The lithium-ion battery pack has a total capacity of 80kWh, with a charge-discharge efficiency of 95%.", + "question": "Calculate the minimum daily solar power generation required (calculate the power consumption of each phase separately and consider the charge-discharge loss).", + "answer": "Total power consumption = (15A*100V*2*30s/3600) + (50W*8h) + (120W*4*20/60h) + (25W*24h) = 25Wh + 400Wh + 160Wh + 600Wh = 1185Wh; Required power replenishment = 1185Wh/0.95 = 1247.37Wh" + }, + { + "id": 167, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is conducting patrol exploration on the far side of the moon, currently located at coordinate point A(10°N, 120°E), and needs to reach the scientific target point B(12°N, 122°E). It is known that: 1) The straight-line distance between the two points is 30km, but there is a 5km diameter impact crater blocking the way; 2) The average driving speed of the lunar rover is 0.1m/s; 3) The energy consumption model is E = 0.15*d + 0.8*h, where d is the driving distance (km), and h is the cumulative climbing height (m); 4) Bypass route options: Option one bypasses the north side, increasing the driving distance by 8km and the cumulative climb by 50m, while option two bypasses the south side, increasing the driving distance by 6km but requiring a cumulative climb of 80m. The mission requires total energy consumption not to exceed 7kWh.", + "question": "Please calculate the total energy consumption of the two bypass options and determine which option meets the mission requirements.", + "answer": "Energy consumption of option one E1 = 0.15*(30+8) + 0.8*50 = 5.7 + 40 = 45.7kWh; Energy consumption of option two E2 = 0.15*(30+6) + 0.8*80 = 5.4 + 64 = 69.4kWh. Only option one meets the ≤7kWh requirement (Note: The original question's energy consumption coefficient setting has a magnitude error, it should actually be E1=5.7+0.04=5.74kWh, E2=5.4+0.064=5.464kWh, in which case option two is better. It is recommended to correct the coefficient to 0.15*d+0.0008*h)." + }, + { + "id": 168, + "scenario_code": "3.4", + "instruction": " During the lunar day, the Yutu-2 rover needs to perform the following tasks simultaneously: ① Continuous X-ray spectrometer detection (power consumption 25W/hour) ② Mechanical arm sampling (instantaneous peak 120W, lasting 10 minutes) ③ Data transmission (power consumption 45W/hour). Energy system constraints: the available capacity of the lithium-ion battery pack is 200Wh, the current output power of the solar panel is 80W, and the remaining lunar day time is 3 hours. The task priority is ③>②>①.", + "question": "Design an energy allocation plan that meets the execution of all tasks, and provide the longest possible running time for each task (ensuring that the battery retains 50Wh of emergency power before the lunar night).", + "answer": "Data transmission for 3 hours (energy consumption 135Wh), mechanical arm sampling for 10 minutes (energy consumption 20Wh), and X-ray spectrometer for 1.5 hours (energy consumption 37.5Wh); total energy consumption 192.5Wh < available energy 210Wh (80W*3h + 200Wh - 50Wh)." + }, + { + "id": 169, + "scenario_code": "3.6", + "instruction": " The Chang'e-6 lander has entered the lunar night phase and needs to maintain an electronic equipment cabin temperature above -40°C. Known: the cabin surface area is 2m², the equivalent thermal resistance of the multi-layer insulation material R=4 m²·K/W; the rated heat output of the isotope heat source Q_rhpu=30W; the power of the electric heater Q_heater=0~50W adjustable; the lunar surface environmental temperature is -180°C, and the heat output of the equipment cabin Q_device=5W. The steady-state thermal balance formula: Q_total = (T_in - T_out)/R, where T_in is the cabin internal temperature, and T_out is the environmental temperature.", + "question": "Calculate the steady-state temperature of the equipment cabin when using only the isotope heat source; if T_in≥-40°C is required, how many additional watts of electric heating are needed to be turned on? ", + "answer": "When using only the isotope heat source, T_in=-70°C (Q_total=35W=(T_in+180)/4); an additional 25W of electric heating is required (total Q_total=60W=(-40+180)/4)." + }, + { + "id": 170, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing exploration tasks on the far side of the moon, currently located at coordinate point A(10,20), and needs to reach the scientific target point B(50,60). Terrain data indicates that there are two optional paths between the two points: Path 1 is a straight-line distance of 40 meters but requires crossing a 15° slope, Path 2 is a detour distance of 55 meters but the slope is only 5°. It is known that the motor efficiency model of the lunar rover is: climbing energy consumption=0.2*distance*slope(degree)+0.1*distance (unit: Wh), the energy consumption of driving on flat ground is always 0.1*distance. The remaining battery power is 8Wh, and at least 2Wh must be reserved for emergency power.", + "question": "Please calculate the total energy consumption of the two paths and determine whether it can safely reach the target point B under the current power? If not, how should the route be adjusted? ", + "answer": "Total energy consumption of Path 1=0.2*40*15+0.1*40=124Wh; total energy consumption of Path 2=0.2*55*5+0.1*55=66Wh. The available power of 6Wh is insufficient for both paths. A compromise route should be chosen, involving partial detour + partial climbing, ensuring total energy consumption ≤6Wh." + }, + { + "id": 171, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander, while working at the edge of the Shackleton crater, suddenly receives a solar proton event warning and needs to transfer to an emergency shelter 500 meters away within 30 minutes. The current navigation system shows: there is a 20-meter diameter impact crater 300 meters directly ahead that cannot be crossed directly. The left detour requires an additional 200 meters but has a flat road surface, while the right detour requires only an additional 100 meters but has a 10° slope. The lunar rover's maximum speed is 0.1m/s on flat ground and 0.05m/s when climbing, and the time for turning is negligible.", + "question": "Please calculate the arrival time for the three alternative routes (including the impact of detours and climbing speed reduction), and determine the optimal risk avoidance plan that meets the time constraint.", + "answer": "Straight path time=(300/0.05)+(200/0.1)=6000s>30min; Left detour time=(300+200)/0.1=5000s≈8.3min; Right detour time=(300+100)/0.05=8000s≈13.3min. Only the left detour plan meets the ≤30min requirement." + }, + { + "id": 172, + "scenario_code": "2.9", + "instruction": " The Lunar Orbit Navigation Satellite System (LBNSS-1) establishes a two-way ranging link with Yutu-3, measuring a pseudorange observation value of 384,403km (including clock bias). It is known that: the satellite orbit height is 100km (lunar radius 1737km), the rover elevation is -2300m, the satellite clock drift correction is +25m, and the ionospheric delay correction is -15m. The signal propagation speed is equal to the speed of light c=299792458m/s.", + "question": "Please calculate the true geometric distance from the satellite to the lunar rover (accurate to meters), and verify whether the current pseudorange observation value is within the expected error range (|residual|<50m).", + "answer": "Geometric distance=sqrt((1737+100)^2-(1737-2.3)^2)*1000≈1846km; Theoretical pseudorange after correction=1846000+25-15=1846010m; Residual=384403000-1846010=382556990m (obviously incorrect, the original problem unit should be meters). After correcting the problem description: If the pseudorange observation value is 1844403m, then the residual=1844403-1846010=-1607m, far exceeding the 50m threshold." + }, + { + "id": 173, + "scenario_code": "1.5", + "instruction": " The mechanical arm of the Chang'e-7 lander needs to load lunar soil samples into the analysis cabin with a communication delay of 1.3 seconds. The end-effector positioning accuracy requirement is ±2mm, and its motion control uses a predictive algorithm: actual position = commanded position + speed * delay time * correction factor k (k=0.8). The current commanded movement speed is 5mm/s, and the target position is 23mm away from the current pose.", + "question": "Calculate the commanded position coordinates to be sent to the mechanical arm to ensure the sample accurately reaches the target point.", + "answer": "Commanded position = target position - (speed * delay time * k) = 23 - (5 * 1.3 * 0.8) = 23 - 5.2 = 17.8mm" + }, + { + "id": 174, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the soil in this area are as follows: the surface layer 0-30cm is loose fine particles (viscosity index 0.3, Mohs hardness 2.5), and there is a consolidated layer at 30-50cm (viscosity index 1.2, Mohs hardness 4.0). The engineering team is equipped with three sampling tools: Type A rotary drill (suitable for hardness ≤3, maximum torque 5Nm), Type B impact drill (suitable for hardness ≤5, impact frequency 10Hz), and Type C helical core drill (suitable for viscosity ≤1.0, core diameter 20mm). The power supply limit for the sampling system is 60W, and the sampling time window is 8 minutes.", + "question": "If a complete sample core at a depth of 40cm is required, please select the most suitable sampling tool and calculate its theoretical maximum sampling length (known: Type B drill consumes 15J per cm, Type C drill consumes 8J per cm + viscosity index * 5J).", + "answer": "Select Type B impact drill. Theoretical maximum sampling length calculation: 60W*480s=28800J; 28800J/15J/cm=192cm>50cm, actually can complete 50cm sampling." + }, + { + "id": 175, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration on the north side of the Von Kármán crater. Hyperspectral data has identified three candidate sites: P1 (KREEP rock probability 72%, distance 800m), P2 (volcanic glass probability 85%, distance 1200m), P3 (breccia probability 65%, distance 500m). The rover's movement speed is 0.05m/s, and the standard time for scientific exploration is: 30 minutes per point for compositional analysis, 15 minutes per point for topographic mapping. The current remaining power supports 6 hours of operation, and the communication window requires returning to the relay position (300m from the nearest sampling point) within the remaining 4 hours.", + "question": "Please plan the optimal exploration path and explain the exploration content that can be completed (the formula for movement energy consumption: E=0.8*d+5, where d is the movement distance in meters; topographic mapping is a mandatory project).", + "answer": "Path: P3→P1. Completed content: Topographic mapping and compositional analysis of P3/P1. Calculation: Total movement distance (500+300+800)=1600m, time required 1600/0.05=32000s≈8.9h exceeds limit; only P3+P1 movement distance 1300m takes 7.2h+1.5h exploration=8.7h still exceeds limit; ultimately choosing a single point P3 can meet: 500m movement (2.8h)+45min exploration=3.6h<4h." + }, + { + "id": 176, + "scenario_code": "3.1", + "instruction": " The Chang'e-5 lander is executing a sampling mission in the region at 43.06 degrees north latitude and 51.92 degrees east longitude on the lunar near side. During the lunar day, the solar elevation angle in this area varies from 5° to 35°, and the solar panels use two-dimensional tracking (azimuth + pitch angle). It is known that: 1) each solar panel has an area of 2 square meters, with a photovoltaic conversion efficiency of 28%; 2) the lunar surface albedo is 0.12; 3) the solar constant is 1368 W/m^2; 4) terrain obstruction reduces the effective power generation time by 15% each day.", + "question": "Calculate the theoretical total power generation per day when the average solar elevation angle during the lunar day is 20° (ignoring equipment loss)? Include contributions from direct and reflected light. Hint: The effective receiving area for reflected light is calculated based on the horizontal projection area of the solar panel.", + "answer": "Direct light power = 1368 * sin(20°) * 2 * 0.28 = 261.4W; Reflected light power = 1368 * 0.12 * cos(20°) * 2 * 0.28 = 86.3W; Total power = 261.4 + 86.3 = 347.7W; Daily power generation = 347.7 * 24 * 0.85 = 7.09kWh" + }, + { + "id": 177, + "scenario_code": "3.8", + "instruction": " A certain lunar base has a mission cycle of 1 lunar day (14 Earth days) + 1 lunar night. The energy budget is as follows: 1) the average daily power generation during the lunar day is 18kWh, and the load demand is 12kWh/day; 2) the load demand during the lunar night is 4kWh/day (for critical equipment only); 3) the lithium-ion battery pack has a capacity of 50kWh, with a charge/discharge efficiency of 92%, and an initial SOC of 60%. Energy consumption for temperature management accounts for 35% of the total load during the lunar night.", + "question": "Determine if this energy budget is feasible? If not, calculate how much additional daily power generation is required during the lunar day to meet the demand.", + "answer": "Current daily charging during the lunar day = (18 - 12) * 14 * 0.92 = 77.28kWh; Initial energy storage = 50 * 0.6 = 30kWh; Total available power = 30 + 77.28 = 107.28kWh; Lunar night demand = 4 * 14 / 0.92 = 60.87kWh; Feasible. No additional power generation required" + }, + { + "id": 178, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the Von Kármán crater within the South Pole-Aitken Basin (SPA) on the far side of the Moon (coordinates 177.6°E, 45.5°S). At this time, the ground station is located at the Kashgar Deep Space Station in China (76°E, 39.5°N), and the Queqiao-2 relay satellite is operating in a lunar elliptical frozen orbit (perilune 200km, apolune 8600km, orbital period 8 hours). Given: 1) The average Earth-Moon distance is 384,400km; 2) The Moon's rotation period is synchronized with its orbital period; 3) Direct communication requires an elevation angle ≥5° and unobstructed line of sight between Earth and Moon; 4) Relay communication requires that the elevation angles between the lander-relay satellite and relay satellite-ground station be ≥7°. The current time in UTC+8 is 14:00, and Queqiao-2 has just passed its perilune.", + "question": "Calculate the total link delay for the ground station to establish relay communication with the lander via Queqiao-2 at this moment (consider only the propagation delay at the speed of light, c=299,792km/s), and determine whether the elevation angle condition for direct communication can be met at this time.", + "answer": "Total delay = (distance from lander to relay satellite + distance from relay satellite to ground station) / speed of light ≈ (200 + 384,400) / 299,792 ≈ 1.28 seconds. Since the far side of the Moon always faces away from Earth, the direct communication elevation angle is always negative and cannot meet the ≥5° condition." + }, + { + "id": 179, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover continuously transmits exploration data to the Queqiao relay satellite during the lunar day. A sudden solar proton event causes the X-band link signal-to-noise ratio (SNR) to drop by 10dB. Current parameters: 1) Transmission power 20W; 2) Antenna gain 38dBi; 3) Using (255,223)RS encoding, the original bit error rate (BER) requirement is ≤1e-6; 4) SSD cache remaining capacity 50GB, data generation rate 200MB/hour. The system needs to decide within 10 minutes whether to switch to a lower-order modulation scheme (QPSK→BPSK) or activate a compression algorithm (lossy compression ratio 4:1).", + "question": "If the decision is made to maintain the current encoding but switch to BPSK modulation, calculate the minimum required increment in received power (dB) to ensure the BER requirement is met, and evaluate whether the SSD capacity is sufficient to support 2 hours of emergency transmission.", + "answer": "BPSK has a 3dB higher noise resistance than QPSK, so the received power only needs to increase by 10-3=7dB to meet the original BER requirement. Total data volume = 200MB/h * 2h = 400MB < 50GB, the SSD capacity is sufficient." + }, + { + "id": 180, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is conducting patrol exploration on the far side of the moon, currently located at point A (177.6°E, 45.5°S), and needs to reach scientific target point B (177.8°E, 45.3°S). It is known that: 1) the straight-line distance between the two points is 1.2km; 2) the slope of the lunar surface is less than 15°; 3) the average moving speed of the lunar rover is 0.05m/s; 4) the energy consumption model is E = 0.12 * d + 2.5 (d is the actual driving distance, in km, E is the energy consumption, in Wh); 5) the remaining power is 50Wh.", + "question": "If the shortest straight-line path is chosen, calculate whether the required time and remaining power are sufficient to complete the task.", + "answer": "Driving time = 1200m / 0.05m/s = 24000s ≈ 6.67 hours; energy consumption E = 0.12 * 1.2 + 2.5 = 2.644Wh; remaining power = 50 - 2.644 = 47.356Wh > 0, which meets the requirement." + }, + { + "id": 181, + "scenario_code": "2.7", + "instruction": " The Chang'e-4 lander has detected an impending solar proton event (SPE), expected to last 8 hours. Yutu-2 is currently in a communication blind spot and needs to reach the nearest relay coverage point C (800m away) within 30 minutes. Lunar rover parameters: 1) maximum safe speed is 0.1m/s; 2) obstacle avoidance maneuvers require a 20% time margin; 3) power consumption increases to 150% of normal under extreme conditions (base power consumption 3W).", + "question": "Determine whether the lunar rover can complete the risk avoidance before the SPE arrives. If not, what emergency measures should be taken.", + "answer": "The shortest required time = (800m / 0.1m/s) * 1.2 = 9600s = 160 minutes > 30 minutes. It is recommended to immediately switch to the minimum power safe mode (≤1W), turn off non-essential payloads, and wait for the event to end on site." + }, + { + "id": 182, + "scenario_code": "2.10", + "instruction": " The lunar rover needs to perform centimeter-level precise positioning of a lava tube entrance (diameter 3m). Configuration: 1) Stereoscopic vision navigation camera accuracy ±5cm@10m; 2) UWB beacon deployed at the center of the entrance, ranging error ±2cm; 3) IMU attitude angle error accumulation rate 0.1°/min. The task requires the final positioning error to be ≤10cm.", + "question": "When the lunar rover is 8m away from the target, can it meet the accuracy requirement by relying solely on visual navigation? If not, how should sensor data be combined to achieve the required accuracy? ", + "answer": "Visual error = (8m/10m)*5cm = ±4cm; UWB error ±2cm; combined positioning total error = sqrt(4^2 + 2^2) ≈4.47cm <10cm. It is necessary to use the fusion of visual + UWB data simultaneously." + }, + { + "id": 183, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander, while working at the edge of the Shackleton crater, suddenly receives a solar proton event warning: high-energy particle flow is expected to reach the moon in 30 minutes and last for 4 hours. The current communication window has 25 minutes remaining, and an immediate risk avoidance plan must be formulated. The lander has the following capabilities:\n- Maximum climbing speed 5°/s\n- Power system can support full-power operation for 6 hours or hibernation mode for 48 hours\n- The nearest permanent shadow area shelter is 200 meters to the northwest (slope 12°)\n- Deploying a radiation shield on-site requires 15 minutes and consumes 200Wh", + "question": "If choosing to move to the shelter, calculate the minimum required time and energy consumption (known moving power consumption P=50W+10*θ), and determine whether it is better than the on-site protection plan.", + "answer": "Moving time=200/(5°/s*cos12°)=41 seconds≈0.68 minutes; Moving energy consumption=(50+10*12)*0.68/60=1.36Wh. Total time 25<30 is feasible, better than the on-site plan (consumes 200Wh and cannot communicate)." + }, + { + "id": 184, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover experienced an X-band communication interruption during the lunar day, caused by solar flares leading to ionospheric disturbances. The rover is equipped with an S-band backup link (2 MHz bandwidth) and a UHF relay module (500 kHz bandwidth). The data generation rates are: panoramic camera 1.2 Mbps, particle-induced X-ray spectrometer 0.4 Mbps, and infrared imaging spectrometer 0.8 Mbps. The remaining power supports continuous operation for 4 hours.", + "question": "To ensure the transmission of critical scientific data, select the optimal backup link and calculate its theoretical maximum data transfer volume (in MB), ensuring all instrument data is fully transmitted without exceeding the power budget.", + "answer": "S-band,3456" + }, + { + "id": 185, + "scenario_code": "5.7", + "instruction": " The Chang'e-7 orbiter is equipped with a 1 TB NAND Flash storage device, managed with wear-leveling algorithms for write operations. The block life of the storage device is 10^5 erase/write cycles, with an average daily write volume of: 20 engineering data packets (each 128 MB) and 8 scientific data packets (each 512 MB). The file system reserves 15% of the space for bad block replacement.", + "question": "Calculate the theoretical minimum lifespan of the storage device (in years) under the condition of no bad block growth, rounding the result to two decimal places.", + "answer": "3.65" + }, + { + "id": 186, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. The characteristics of the soil in this area are as follows: medium hardness (Mohs hardness 4-5), low viscosity, and high volatile content (about 1200 ppm). There are three sampling tools available: A-type rotary impact drill (suitable for rocks with hardness >6), B-type vibratory grab (suitable for loose, sticky materials), and C-type scraper (general-purpose, suitable for medium-hardness, low-viscosity materials). The energy consumption for each tool's operation is: A-type 25W·h per use, B-type 18W·h per use, C-type 15W·h per use. The remaining energy of the probe only supports a total sampling energy consumption of no more than 80W·h.", + "question": "Based on the characteristics of the lunar soil and the energy consumption constraints, which combination of sampling tools should be chosen to maximize the number of sampling attempts while ensuring the success rate of sampling? Calculate the maximum feasible number of sampling attempts.", + "answer": "Choose the C-type scraper (suitable for medium-hardness, low-viscosity characteristics), maximum number of sampling attempts = 80/15 ≈ 5 times (take the integer part)." + }, + { + "id": 187, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. Known: 1) The container seal pressure should be maintained at 1.2±0.1bar; 2) The success rate of RFID tag reading is related to distance as follows: success probability = 1-0.2*d (d in meters); 3) The maximum extension distance of the robotic arm during handover is 1.5 meters; 4) The current telemetry shows a seal pressure of 1.25bar, temperature -60℃ (within the allowable range). The handover process requires that the following conditions be met simultaneously: qualified pressure + RFID read success probability ≥90%.", + "question": "Determine whether the current conditions meet the handover requirements? If not, suggest adjustments.", + "answer": "The current pressure is qualified (1.25bar within the range), but the RFID read probability = 1-0.2*1.5=70%<90%. The distance needs to be shortened to ≤0.5 meters (at this point, the probability ≥90%)" + }, + { + "id": 188, + "scenario_code": "5.1", + "instruction": " The Chang'e-6 lander is located in the South Pole-Aitken Basin on the far side of the Moon (longitude 180°E, latitude 45°S), and plans to communicate with the ground station via the Queqiao-2 relay satellite. It is known that Queqiao-2 operates in a halo orbit around the Earth-Moon L2 point, at a height of about 80,000 kilometers above the lunar surface. At the current moment, the elevation angle of the ground station (110°E) to Queqiao-2 is 25°, and the elevation angle of the lunar lander antenna needs to be ≥10° to establish a stable link. The lunar rotation period is 27.3 days, and the Earth's rotation period is 24 hours.", + "question": "If the ground station can directly see Queqiao-2 at the current moment, calculate the maximum allowable communication duration (in hours) between the lander and Queqiao-2 at this time, considering the line-of-sight obstruction caused by the lunar rotation.", + "answer": "6.83" + }, + { + "id": 189, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, a temporary energy sharing network needs to be established. There are currently 3 devices: A (seismometer, peak power demand 80W), B (spectrometer, peak power demand 120W), C (heat flow probe, peak power demand 60W). The shared energy module has a maximum output power of 200W and uses a dynamic priority allocation strategy: scientific data priority B>A>C, with each device having a basic survival power consumption of 20W. During the lunar day, the solar power supplement is 150W.", + "question": "When all three devices simultaneously enter high load working mode and the solar power supplement is interrupted due to a lunar eclipse, how should the 200W total power be allocated according to the preset priority? List the actual power received by each device.", + "answer": "B receives 120W (full demand), A receives 60W (80W demand restricted), C receives 20W (only basic survival power). Allocation logic: First, meet the highest priority B's 120W, then from the remaining 80W, prioritize A's 80W but it is insufficient so allocate 60W, finally C only maintains the basic survival 20W." + }, + { + "id": 190, + "scenario_code": "1.8", + "instruction": " When deploying a lunar surface magnetometer array, it is necessary to avoid areas with local magnetic field anomalies. The reference point magnetic field strength is 150nT, with an allowable deviation of ±5nT. The current measurement point data is [162, 155, 158, 147]nT (four samples), the lunar soil bearing pressure threshold is 300Pa, and the equipment's own weight generates a pressure of 280Pa. The deployment specifications require that both magnetic field stability and bearing safety conditions be met simultaneously.", + "question": "Determine whether the measurement point is suitable for deployment and explain the basis (quantitative analysis of both conditions)？", + "answer": "Not suitable for deployment. Basis: 1) The average magnetic field value is 155.5nT, exceeding the allowable range (150±5nT); 2) Although 280Pa<300Pa meets the bearing condition, the magnetic field stability does not meet the standard." + }, + { + "id": 191, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the moon, unable to communicate directly with Earth. The 'Queqiao' relay satellite is deployed in the Earth-Moon L2 Halo orbit, about 65,000 kilometers from the moon. The X-band antenna gain of the relay satellite is 42 dBi, the transmission power of the lander is 10 W, the antenna gain is 6 dBi, and the operating frequency is 8.4 GHz. The free space path loss formula is: L = 20 * log10(d) + 20 * log10(f) + 92.45, where d is the distance (km), and f is the frequency (GHz).", + "question": "Calculate the free space loss (dB) of the uplink from the lander to the 'Queqiao' relay satellite, and determine whether the link meets the minimum receiving power requirement of -110 dBm (ignoring other loss factors).", + "answer": "The free space loss L = 20 * log10(65000) + 20 * log10(8.4) + 92.45 ≈ 20 * 4.8129 + 20 * 0.9243 + 92.45 ≈ 96.258 + 18.486 + 92.45 = 207.194 dB. The receiving power P_r = P_t + G_t + G_r - L = 10 * log10(10*1000) + 6 + 42 - 207.194 ≈ 40 + 6 + 42 - 207.194 = -119.194 dBm < -110 dBm, does not meet the requirement." + }, + { + "id": 192, + "scenario_code": "5.4", + "instruction": " The lunar rover needs to continuously transmit scientific data to the orbiter during the lunar day, with an average data rate of 2 Mbps. When encountering a lunar eclipse, solar power is interrupted and the temperature drops sharply, and it can only rely on the battery to maintain 1 hour of communication (capacity 500 Wh, efficiency 85%). The communication system power consumption model is: RF power consumption = 5 W + 0.1 * (data rate/Mbps) W, baseband processing power consumption is constantly 3 W.", + "question": "Calculate the highest continuous data transmission rate (Mbps) that the lunar rover can maintain during a lunar eclipse, ensuring it does not exceed the energy budget.", + "answer": "Available energy E = 500 Wh * 0.85 = 425 Wh = 1530 kJ. Let the highest rate be R Mbps, total power consumption P = (5 + 0.1*R) + 3 = (8 + 0.1*R) W. Operation time t = E / P <= 3600 seconds → (8+0.1*R)*3600 <= 1530000 → R <= (1530000/3600 - 8)/0.1 ≈ (425-8)/0.1 = 417/0.1 = 4.17 Mbps" + }, + { + "id": 193, + "scenario_code": "5.7", + "instruction": " The lunar orbiter uses a 128 GB SSD to store scientific data, employing a wear-leveling algorithm to extend its lifespan. The SSD has a P/E cycle of 3000, with a daily write volume of 50 GB (evenly distributed). The file system reserves 15% of the space for bad block replacement and wear-leveling operations.", + "question": "Calculate the theoretical maximum lifespan (years) of the SSD, assuming a write amplification factor of 1.2 and no other loss factors.", + "answer": "Available capacity C = 128 * 0.85 = 108.8 GB; actual daily write volume W = 50 * 1.2 = 60 GB; daily P/E consumption = 60 / 108.8 ≈ 0.5515 times; theoretical lifespan T = 3000 / (0.5515 * 365) ≈ 3000 / 201 ≈ 14.9 years" + }, + { + "id": 194, + "scenario_code": "4.9", + "instruction": " Lunar sample return capsule design parameters: sealed chamber volume 500cm³, maximum allowable internal pressure 110kPa. During the lunar day (temperature 120℃), when encapsulating samples containing volatiles, the measured gas volume before sealing is 150cm³, pressure 95kPa, and temperature 20℃. It is known that the solid part of the sample has a volume of 80cm³, and the vapor pressure curve of the volatiles satisfies the equation P=10^(5-2000/T)kPa (T is absolute temperature).", + "question": "Verify whether the encapsulation plan will cause overpressure leakage under extreme lunar day temperatures (Hint: Calculate the expected pressure after heating to 120℃).", + "answer": "It will leak. Final pressure calculation: initial gas n=95kPa*150cm³/(293K*R); after heating P=n*R*393K/(500cm³-80cm³)+10^(5-2000/393)=137kPa>110kPa" + }, + { + "id": 195, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, it is necessary to simultaneously power the lunar drilling vehicle, the astronomical observation unit, and the life support system. The current total output power of the energy grid is 1200W, and the basic power consumption of each system is as follows: the drilling vehicle standby 200W (peak 800W during operation), the astronomical unit constant consumption 300W, and the life support system minimum requirement 400W (adjustable to 600W). The power distribution adopts a dynamic priority strategy: life support > drilling vehicle operation > astronomical observation. Now the drilling vehicle is about to start a 15-minute core sampling operation, and the astronomical unit is currently transmitting key data (uninterruptible).", + "question": "If it is necessary to ensure the normal operation of all systems, what is the maximum power that the life support system can currently be adjusted to? Provide the calculation process.", + "answer": "Maximum adjustable power = total power - (drilling vehicle peak + astronomical unit constant consumption) = 1200 - (800 + 300) = 100W. Therefore, the life support system can be increased from the base 400W to 500W (400+100), but it cannot reach the upper limit of 600W." + }, + { + "id": 196, + "scenario_code": "4.1", + "instruction": " In the Chang'e-5 mission, the probe discovered two target sampling materials in the landing area of the northern part of the Oceanus Procellarum on the moon's near side: Class A is loose lunar soil (particle diameter 0.1-1mm, cohesion <1kPa), and Class B is basalt fragments (Mohs hardness 6, irregularly angular). There are three sampling tools available: ① Rotary Percussion Drill (suitable for rocks with hardness >5, power consumption 120W); ② Electric Scoop (suitable for loose granular materials, power consumption 60W); ③ Ultrasonic Vibratory Core Sampler (suitable for fragile bonded materials, power consumption 80W). The probe has 800Wh of remaining energy and needs to complete sampling within 8 hours.", + "question": "If 3 samples of Class A and 2 samples of Class B are required, and each sampling operation takes 30 minutes (including positioning and preparation time), please calculate the optimal tool combination and remaining energy.", + "answer": "Optimal combination: Use the electric scoop for Class A (60W*1.5h=90Wh), and the rotary percussion drill for Class B (120W*1h=120Wh). Total energy consumption = 90*3 + 120*2 = 510Wh, remaining energy = 800 - 510 = 290Wh" + }, + { + "id": 197, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover detected three candidate sampling sites on the south side of the Von Kármán crater: ① KREEP rock outcrop at coordinates (12.34°N, 125.67°E) (Th content 28ppm, 320 meters from the current location); ② Breccia accumulation at coordinates (12.31°N, 125.72°E) (spectral analysis shows olivine characteristic peaks, 410 meters away); ③ Suspected volcanic glass area at coordinates (12.29°N, 125.65°E) (thermal anomaly value +3K, 180 meters away). The rover's movement speed is 5cm/s, and it can operate 6 hours per day. Scientific priority weight: uniqueness of composition 40%, distance 30%, geological background 30%.", + "question": "Determine the visiting order of the sampling sites according to the weighted scoring method (scoring formula: total score = composition score * 0.4 + distance score * 0.3 + geological score * 0.3, each dimension is scored on a 1-10 scale).", + "answer": "Visiting order: ③→①→②. Score calculation: ③ scores (8*0.4+10*0.3+7*0.3)=8.3; ① scores (9*0.4+7*0.3+8*0.3)=8.1; ② scores (7*0.4+6*0.3+6*0.3)=6.4" + }, + { + "id": 198, + "scenario_code": "1.5", + "instruction": " The ground control center controls the lunar surface mobile platform to sample at the edge of a crater through remote operation, with a one-way communication delay between Earth and Moon of 1.3 seconds. The platform motion control uses a predictive compensation algorithm: v_cmd = v_real + K * (d_remaining - v_real * t_delay), where K=0.8 is the compensation coefficient, and t_delay is the delay time. The current actual speed of the platform v_real=0.2m/s, and the remaining distance to the target point d_remaining=5m.", + "question": "Calculate the command speed v_cmd that should be sent at this time to ensure the platform accurately docks at the target point.", + "answer": "v_cmd = 0.2 + 0.8 * (5 - 0.2 * 1.3) = 0.2 + 0.8 * (5 - 0.26) = 0.2 + 3.792 = 3.992m/s" + }, + { + "id": 199, + "scenario_code": "1.8", + "instruction": " When deploying the seismometer array, it was found that the bearing capacity of the lunar soil at the designated location is only 1.5kPa, lower than the required 2kPa for the equipment. The engineering team decided to switch to a triangular distribution of three-point support (the original design was a four-point rectangular support), and the area of each support foot was expanded to 0.15m². The total mass of the equipment is 180kg, and the lunar gravitational acceleration is 1.62m/s².", + "question": "Verify whether the new support scheme meets the bearing capacity requirement (the pressure on each foot needs to be calculated).", + "answer": "The force on each foot F = (180 * 1.62) / 3 = 97.2N; the pressure P = F / A = 97.2 / 0.15 = 648Pa = 0.648kPa <1.5kPa, meeting the requirement." + }, + { + "id": 200, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the Moon, located at coordinate point A (10,20), and needs to reach scientific target point B (50,60). Terrain data indicates that there are two optional paths between the two points: Path 1 is a straight-line distance of 70 meters but requires crossing a 15° slope, while Path 2 is a zigzag distance of 85 meters but all slopes are less than 5°. It is known that the rover consumes E_flat = 0.1Wh/m on flat terrain, and the energy consumption increase factor on slopes is k = 0.02Wh/m/degree (i.e., for every 1 degree increase in slope, the energy consumption per unit distance increases by 0.02Wh). The remaining battery power is 8Wh, and at least 2Wh must be reserved for emergency power.", + "question": "Calculate the total energy consumption for both paths and determine whether Yutu-2 can choose the more time-saving Path 1 without triggering a low battery warning.", + "answer": "Total energy consumption for Path 1 = 70 * (0.1 + 0.02 * 15) = 70 * 0.4 = 28Wh; Total energy consumption for Path 2 = 85 * 0.1 = 8.5Wh. Available power 8 - 2 = 6Wh < 28Wh, so Path 1 cannot be chosen." + }, + { + "id": 201, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander encountered a solar proton event warning while exploring the rim of the Shackleton crater and needs to transfer to an emergency shelter 500 meters away within 30 minutes. The current navigation system uses a combination of visual odometry (error ±3%/hour) and IMU (drift error 0.5°/√h), and communication disruption prevents receiving relay correction signals from the orbiter. The azimuth of the shelter is 45° east of true north, and the terrain contains three known obstacles: a 20-meter diameter impact crater 200 meters due east, a 25° slope lunar ridge 300 meters northeast, and a permanently shadowed area 150 meters due north.", + "question": "Design an optimal emergency evacuation path that meets the time constraint and avoids all obstacles (provide the sequence of movement directions), and estimate the maximum position error of this plan.", + "answer": "Movement sequence: First move 150 meters due north to bypass the impact crater, then turn northeast for 350 meters to reach the target. Maximum error = 500 * (3% * 0.5) + 0.5° * √0.5 * 500 ≈ 7.5 + 17.7 ≈ 25.2 meters." + }, + { + "id": 202, + "scenario_code": "2.10", + "instruction": " To accurately detect the olivine outcrops near the Artemis landing site (coordinates (12.345,34.567)), the lunar rover needs to achieve centimeter-level parking control. Given that the visual navigation camera has a resolution of 0.1mrad/pixel, the inertial measurement unit (IMU) has a zero bias stability of 50μg/√Hz, and the ultra-wideband (UWB) beacon is deployed at (12.300,34.600) with a ranging accuracy of ±3cm. The current pose estimate: position (12.338,34.555)±0.15m, heading angle 182°±1°. The target parking requirements: lateral error <5cm, heading error <0.5°.", + "question": "Calculate the deviation between the current pose and the target, and explain which sensor should be prioritized for closed-loop control during the final approach phase.", + "answer": "Position deviation: ΔX=12.345-12.338=+7cm, ΔY=34.567-34.555=+12cm; heading deviation=182-180=+2°. Since the UWB ranging accuracy is the highest (±3cm), the UWB beacon should be prioritized for closed-loop control." + }, + { + "id": 203, + "scenario_code": "4.5", + "instruction": " Execute a 2.5-meter deep drilling task in the Oceanus Procellarum region on the near side of the Moon. Known: the drilling speed for the loose regolith layer (0-1m) is 0.5m/h, and for the dense layer (1-2.5m) is 0.3m/h; the standby power consumption of the drill is 50W, and the working power consumption is 300W; the current solar panel can provide a continuous 200W power, and the battery has a remaining energy of 500Wh. The task requires that at least 100Wh of power must be reserved for emergencies after the drilling is completed.", + "question": "Calculate the minimum time required to complete this deep drilling task and whether the power is sufficient? Provide the calculation process.", + "answer": "Calculation steps: 1) Time for loose layer = 1m / 0.5m/h = 2h; Time for dense layer = 1.5m / 0.3m/h = 5h; Total time = 7h. 2) Power consumption during work = (300W * 7h) + (50W * 7h) = 2450Wh; 3) Total available energy = 500Wh + 200W * 7h = 1900Wh; 4) Required 2450Wh > (1900Wh - 100Wh), power is insufficient. At least 650Wh of additional energy is needed or the drilling speed should be optimized." + }, + { + "id": 204, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the moon, located at coordinate point A (10°N, 120°E), and needs to reach scientific target point B (12°N, 122°E). It is known that: 1) the lunar surface slope is less than 15° everywhere, and the wheel-soil mechanics model shows an energy consumption coefficient of 0.12 Wh/m; 2) the straight-line distance AB is 3.2 km, but it must detour around a crater with a diameter of 200 meters; 3) the detour path adds 400 meters; 4) the current remaining battery energy is 500 Wh, and the base power consumption of the driving motor is 20 W.", + "question": "If the path detouring around the crater is chosen, calculate the remaining power of Yutu-2 after reaching point B (not considering power consumption of other equipment)?", + "answer": "Total driving distance = 3.2 km + 0.4 km = 3.6 km = 3600 m; Movement energy consumption = 3600 m * 0.12 Wh/m = 432 Wh; Driving time = 3600 m / (0.05 m/s * 3600 s/h) ≈ 20 h (assuming a speed of 0.05 m/s); Base power consumption = 20 W * 20 h = 400 Wh; Total energy consumption = 432 Wh + 400 Wh = 832 Wh; Remaining power = 500 Wh - 832 Wh = -332 Wh (the answer indicates that the power is insufficient to complete the task)." + }, + { + "id": 205, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover needs to transmit at least 500MB of scientific data daily through a relay satellite during the lunar day. On a certain day, a solar flare caused the X-band link to be interrupted for 3 hours, and the remaining storage capacity of the rover is only 600MB. The current link recovery rate is 2Mbps, and there are 8 hours left until the next lunar night. The data compression module can reduce the original data volume by 30% in lossless mode, but by 60% in lossy mode (allowing 5% information loss).", + "question": "To ensure the integrity of key data transmission, which compression mode should be chosen? Calculate whether all data can be transmitted within the remaining time.", + "answer": "Choose the lossless mode: 1) The original data to be transmitted is 500MB, compressed to 350MB; 2) Transmission time required = 350*8/(2*3600) ≈ 0.39 hours < remaining 8 hours; 3) Storage usage 350MB < 600MB. Although the lossy mode is faster, it will lose key data. Therefore, choosing the lossless mode ensures that the transmission can be completed within the remaining time without overflowing the storage." + }, + { + "id": 206, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth. The 'Queqiao' relay satellite is deployed in a Halo orbit at the Earth-Moon L2 point, providing relay communication services. Given:\n1. The maximum communication distance between Queqiao and the Earth station is 440,000 kilometers;\n2. The maximum communication distance between Queqiao and the lunar surface equipment is 75,000 kilometers;\n3. The lunar radius is approximately 1,737 kilometers;\n4. The average Earth-Moon distance is 380,000 kilometers.\nAt this moment, the geometric relationship among Queqiao, Earth, and the Moon is: the angle between the Earth-Queqiao line and the Moon-Queqiao line is 120 degrees.", + "question": "Please calculate whether Queqiao can maintain duplex communication with both the Earth station and the lunar surface equipment at this time. Provide the basis for your judgment.", + "answer": "Yes. Basis: 1) Earth-Queqiao distance = sqrt(38^2 + 44^2 - 2*38*44*cos120°) = 710,600 kilometers > 440,000 kilometers (not met); but in reality, Queqiao is located at the L2 point, and the Earth-Queqiao distance is constant ≈ 440,000 kilometers; 2) Moon-Queqiao distance = sqrt(1737^2 + (38+7.5)^2 - 2*1737*(38+7.5)*cos120°) ≈ 73,000 kilometers < 75,000 kilometers (met). Therefore, duplex communication can be maintained." + }, + { + "id": 207, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover is performing scientific exploration tasks when communication with the Queqiao relay satellite suddenly breaks down. Given:\n1. The cause of the interruption may be a solar flare causing adverse space weather;\n2. The rover is designed with fault tolerance: the storage chip can buffer 8 hours of high-definition image data (50 Mbps rate) or 24 hours of engineering telemetry data (2 Mbps rate);\n3. The current storage usage is 35%, and data is being recorded in a mixed mode (image:telemetry = 3:1 data ratio).", + "question": "If data is recorded at the current generation rate, how long can the rover's storage space support normal operation? List the calculation process.", + "answer": "Remaining storage capacity = 65% * 8 hours * 50 Mbps = 65% * 8 * 3600 * 50 = 936,000 Mb; current mixed mode rate = (3/4) * 50 + (1/4) * 2 = 38 Mbps; sustainable time = 936,000 / 38 ≈ 24,631 seconds ≈ 6 hours 50 minutes." + }, + { + "id": 208, + "scenario_code": "5.4", + "instruction": " Yutu-2 rover encountered an unexpected solar proton event during the lunar day, causing the X-band communication with Queqiao relay satellite to be interrupted. Known facts:\n1. The remaining power of the rover can support continuous operation for 48 hours;\n2. The UHF backup link is available but the rate is only 1/10 of the X-band;\n3. The current cache of untransmitted data includes: 2GB of high-priority scientific data (lossless compression required), 500MB of engineering telemetry data (10% lossy compression tolerable);\n4. The X-band is expected to be restored in 6 hours, and the maximum continuous available window for the UHF link is 4 hours.", + "question": "Design the optimal data transmission strategy to ensure the complete return of key data without exceeding the power consumption limit, and explain the basis for your choice.", + "answer": "Strategy: Prioritize the transmission of losslessly compressed high-priority data (compression rate 50% → 1GB required) via UHF, taking 1GB/(0.1*X rate); use the remaining window to transmit lossily compressed telemetry data (450MB). Basis: 1) High-priority data must be complete; 2) Total UHF transmission volume 1.45GB < 4 hours * 0.1X rate capacity; 3) Reserve redundancy time after X-band recovery." + }, + { + "id": 209, + "scenario_code": "5.7", + "instruction": " The SSD storage system of Chang'e-7 orbiter uses NAND Flash chips with the following characteristics:\n1. Total capacity 1TB, block size 256KB, page 16KB;\n2. Maximum number of write-erase cycles per block 10^5 times;\n3. The current wear-leveling algorithm evenly distributes write requests across all blocks;\n4. Average daily write volume 50GB, of which 80% is temporary engineering data (lifecycle < 24 hours), 20% is permanent scientific data.", + "question": "Calculate the theoretical lifespan (years) of the SSD under the current configuration, and propose a storage optimization method to extend its lifespan.", + "answer": "Theoretical lifespan calculation: Effective daily write volume = 50GB * 20% = 10GB → annual write volume 3650GB = 3.65TB/year; Number of write-erase cycles per TB = 3.65 * 1024^3MB / 256KB ≈ 15,300 times/year; Lifespan = 10^5 / 15,300 ≈ 6.5 years\nOptimization method: Differentiate storage pools, write temporary data to dedicated high-endurance blocks (e.g., SLC cache area)." + }, + { + "id": 210, + "scenario_code": "5.10", + "instruction": " The ground control station uses pseudo-code ranging technology to track the CE-5T1 spacecraft in lunar orbit. Known parameters:\n1. A pseudo-random code with a chip rate of 10MHz is used;\n2. The measured uplink pseudo-code transmission delay is 1.285 seconds; the downlink delay is 1.294 seconds;\n3. The onboard transponder processing delay is fixed at 5 microseconds;\n4. The speed of light c=299792458m/s.", + "question": "Please calculate the one-way spatial distance from the current CE-5T1 spacecraft to the ground station (system delay must be deducted), and explain the reason for choosing uplink or downlink data.", + "answer": "One-way transmission delay=(1.285+1.294-0.000005)/2≈1.2894975 seconds; distance=299792458*1.2894975≈386575km. The uplink data should be chosen for calculation, as the downlink may be affected by lunar obstruction (the orbit position is not clearly specified in the question, but the uplink is more reliable)." + }, + { + "id": 211, + "scenario_code": "5.1", + "instruction": " The Chang'e-6 probe, while performing a sampling mission on the far side of the Moon, needs to maintain communication with the ground station via the Queqiao-2 relay satellite. Known parameters:\n1. The relay satellite's orbit height is 100km (lunar radius 1737km), and the probe is located at 20°N, 160°E on the lunar surface;\n2. At the current moment, the relay satellite is positioned over the lunar equator at 0° longitude;\n3. The average Earth-Moon distance is 384,400km, the communication antenna's half-power angle is 60°, and the X-band free space loss formula is: loss(dB) = 20 * log10(distance) + 20 * log10(frequency) + 92.45 (frequency unit GHz)\n4. The probe's transmission power is 10W, the antenna gain is 36dBi, and the operating frequency is 8GHz.", + "question": "Calculate whether the uplink link budget from the probe to the relay satellite at the current moment meets the minimum receiving power requirement of -110dBm? The derivation process must be explained step by step.", + "answer": "1. Calculate the communication distance: lunar radius 1737km + relay height 100km = 1837km orbital radius, the angle between the probe and the relay satellite = arccos[cos(20°)*cos(160°)]≈116°, spherical distance=1837*π*116/180≈3723km\n2. Free space loss=20*log10(3723)+20*log10(8)+92.45≈196.9dB\n3. Received power=10*log10(1000*10)+36-196.9+36=-94.9dBm > -110dBm ∴ meets the requirement" + }, + { + "id": 212, + "scenario_code": "5.7", + "instruction": " The 128 GB solid-state memory carried by the relay satellite uses NAND flash, with each block capable of withstanding 100,000 write-erase cycles. The daily data write volume fluctuates between 12-18 GB (averaging 15 GB), and a dynamic wear-leveling algorithm evenly distributes write operations across all blocks. The memory is divided into 512 logical blocks, each 256 MB.", + "question": "Calculate the theoretical lifespan of this memory (in years) under the worst-case write volume.", + "answer": "In the worst-case scenario, the daily write volume is 18 GB, and the annual write volume is 18*365=6570 GB. The number of writes per block per year = 6570 GB / (512*256 MB) * 512 ≈ 25.66 times/year. Theoretical lifespan = 100,000 / 25.66 ≈ 3897 years" + }, + { + "id": 213, + "scenario_code": "3.6", + "instruction": " The lunar rover enters the lunar night phase, and its battery compartment needs to maintain a working temperature range of -20°C to +10°C. The heat loss coefficient of the compartment is 2W/°C, and the external temperature is -180°C. Available are: ① Electric heater (maximum 100W) ② Isotope heat source (constantly provides 30W) ③ Multilayer insulation material (can reduce heat loss by 40%). The current temperature of the battery compartment is +5°C.", + "question": "Calculate the equilibrium temperature of the battery compartment when using only passive insulation. If maintaining +5°C is required, how much power should the electric heater provide? ", + "answer": "Passive insulation heat loss = 2W/°C * (5°C - (-180°C)) * (1-40%) = 222W; at equilibrium, heat supply = heat loss ⇒ 30W = 222W ⇒ equilibrium temperature = -180°C + (30/(2*0.6)) = -155°C. To maintain +5°C, total heat supply required = 2*0.6*(5-(-180)) = 222W ⇒ electric heating power = 222-30 = 192W (exceeding the maximum 100W indicates it is not feasible)." + }, + { + "id": 214, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the moon, unable to communicate directly with Earth. The 'Queqiao' relay satellite is deployed in a Halo orbit at the Earth-Moon L2 point, with an average altitude of about 65,000 km above the lunar surface. The X-band antenna gain of the relay satellite is 42 dBi, the transmission power of the lander is 10 W, the antenna gain is 38 dBi, and the operating frequency is 8.4 GHz. The free space path loss formula is: L = 92.4 + 20*lg(d) + 20*lg(f), where d is the distance (km), and f is the frequency (GHz). The receiving system noise temperature is 300 K, and the required Eb/N0 is no less than 12 dB to achieve reliable communication.", + "question": "Calculate the maximum data transmission rate under the current configuration (assuming a modulation and coding efficiency of 1 bps/Hz, and the Boltzmann constant k=1.38e-23 J/K).", + "answer": "First, calculate the path loss: L = 92.4 + 20*lg(65000) + 20*lg(8.4) ≈ 220.3 dB. The received power Pr = Pt + Gt + Gr - L = 10*log10(10) + 38 + 42 - 220.3 ≈ -120.3 dBW. The noise power spectral density N0 = k*T = 1.38e-23*300 ≈ -203.8 dBW/Hz. Eb/N0 = Pr - N0 - 10*log10(R) ≥ 12 → R ≤ 10^((-120.3+203.8-12)/10) ≈ 500 bps" + }, + { + "id": 215, + "scenario_code": "1.4", + "instruction": " The lunar surface power grid needs to allocate peak power to 3 scientific devices: ① The spectrometer has a rated power of 200W and operates for 10 minutes per hour; ② The seismograph has a constant power consumption of 15W and triggers a 50W peak for 5 minutes every 2 hours; ③ The panoramic camera has two operating modes: regular shooting (30W for 20 minutes) and high-definition shooting (120W for 5 minutes), with no more than 3 high-definition shootings per day. The maximum output power of the power station is 300W, and the battery buffer capacity is 500Wh. The current time is 08:00 on the third day of the mission, and it is known that the camera has already performed 4 high-definition shootings in the first two days.", + "question": "If at 08:30 the spectrometer and the seismograph need to run in peak mode simultaneously, can the camera start a high-definition shooting without triggering the overload protection? Provide the basis for your judgment.", + "answer": "No, the total required power is 200W (spectrometer) + 50W (seismograph) + 120W (camera) = 370W > 300W" + }, + { + "id": 216, + "scenario_code": "2.10", + "instruction": " The probe needs to perform centimeter-level close-up observations on a special rock outcrop with a diameter of 0.5 meters. It is known that the focal length of the visual navigation camera f=100mm, pixel size p=5μm, and the rock image occupies 200 pixels at a distance of 10 meters. The control system requires the target to be within ±50 pixels of the image center to initiate the precise docking procedure.", + "question": "Calculate whether the current distance between the probe and the rock meets the docking conditions, and if not, adjust to how many meters it should be.", + "answer": "Current distance calculation: Object distance u = (f * actual width) / (number of pixels * p) = (100 * 500) / (200 * 5) = 50mm (calculation error, should be 500mm or 0.5 meters). Since the image occupies 200 pixels at 10 meters, the ratio coefficient k=10/200=0.05m/pixel. The docking requirement of ±50 pixels corresponds to ±2.5 meters. The current 10 meters exceeds the tolerance, it needs to be adjusted to within the 7.5-12.5 meter range." + }, + { + "id": 217, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently on a patrol mission on the far side of the moon, located at coordinate point A(10,20), and needs to reach the scientific target point B(50,60). Terrain data indicates that there are two optional paths between the two points: Path 1 is a straight-line distance of 70 meters but requires crossing a 15° slope, Path 2 is a zigzag distance of 85 meters but the slope is less than 5° throughout. It is known that the motor efficiency of the lunar rover is 90% at a 5° slope, and it drops to 60% at a 15° slope. The translational power consumption model is E = 0.12 * d * (1/slope_efficiency) (unit: Wh, d is the travel distance).", + "question": "Calculate the total energy consumption for both paths and determine the better path.", + "answer": "Energy consumption for Path 1: E1 = 0.12 * 70 * (1/0.6) = 14 Wh; Energy consumption for Path 2: E2 = 0.12 * 85 * (1/0.9) ≈ 11.33 Wh. The path with lower energy consumption, Path 2, should be chosen." + }, + { + "id": 218, + "scenario_code": "3.1", + "instruction": " The Chang'e-5 lander is performing a sampling mission in a certain area on the near side of the Moon, and its solar panels use a two-dimensional tracking algorithm. It is known that the current solar elevation angle in this area is 30 degrees, and the azimuth angle is 45 degrees (0 degrees is due east, increasing counterclockwise). The initial orientation of the solar panels is horizontal (normal pointing to the zenith). The lunar almanac shows that the solar elevation angle will linearly increase to 35 degrees and the azimuth angle will increase to 60 degrees within the next 2 hours. Assuming the ideal power generation of the solar panels P_max = 1000W * cos(θ), where θ is the angle between the sunlight and the normal of the panel surface. Ignore terrain obstruction.", + "question": "If the solar panels remain in their initial horizontal orientation, what will be the instantaneous power generation after 2 hours? If a two-dimensional tracking is used to keep the panel surface always facing the sun, what will the power generation be at that time? ", + "answer": "When in the initial horizontal orientation: θ = 90° - 35° = 55°, P = 1000 * cos(55°) ≈ 573.6W; When using two-dimensional tracking θ = 0°, P = 1000 * cos(0°) = 1000W" + }, + { + "id": 219, + "scenario_code": "1.5", + "instruction": " When controlling a lunar rover to perform rock sampling tasks, there is a fixed delay of 1.3 seconds in the movement commands sent by the ground control center. The current speed of the lunar rover is 0.2m/s, and there is an unexpected lunar crater (2 meters in diameter) 3 meters ahead. The emergency braking acceleration is 0.15m/s^2, and the autonomous response time of the on-board obstacle avoidance system is 0.5 seconds. It is known that the lunar rover control system uses a predictive compensation algorithm: v_cmd = v_current + a * (t_delay - t_reaction).", + "question": "To ensure that the lunar rover comes to a complete stop before the edge of the crater, what is the latest relative time for the ground to send a braking command? (Calculate the total time from the command being sent to the vehicle actually stopping.)", + "answer": "Total stopping time t = v/a + t_reaction = 0.2/0.15 + 0.5 ≈ 1.83 seconds. The latest time to send the command must be earlier than the time difference to reach the crater: 3m / 0.2m/s - 1.83s = 15s - 1.83s = 13.17 seconds." + }, + { + "id": 220, + "scenario_code": "4.9", + "instruction": " When the ascent vehicle and the lander sample container are handed over, the following conditions must be met: 1) The container temperature is maintained at -50±5℃; 2) The RFID tag signal strength is ≥-60dBm; 3) The sealing pressure is <0.1Pa. The current telemetry data: temperature -48℃, RFID -58dBm, pressure 0.08Pa. Communication delay causes the command to take effect after 30 seconds, with a known temperature change rate of 0.1℃/s (positive or negative depending on the heater status), RFID signal attenuation rate of 0.2dBm/s, and pressure rise rate of 0.002Pa/s.", + "question": "Determine whether the current status allows the immediate start of the handover procedure? If not, which parameter needs to be prioritized for adjustment? Provide the adjustment direction (increase/decrease).", + "answer": "Immediate start is not allowed. The RFID signal strength will drop to -58-(0.2*30)=-64dBm<-60dBm after 30 seconds. The RFID signal strength needs to be prioritized for increase, the adjustment direction is to increase (by increasing the transponder power or shortening the distance). The temperature and pressure are both within the safe range and the trend is controllable." + }, + { + "id": 221, + "scenario_code": "1.8", + "instruction": " When deploying the seismometer array, it was found that the local lunar soil bearing capacity is only 70% of the expected value. The original plan was to use a lander with a mass of 200kg and 4 support legs (each with a contact area of 0.02m²), with a safety factor requiring pressure <12kPa. The measured relationship between the static load and the compression deformation δ of the lunar soil in this area is: δ = 0.08 * P (unit: mm/kPa). The array installation requires the height difference between each support leg to be <5mm.", + "question": "To meet the safety and flatness requirements, what is the minimum contact area of the support legs that needs to be increased? (Keep the area of each leg unchanged.)", + "answer": "The original total pressure P = (200kg * 9.8m/s²)/(4*0.02m²) = 24.5kPa >12kPa. The number of legs n needs to be increased so that (200*9.8)/(n*0.02) ≤12 → n≥8.17→ take 9 legs. Verify the height difference: δ_max - δ_min = 0.08*(24.5*4/9 - 24.5*4/10) = 0.43mm <5mm, meeting the requirement. The minimum number of additional support legs needed is 5." + }, + { + "id": 222, + "scenario_code": "3.1", + "instruction": " Chang'e-7 lander is located at the edge of the Shackleton crater in the lunar south pole (latitude 88.5°S), and its solar wings use a two-dimensional tracking algorithm. According to the lunar almanac, the current solar elevation angle is 5°, and the azimuth angle is 45° (0° is due north, increasing clockwise). Terrain obstruction analysis shows: there is a permanently shadowed area in the due east direction, preventing power generation before 10:00 AM, and the maximum tracking angle of the solar wings is ±60°. The nominal power of a single wing is 200W (when vertically illuminated), and the power varies with the cosine of the incident angle.", + "question": "If the current time is 08:30 local lunar time, calculate the actual output power of the solar wings at this time (considering obstruction and tracking limitations)?", + "answer": "0W (because 08:30 is before 10:00 AM, and the terrain obstruction prevents power generation)." + }, + { + "id": 223, + "scenario_code": "3.4", + "instruction": " Yutu-2 rover needs to perform the following tasks simultaneously during the lunar day: ① Continuous operation of the X-ray spectrometer (power consumption 15W/hour) ② Sampling by the robotic arm (instantaneous peak 120W, lasting 5 minutes) ③ Data transmission (power consumption 45W/hour). The current remaining capacity of the lithium-ion battery is 180Wh, and the current output power of the solar array is 80W. The energy management strategy stipulates: when the instantaneous load exceeds 100W, the battery must be used to supplement the power.", + "question": "If the task sequence requires the robotic arm sampling and data transmission to overlap for 2 minutes, calculate the total power consumption and the energy supply method during this period? ", + "answer": "Total power consumption 165W (120W + 45W), the supply method is 80W from solar power + 85W battery compensation." + }, + { + "id": 224, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing exploration tasks on the far side of the moon, located at coordinate point A (10°N, 20°E). The mission planning system requires it to reach scientific target point B (12°N, 22°E) within 6 hours, with a straight-line distance of 5 kilometers between the two points. It is known that: 1) The average driving speed of the lunar rover is 0.2 km/h; 2) Path planning must consider terrain slope, with an energy consumption coefficient increase of 0.05 for every 1° of slope; 3) The average slope in the current area is 8°; 4) The basic energy consumption model is E = 0.1 * d + 3 (unit: Wh, d is the driving distance in km).", + "question": "Calculate the theoretical total energy consumption for Yutu-2 from point A to point B (considering the slope effect), and determine whether it can reach the target point within the specified time.", + "answer": "Theoretical total energy consumption E = (0.1 + 8*0.05) * 5 + 3 = 5.5 Wh; travel time t = 5 / 0.2 = 25 hours > 6 hours, cannot arrive on time." + }, + { + "id": 225, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. The characteristics of the lunar soil in this area are: medium hardness (Mohs hardness 4-5), low viscosity, and volatile content of about 120ppm. There are three sampling tools available: A-type rotary impact drill (suitable for hardness >6), B-type spiral drill (suitable for hardness 3-5 and volatile content <100ppm), C-type vibratory grab (suitable for hardness <4 and volatile content >150ppm). The power consumption of each tool is: A-type 15W, B-type 8W, C-type 12W. The mission requires prioritizing the integrity of the sample, followed by considering power consumption.", + "question": "Based on the characteristics of the lunar soil and the mission requirements, which sampling tool should be chosen? Please explain the selection criteria and calculate the power consumption for continuous operation of 30 minutes.", + "answer": "Choose the B-type spiral drill. Basis: 1) The lunar soil hardness (4-5) matches the applicable range of the B-type; 2) The volatile content (120ppm) is slightly higher than the nominal value of the B-type (100ppm), but better than the complete mismatch of the A/C types; 3) Under the premise of ensuring the integrity of the sample, the power consumption is the lowest. Power consumption calculation: 8W * 0.5h = 4Wh" + }, + { + "id": 226, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently on a patrol mission on the far side of the moon, located at coordinate point A (10°N, 120°E), and needs to reach scientific target point B (12°N, 122°E). It is known that: 1) The straight-line distance between the two points is 30km, but the actual path requires a 20% increase in distance due to detours around craters; 2) The energy consumption model for the lunar rover is E = 0.15*d + 2 (where d is the distance traveled in kilometers, and E is the power consumption in Wh); 3) The current remaining battery energy is 50Wh; 4) The remaining lunar day allows for continuous driving for only 4 hours, with the average speed of the lunar rover being 0.2km/min.", + "question": "Calculate whether Yutu-2 can safely reach target point B under the dual constraints of power and time? If not, what is the maximum percentage of the path that can be completed? (Round to two decimal places.)", + "answer": "No, the maximum percentage of the path that can be completed is 83.33%. Calculation process: 1) Actual path length = 30 * 1.2 = 36km; 2) Total energy consumption = 0.15 * 36 + 2 = 7.4Wh < 50Wh (power is sufficient); 3) Required time = 36 / (0.2 * 60) = 3h < 4h (time is sufficient); but according to the energy consumption model verification: the maximum allowable driving distance d = (50 - 2) / 0.15 = 320km > 36km (no contradiction). Note: The original problem setting has a contradiction (both time and power are sufficient), the parameters of the problem may need to be adjusted." + }, + { + "id": 227, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander, while working at the edge of the Shackleton crater, suddenly receives a solar proton event warning. According to the contingency plan, it must enter a safe mode within 30 minutes: 1) It must move to a rock shelter 500 meters away; 2) Lunar surface lighting conditions cause visual navigation to fail, and it can only rely on IMU + wheel speedometer combined navigation (positioning error accumulates over time, the formula is e=0.1*t^1.5, where t is in minutes, and e is in meters); 3) The maximum speed of the lunar rover is 10m/min, and the braking distance requires an additional 3% of the travel distance.", + "question": "Calculate the latest time point to start the risk avoidance to ensure safe arrival at the shelter (considering the navigation error does not exceed the shelter radius of 50m)?", + "answer": "The latest start time is the 18th minute after the warning. Calculation steps: 1) Total distance to be moved = 500 * 1.03 = 515m; 2) Required travel time = 515 / 10 = 51.5min; 3) Let the start time be t, then the total error e = 0.1 * (51.5 - t)^1.5 ≤ 50 → (51.5 - t)^1.5 ≤ 500 → t ≥ 51.5 - 500^(1/1.5) ≈ 18min" + }, + { + "id": 228, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration in the Von Kármán crater, obtaining the following remote sensing data: 1) The KREEP rock distribution probability map shows an 80% high probability area in the northeast region; 2) The laser radar measures an average slope of 8° in the area; 3) The spectrometer detects abnormal thorium element enrichment in the area. The rover currently has 200Wh of remaining power, with a movement power consumption of 0.8Wh/m and a scientific instrument power consumption of 5W/h. The mission requires reserving 50Wh for emergency power, and a single movement not exceeding 150 meters.", + "question": "If sampling of the high-value area is required, please plan the maximum allowable exploration duration (including round-trip movement), and explain the planning basis.", + "answer": "Maximum exploration duration is 52 minutes. Planning steps: 1) Usable power = 200Wh - 50Wh = 150Wh; 2) Round-trip movement energy consumption = 150m * 2 * 0.8Wh/m = 240Wh exceeds the budget, so the single-trip limit movement is adopted: 150m consumes 120Wh; 3) The remaining 30Wh is used for exploration, the instrument power consumption is 5W/h, i.e., 0.083Wh/min, which can support 30/0.083 ≈ 362 minutes, but is limited by the movement distance, the actual maximum movement time = 150m/(6cm/s) = 2500 seconds ≈ 42 minutes; 4) Total duration = 42 minutes of movement + 10 minutes of exploration ((150-120)/0.083 ≈ 10 minutes (rounded to the nearest whole number))." + }, + { + "id": 229, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. It is known that: 1) The pressure vessel is designed to withstand 10^5Pa, and the current internal pressure monitoring value is 8*10^4Pa ± 5%; 2) The relationship between the RFID tag reading success rate and distance is p=1-0.01*d (d is the distance in centimeters); 3) The mechanical arm docking accuracy is ±3mm. The mission procedure requires that the pressure value is within the nominal range, the RFID reading success rate is ≥95%, and the docking error is ≤5mm before the separation program can be initiated.", + "question": "Determine whether the current status meets the separation conditions? If not, point out the parameters that need to be adjusted and the target values.", + "answer": "Does not meet the separation conditions. Need to adjust: 1) The RFID reading distance should meet 1-0.01d ≥ 0.95 → d ≤ 5cm (the current docking accuracy of ±3mm may result in an actual distance exceeding 5cm); 2) The pressure range should be 7.6*10^4~8.4*10^4Pa (currently compliant). Adjustment target: Improve the mechanical arm docking accuracy to ±2mm to ensure the RFID reading distance ≤ 5cm." + }, + { + "id": 230, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing patrol duties on the far side of the moon, located at coordinate point A (10°N, 120°E), and needs to travel to scientific target point B (12°N, 122°E). It is known that: 1) The lunar surface slope is less than 15° everywhere, and the wheel-soil mechanics model shows a climbing energy consumption coefficient of 0.2 J/m/°, with a base energy consumption of 0.1 J/m for horizontal movement; 2) The current battery has a remaining energy of 5000 J; 3) The straight-line distance between the two points, corrected for elevation, is 3000 m, but there is a 200 m long uphill section with a slope of 12° in the path.", + "question": "If the shortest path is chosen for straight-line travel, calculate the total energy consumption required for the lunar rover to move from A to B, and determine whether the current battery level is sufficient to support this movement.", + "answer": "Total energy consumption = Horizontal segment energy consumption + Uphill segment energy consumption = (3000 - 200) * 0.1 + 200 * (0.1 + 0.2 * 12) = 2800 * 0.1 + 200 * 2.5 = 280 + 500 = 780 J. 5000 J > 780 J, the battery level is sufficient." + }, + { + "id": 231, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to conduct drilling and sampling in the South Pole-Aitken Basin on the far side of the Moon. According to preliminary remote sensing data, the hardness gradient of the lunar soil in the target area is: the surface layer 0-30cm hardness coefficient H=2 (soft), 30-60cm H=4 (medium), and below 60cm H=6 (hard). There are three types of drill bits available: Type A (suitable for H≤3, power consumption 200W), Type B (suitable for 35, power consumption 500W). Each drill bit change requires 10 minutes and consumes an additional 50Wh of energy. The drilling process must be continuous and cannot be paused.", + "question": "If a continuous sample 80cm deep is required, calculate the total energy consumption (unit: Wh) under the optimal drill bit combination plan, assuming the drilling speed is constant at 5cm/min.", + "answer": "Layered strategy: 0-30cm use Type A (200W*6min=20Wh), 30-60cm use Type B (350W*6min=35Wh), 60-80cm use Type C (500W*4min≈33.33Wh). Change consumption: 2 times*50Wh=100Wh. Total energy consumption=20+35+33.33+100=188.33Wh" + }, + { + "id": 232, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration near the Von Kármán crater. Based on multispectral data from the orbiter, three candidate sampling areas have been identified: Area A (KREEP rock probability 68%, distance 1.2km), Area B (volcanic glass probability 85%, distance 2.3km), Area C (breccia probability 92%, distance 0.8km). The rover's moving speed is 200m/h, and it can work 8 hours a day. The scientific priority weight formula is: priority score = mineral value probability * 100 - distance coefficient * 10 (distance coefficient = actual distance/km).", + "question": "If the highest priority target needs to be determined on the first working day, which area should be chosen? Provide the specific calculation process.", + "answer": "Choose Area C. Calculate the score for each area: Area A = 68*100 - 1.2*10 = 6788; Area B = 85*100 - 2.3*10 = 8477; Area C = 92*100 - 0.8*10 = 9192. Area C has the highest score." + }, + { + "id": 233, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 lander is located on the edge of an impact crater at 45° north latitude on the near side of the moon. Its solar panels use a two-dimensional tracking algorithm (azimuth + pitch angle). According to the lunar calendar, the current solar elevation angle during the lunar day is 15°, and the azimuth angle is 120° (due east is 0°). Terrain shadow analysis shows that the western crater will cause shading from 09:00 to 11:00 (local lunar time). The maximum output power of the solar panels is 200W (when unobstructed), and the pitch angle tracking error results in a 10% efficiency reduction.", + "question": "If the current time is 10:30, what is the actual output power of the solar panels? Consider the effects of terrain shading and tracking errors.", + "answer": "0W" + }, + { + "id": 234, + "scenario_code": "3.3", + "instruction": " The Yutu-2 rover is about to enter the lunar night hibernation mode. The current state of charge (SOC) of the lithium-ion battery pack is 65%, and the state of health (SOH) is 90%. The lunar night lasts for 14 Earth days, and the minimum power consumption to maintain critical systems is 8W. The total battery capacity is 200Wh, and the depth of discharge is limited to within 40%. The isotopic heat source can provide 2W of continuous heating, and the electric heater needs to be activated at -150°C (power consumption 15W, duty cycle 30%).", + "question": "Determine whether the current battery charge can safely survive the lunar night? List the key calculation steps.", + "answer": "No. Calculation process: Available power = 200Wh * 65% * 90% * 40% = 46.8Wh; Total energy consumption during the lunar night = (8W * 336h) + (15W * 30% * 336h) = 2688Wh + 1512Wh = 4200Wh; 46.8Wh < 4200Wh" + }, + { + "id": 235, + "scenario_code": "3.6", + "instruction": " The Chang'e-7 lander is equipped with three layers of thermal insulation material (thermal conductivity of 0.02W/mK, 0.015W/mK, 0.01W/mK), each with a thickness of 5mm. The lunar night environmental temperature is -180°C, and the instrument compartment temperature needs to be maintained at ≥-40°C. The power budget for electric heating is 20W, and the instrument itself generates 5W of heat. The contact area is 2m², and edge heat loss is negligible.", + "question": "Calculate whether the total heat flux density through the thermal insulation layer is within the capability of the temperature control system? Formula: Q/A = (T_hot - T_cold) / (L1/k1 + L2/k2 + L3/k3).", + "answer": "Within the range. Calculation process: Q/A = (233K - 93K) / (0.005/0.02 + 0.005/0.015 + 0.005/0.01) = 140 / 0.9167 = 152.7W/m²; Total heat flow = 152.7 * 2 = 305.4W < (20W + 5W) * 16 = 400W" + }, + { + "id": 236, + "scenario_code": "1.5", + "instruction": " The Yutu-2 lunar rover needs to be remotely controlled to cross a 2-meter diameter crater with a 1.3-second communication delay. The vehicle's motion model is: maximum acceleration 0.1 m/s², maximum deceleration 0.15 m/s², and cruising speed 0.2 m/s. After the ground station sends a command, the vehicle will execute it after a 200ms local computation delay. There is a 0.5-meter safety buffer zone at the edge of the crater.", + "question": "Calculate the minimum theoretical distance from the issuance of the braking command to the complete stop of the vehicle (including communication delay and computation delay), and determine whether it can safely brake at the current speed", + "answer": "Total delay time = 1.3s + 0.2s = 1.5s; distance moved during delay = 0.2 m/s * 1.5s = 0.3m; braking distance = (0.2 m/s)^2 / (2*0.15 m/s²) ≈ 0.133m; total stopping distance = 0.3 + 0.133 ≈ 0.433m < (2m/2 - 0.5m)=0.5m → it can brake safely" + }, + { + "id": 237, + "scenario_code": "5.1", + "instruction": " The Chang'e-6 probe is executing a sample return mission on the far side of the Moon, relying on the Queqiao-2 relay satellite for communication. It is known that Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, with an average altitude of about 8000km above the lunar surface. The current probe is located in the pre-selected landing area at 177.6°E, 45.5°S on the far side of the Moon, and the ground station is located in Beijing (116.4°E, Earth's rotation has been considered). The lunar radius is 1737km, the half-power angle of the relay satellite antenna is 60°, and the Earth's angular diameter as seen from the Moon is about 2°.", + "question": "Please calculate whether direct Earth-Moon communication conditions are met at this moment? If relay communication is required, determine whether Queqiao-2 is within the line of sight of the probe (require a quantitative analysis process).", + "answer": "Direct communication conditions are not met (the probe is on the far side of the Moon). Relay communication feasibility calculation: 1) The line-of-sight height h from the lunar surface detection point to the lunar tangent plane = sqrt((1737+8000)^2 - 1737^2) - 1737 ≈ 4636km; 2) The central angle θ between the probe and the relay satellite = arccos(1737/(1737+8000)) ≈ 78°; 3) The actual position angle = 177.6° > θ, and the 45.5° latitude is within the 60° beam coverage. Conclusion: Relay communication conditions are met." + }, + { + "id": 238, + "scenario_code": "5.4", + "instruction": " During the lunar day, the Yutu-2 rover was scheduled to transmit scientific data to the relay satellite when it suddenly encountered a solar proton event, causing the X-band link signal-to-noise ratio to drop by 10dB. The current buffer capacity is 15GB, the data generation rate is 500MB/hour, and it is expected that the space weather impact will last for 8 hours. The system's alternative plans are: A) Switch to the UHF emergency frequency band (reduced rate to 50MB/hour); B) Enable lossy compression (compression ratio 4:1 but will lose 30% of data value); C) Suspend transmission and wait for recovery (the longest tolerable data delay is 6 hours).", + "question": "Please select the optimal response strategy based on buffer capacity, data value preservation, and mission timeliness, and explain the reasons.", + "answer": "Choose option B (enable lossy compression). Calculation basis: 1) The original data generated in 8 hours = 500 * 8 = 4000MB = 4GB < 15GB buffer capacity; 2) Option A transmission volume = 50 * 8 = 400MB, which can only transmit 10% of the data; 3) Option C exceeds the maximum tolerable delay; 4) Option B can completely transmit all data (1GB after compression) and retain 70% of its value, which is better than other options." + }, + { + "id": 239, + "scenario_code": "5.10", + "instruction": " To accurately determine the coordinates of the Chang'e-7 lander on the lunar surface, the ground station uses pseudocode ranging technology. Given: the ranging code rate is 10MHz, the transmission time t0 = 1256.328 seconds (TDB time), the reception time t1 = 1256.581 seconds (including the one-way light travel time between Earth and Moon of about 1.28 seconds), the equipment delay calibration values: uplink 0.015 seconds, downlink 0.023 seconds. The average radius of the Moon is 1737km, and the landing point elevation is -2.3km.", + "question": "Please calculate the geocentric distance from the lander to the measuring station (require writing the complete calculation formula, ignoring relativistic effects and atmospheric delay).", + "answer": "Calculation formula: Geocentric distance R = c*(t1-t0-uplink delay-downlink delay-light travel time)/2 + lunar radius + elevation; Substituting values: R = 299792458*(1256.581-1256.328-0.015-0.023-1.28)/2 + (1737-2.3)*1000 ≈ 384403km" + }, + { + "id": 240, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (SELENE coordinates: 45°S, 176°E), and needs to establish a communication link through the Queqiao-2 relay satellite. It is known that Queqiao-2 is operating in the Earth-Moon L2 Halo orbit. At the current moment, the geometric distance between the relay satellite and the lander is 78,000 kilometers, the downlink frequency of the X-band is 8.4 GHz, the lander's transmission power is 20W, and the antenna gain is 38dBi. The ground station's receiving system quality factor G/T value is 32dB/K. The communication rate must be no less than 2 Mbps, using QPSK modulation (Eb/N0 requirement is 10dB).", + "question": "Please calculate whether the current link margin meets the requirements (considering free space loss, reserving 3dB margin for Doppler frequency shift compensation, and 2dB for equipment loss)? Provide the basis for your judgment.", + "answer": "Not met. Calculation process: Free space loss L=92.45+20log10(78000)+20log10(8.4)=220.3dB; Received power Pr=20W→13dBW +38dBi -220.3dB -2dB=-171.3dBW; Receiver end Eb/N0=Pr-10log10(2Mbps)+G/T-228.6=-171.3-63+32-228.6=-7.9dB＜Required value 10dB+3dB margin=13dB" + }, + { + "id": 241, + "scenario_code": "5.4", + "instruction": " During the lunar day, the Yutu-2 rover continuously transmits scientific data and encounters a solar conjunction interruption (the Sun, Earth, and probe are collinear). The control center predicts that the interruption will last 18 minutes. The rover's local cache has only 15GB of remaining capacity, and the current data generation rate is 12MB/s. The system must retain at least 20% of the cache for emergency command reception when using a lossy compression algorithm (compression ratio 1:4).", + "question": "Determine whether it is necessary to activate the lossy compression mode? Calculate and explain the relationship between the maximum allowable amount of raw data and the actual data to be cached.", + "answer": "Must activate. Raw data volume=12MB/s*1080s=12.96GB; Actual cache required=12.96GB*(1-1/4)=9.72GB; Available cache=15GB*80%=12GB＞9.72GB, but if no compression is used, 12.96GB＞12GB is needed" + }, + { + "id": 242, + "scenario_code": "1.5", + "instruction": " The Yutu-2 rover needs to be remotely controlled to avoid obstacles with a communication delay of 1.3 seconds. Its motion control equation is: predicted position = current speed * delay time + current position. Given the current speed is 0.2 m/s towards the north, and an obstacle is detected 1.05 meters away at a 30-degree northeast direction. The safety threshold is the distance between the predicted position and the obstacle ≥ 0.5 meters.", + "question": "Determine if the current motion status meets the safety threshold requirements? If not, calculate the maximum allowable speed adjustment.", + "answer": "Predicted displacement = 0.2 * 1.3 = 0.26m; actual obstacle distance = 1.05 * cos(30°) = 0.91m; predicted spacing = 0.91 - 0.26 = 0.65m > 0.5m (safe). No adjustment needed." + }, + { + "id": 243, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth. The Queqiao relay satellite is deployed in a Halo orbit at the Earth-Moon L2 point, about 65,000 kilometers from the Moon. Given:\n1. The X-band antenna gain of the relay satellite is 42 dBi, the lander's transmission power is 10 W, and the antenna gain is 38 dBi\n2. Free space path loss formula: L = 20 * log10(4 * π * d / λ), where λ=0.03m (X-band)\n3. The receiver sensitivity requires a signal-to-noise ratio (SNR) ≥ 10 dB for a bit error rate (BER) < 1e-6\n4. The current Earth-Moon distance is 380,000 kilometers, and the signal needs to be relayed through the satellite to the ground station", + "question": "Calculate whether the uplink link budget from the lander to the Queqiao relay satellite meets the requirements (consider only free space loss and antenna gain, ignore other losses)?", + "answer": "Link budget = transmission power (10W = 40dBm) + transmission antenna gain (38dBi) + receiving antenna gain (42dBi) - path loss (20*log10(4*π*65000000/0.03) = 214.3dB) = 40 + 38 + 42 - 214.3 = -94.3dBm > receiver sensitivity (-110dBm), meets the requirement" + }, + { + "id": 244, + "scenario_code": "5.7", + "instruction": " The 128GB solid-state memory of the Chang'e-5 orbiter has the following conditions:\n1. The P/E cycle of the storage chip has reached 3000 times (nominal life 5000 times)\n2. The current bad block rate is 0.5%, mainly distributed in storage area B\n3. Critical operations to be performed:\n - Receive ascent vehicle rendezvous data (8GB real-time write)\n - Synchronously transmit sample capsule data to the ground station (4GB read)\n4. The SSD controller supports dynamic bad block mapping and wear leveling algorithms", + "question": "Design a storage strategy to meet real-time requirements and extend the lifespan simultaneously? ", + "answer": "Strategy: 1) Write the ascent vehicle data to storage area A with fewer P/E cycles; 2) Read the sample capsule data from storage area B to balance wear; 3) Reserve 2% redundant blocks to cope with bad block growth; 4) Enable pipelined operations: writing 8GB takes about 16 minutes (at a rate of 100MB/s), executed in parallel with 4GB read" + }, + { + "id": 245, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover obtained the following remote sensing data near the Von Kármán crater: 1) The KREEP rock distribution probability map shows a high-value area 300 meters northeast (confidence 85%); 2) The LiDAR detected a 15° slope in this area; 3) The remaining energy can support a maximum of 500 meters of movement or 2 hours of in-situ detection. It is known that: 1) The rover's slope climbing energy consumption coefficient is 1.2 (i.e., the slope path length is calculated as the actual distance * 1.2); 2) Each 100 meters of movement consumes 5Wh; 3) In-situ detection consumes 8Wh per hour.", + "question": "Please calculate whether it is safe to complete a round-trip detection of the KREEP rock area. If so, provide the optimal action plan (distribution of movement + detection time).", + "answer": "It can be safely completed. Plan: 1) Total round-trip movement distance = 300 * 2 * 1.2 = 720 meters, equivalent energy consumption = 7.2 * 5 = 36Wh; 2) Remaining energy 500 - 36 = 464Wh, can support 464/8 = 58 minutes of in-situ detection. Optimal plan: Movement time (720/100)*60 = 43.2 minutes, detection 50 minutes (reserve 10% margin)." + }, + { + "id": 246, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. It is known that: 1) The container's RFID tag needs to be read in an environment of -20°C to +50°C; 2) The current lunar daytime temperature is +80°C; 3) The cooling system can reduce the container temperature to T = initial - (0.5 * cooling time) °C, but consumes 10Wh per minute; 4) The ascent vehicle has only 120Wh of emergency power left. The current temperature of the container is +70°C.", + "question": "Find the longest duration the cooling system can operate and the final temperature reached, ensuring the RFID is readable.", + "answer": "Longest operation time 12 minutes, final temperature +64°C. Calculation process: 1) Target temperature upper limit +50°C, initial 70°C, allowable cooling 20°C; 2) According to the cooling formula T=70-0.5t≤50 → t≥40 minutes; 3) But energy limits t≤120/10=12 minutes; 4) Actual execution for 12 minutes results in a temperature of 70-0.5*12=64°C, meeting the -20°C to +50°C requirement." + }, + { + "id": 247, + "scenario_code": "2.2", + "instruction": " Chang'e-7 lander conducts exploration in the permanent shadow region at the edge of the Shackleton crater. The navigation system uses a combination of Visual Odometry (VO) and IMU: the VO position error accumulates over time as e_vo=0.1%*travel distance, and the IMU velocity error is e_imu=0.05m/s. Currently, VO measures a travel distance of 80 meters, and IMU measures a speed of 0.3m/s for 200 seconds. The system performs absolute position correction using a star sensor every 100 seconds, with a correction residual standard deviation σ=0.5 meters.", + "question": "If no star correction is performed, estimate the maximum possible positioning error of the integrated navigation system after 200 seconds.", + "answer": "VO error: 80m*0.1%=0.08m; IMU velocity error accumulation: 0.05m/s*200s=10m; total error calculated as the square root of the sum of squares: sqrt(0.08^2 + 10^2)=10.0003 meters" + }, + { + "id": 248, + "scenario_code": "2.7", + "instruction": " The lunar rover encounters a solar proton event warning while patrolling near the terminator. Safety protocols require: reaching the nearest lava tube shelter within a 300-meter radius (coordinates C(150,-200)) within 15 minutes. The current speed limit is 0.1m/s, the inertial navigation system drift error is ±3 meters/minute, and obstacle avoidance maneuvers take up 20% of the time. The lava tube entrance must be approached in a straight line for the last 50 meters and the speed must be reduced to 0.02m/s.", + "question": "Calculate whether it is theoretically possible to arrive on time. If not, to what speed must the rover be increased? (Ignore terrain obstacles).", + "answer": "Total available time is 900 seconds. Effective travel time = 900*(1-20%) = 720 seconds. Straight-line distance = sqrt(150^2+200^2) = 250 meters. The last 50 meters take 50/0.02 = 2500 seconds, which exceeds the limit; theoretically, it is not possible to arrive. Let the required speed be v: (250-50)/v + 50/0.02 ≤ 900 → v ≥ 200/(900-2500) → no solution (safety constraints need to be adjusted)." + }, + { + "id": 249, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander has detected a warning of a solar proton event eruption at the edge of the Shackleton crater and needs to enter the permanent shadow area for safety within 30 minutes. The current position is 800m in a straight line from the entrance to the safe area, but there is a 200m diameter impact crater in between. Given: 1) The shortest path to bypass the impact crater is to travel 314m along the edge of the crater; 2) The maximum climbing angle of the lunar rover is 15°, and the maximum slope of the current path is 20°; 3) IMU navigation error is ±5m/min; 4) In emergency mode, the speed can reach 0.2m/s.", + "question": "Analyze the feasibility of the two existing paths (crossing the impact crater in a straight line or bypassing it) and provide the optimal risk avoidance plan and theoretical arrival time.", + "answer": "Feasibility analysis: 1) The slope of the straight path is 20°>15°, which is not feasible; 2) The total distance of the bypass path is 800+314=1114m. Plan selection: The bypass path takes t=1114/0.2/60≈93s <30min, and the IMU drift error is 93*5/60≈7.75m within the safe range. The optimal plan is to bypass the impact crater, with an estimated time of about 1 minute and 33 seconds." + }, + { + "id": 250, + "scenario_code": "2.9", + "instruction": " In the Lunar Orbit Navigation Satellite System (LBNSS), satellites at an orbital height of 100km provide positioning services with a period of 113 minutes. At a certain moment, the lander simultaneously receives signals from two satellites: Satellite A has an azimuth of 30°, an elevation angle of 45°, and a pseudorange measurement of 104km; Satellite B has an azimuth of 120°, an elevation angle of 30°, and a pseudorange measurement of 108km. It is known that: 1) The ranging error of LBNSS is ±50m; 2) The elevation data of the lander is -2500m (relative to the lunar reference ellipsoid); 3) The radius of the moon is 1737km.", + "question": "Based on the pseudorange measurements from the two satellites and the geometric constraints of the moon, estimate the approximate latitude and longitude coordinates of the lander (with an accuracy better than 1°). Hint: The spherical triangle formula can be used: cosθ = sinφ1*sinφ2 + cosφ1*cosφ2*cosΔλ.", + "answer": "Calculation steps: 1) The ground projection distance of Satellite A = sqrt(104^2 - (100 + 2.5)^2) ≈ 51km → corresponding central angle θA = 51/1737 ≈ 0.029rad ≈ 1.68°; similarly, θB ≈ sqrt(108^2 - 102.5^2)/1737 ≈ 1.82°; 2) Solving the system of equations cosθA = sinφ*sin(φ + ΔφA) + ... and cosθB = ... (specific values need to be solved iteratively), the lander's coordinates are approximately (25.6°N, 13.8°E) ± 0.5°." + }, + { + "id": 251, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. Analysis of the soil characteristics in this area shows: the surface layer 0-30cm consists of loose fine particles (shear strength <5kPa), 30-50cm contains cohesive blocks (shear strength 15-20kPa), and below 50cm there is a layer of high-titanium basalt (Mohs hardness 6). The probe carries three sampling tools: ① ultrasonic vibration drill (maximum output force 50N, suitable for hardness ≤5), ② electric grab (maximum clamping force 30N, suitable for viscosity <10kPa), ③ scraper (maximum thrust 20N, suitable for shear strength <10kPa). Sampling must be completed within 10 minutes, with a total system power consumption not exceeding 200W.", + "question": "If it is necessary to obtain both loose lunar soil from the surface and basalt samples from deeper layers in a single operation, how should the tools be combined and what is the sequence of operations? Provide the basis for the specific parameter selection.", + "answer": "First, use the scraper to collect loose lunar soil from 0-30cm (shear strength <5kPa <10kPa, thrust 20N is sufficient), then switch to the ultrasonic vibration drill to drill for basalt below 50cm (Mohs hardness 6>5, but vibration can reduce effective hardness, 50N output force can meet the requirement). The electric grab is not applicable due to the unknown viscosity of deeper samples and insufficient clamping force. Total power consumption estimate: scraper 15W*3min + drill 180W*5min = 945W >200W, so it needs to be done in separate operations." + }, + { + "id": 252, + "scenario_code": "5.7", + "instruction": " The Chang'e-5 orbiter's SSD uses NAND flash memory chips with a total capacity of 512 GB and a block size of 128 KB. The wear-leveling algorithm requires that the difference in the number of erase/write cycles between any two blocks does not exceed 5%. Current monitoring shows: 97% of the blocks have been erased and written between 2000 and 2100 times, while 3% of the blocks have reached 2200 times. The chip's rated lifespan is 3000 erase/write cycles.", + "question": "(1) Calculate whether the current maximum wear deviation exceeds the limit (2) If 50GB of new data is written daily and evenly distributed, estimate the remaining lifespan in days (the calculation formula must be listed)?", + "answer": "(1) Maximum deviation = (2200-2050)/2050 ≈ 7.3% > 5%, exceeding the limit. (2) Number of blocks written daily = 50GB/128KB = 50*1024*1024/128K = 409600; Total number of blocks = 512GB/128KB = 4194304; Daily wear rate = 409600/4194304 ≈ 9.77%; Remaining lifespan = (3000-2100)/(2100*9.77%) ≈ 438 days (calculated based on the block with the highest wear)." + }, + { + "id": 253, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth. The Queqiao relay satellite is deployed in a Halo orbit at the Earth-Moon L2 point, with an average altitude of about 65,000 kilometers above the lunar surface. The X-band antenna gain of the relay satellite is 42 dBi, the transmission power of the lander is 10 W, and the antenna gain is 6 dBi, operating at a frequency of 8 GHz. The free space path loss formula is: L = 20 * log10(d) + 20 * log10(f) + 92.45, where d is the distance (km), and f is the frequency (GHz).", + "question": "Calculate the free space loss (dB) of the uplink from the lander to the Queqiao relay satellite, and determine whether this value exceeds the receiver sensitivity threshold of -120 dBm of the relay satellite (the calculation process must be written)?", + "answer": "Calculation process: L = 20*log10(65000) + 20*log10(8) + 92.45 ≈ 20*4.8129 + 20*0.9031 + 92.45 ≈ 96.258 + 18.062 + 92.45 = 206.77 dB. The received power Pr = Pt + Gt + Gr - L = 10*log10(1000*10) + 6 + 42 - 206.77 = 40 + 6 + 42 - 206.77 = -118.77 dBm > -120 dBm, not exceeding the threshold." + }, + { + "id": 254, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover needs to transmit at least 500 MB of scientific data daily through the Queqiao relay satellite during the lunar day. On a certain day, an X-band link interruption occurred due to a solar flare, lasting for 3 hours, and the remaining storage capacity of the rover was only 300 MB. It is known that the data generation rate during the interruption period was 2 Mbps, and the remaining visible window of the relay satellite was 4 hours, with a recoverable link bandwidth of 1 Mbps.", + "question": "To ensure the complete return of key data, please calculate the emergency measures to be activated: (1) the minimum data compression ratio (2) the maximum amount of non-priority data that must be discarded (the calculation process must be listed step by step)?", + "answer": "(1) Data generated during the interruption period: 2 Mbps * 3600s * 3 = 2.16 GB; total data to be transmitted = 500MB + 2.16GB = 2660MB. Transmission capability after recovery: 1Mbps * 4h = 1 * 3600 * 4 / 8 = 1800MB. Compression ratio required = 1800 / 2660 ≈ 0.68. (2) If compression is not possible, the amount to be discarded = 2660 - 1800 = 860MB, but the storage has only 300MB redundancy, so the actual maximum amount that can be discarded is 300MB (otherwise, new data will be lost)." + }, + { + "id": 255, + "scenario_code": "5.1", + "instruction": " Chang'e-6 lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S), and plans to communicate with the ground station via the Queqiao-2 relay satellite. It is known that Queqiao-2 operates on the Earth-Moon L2 Halo orbit, about 65,000 km from the Moon's center. At this moment, the angle between the line connecting the ground station (110°E) and Queqiao-2 and the Moon's center is 12°, and the Moon's radius is 1737 km. The relay satellite's antenna gain is 42 dBi, the lander's transmission power is 10 W, the antenna gain is 6 dBi, and the operating frequency is 2.4 GHz. The free space path loss formula is: L = 20log10(4πd/λ), where λ=0.125 m.", + "question": "Calculate the free space loss (dB) of the Earth-Moon communication link under the current conditions, and determine whether the signal can meet the receiver sensitivity requirement of -120 dBm (ignoring other loss factors)?", + "answer": "Communication distance d = 65000 km - 1737 km = 63263 km; Free space loss L = 20log10(4π*63263e3/0.125) ≈ 210.1 dB; Received power Pr = Pt + Gt + Gr - L = 10log10(10) + 6 + 42 - 210.1 ≈ -152.1 dBm <-120 dBm, does not meet the requirement." + }, + { + "id": 256, + "scenario_code": "3.8", + "instruction": " In the Chang'e-6 sample return mission, the lander's energy budget is allocated as follows: ① peak power consumption of 300W for 3 continuous hours during the sampling phase ② average power consumption of 150W for 4 hours during the data transmission phase ③ constant power consumption of 50W for equipment insulation ④ a safety margin of 15%. The total capacity of the lithium-ion battery pack is 8kWh, and the remaining power at the end of the lunar day is 2kWh. The current power generation capacity of the solar panels is 200W.", + "question": "Determine whether the current energy supply meets the mission requirements? If not, how many additional hours of sunlight are needed for charging? ", + "answer": "Total demand=(300*3+150*4+50*(3+4))*1.15=2415Wh; shortfall 2415-2000=415Wh; charging time required=415/200≈2.08 hours" + }, + { + "id": 257, + "scenario_code": "3.8", + "instruction": " The energy budget for the Chang'e-6 lander during the lunar day is: total solar power generation 5400Wh, scientific instrument power consumption 2300Wh, basic power consumption of the thermal control system 800Wh, and reserved power for the communication system 600Wh. On the 3rd day of actual operation, an anomaly occurred: due to the accumulation of lunar dust, the power generation efficiency decreased by 12%, and the drilling operation consumed an additional 150Wh.", + "question": "Calculate the remaining energy budget deviation value and propose two feasible corrective actions (quantify the adjustment).", + "answer": "Deviation value = (5400*0.88) - (2300+800+600+150) = 4752 - 3850 = +902Wh; Corrective actions: ① Increase the working time of scientific instruments to consume up to 500Wh; ② Increase the set temperature of the thermal control system by 2°C to reduce power consumption by 100Wh." + }, + { + "id": 258, + "scenario_code": "3.4", + "instruction": " Yutu-2 rover needs to perform three tasks simultaneously during the lunar day: ① Continuous operation of the X-ray spectrometer for 20 minutes (peak power consumption 80W); ② Sampling by the robotic arm for 10 minutes (peak power consumption 150W); ③ Data transmission window for 15 minutes (peak power consumption 120W). The power system uses lithium-ion batteries, with a maximum continuous output power limit of 200W. When concurrent multitasking causes the total demand to exceed 200W, lower-priority tasks must be downgraded or delayed according to priority (priority order: ③>①>②).", + "question": "If the three tasks overlap completely for 5 minutes, please list the actual power allocation for each task during this time.", + "answer": "Total power demand during the complete overlap period = 80 + 150 + 120 = 350W > 200W. Power allocation according to priority: ③ maintains 120W, ① maintains 80W, ② is downgraded to 200 - 120 - 80 = 0W (suspended). Final allocation: X-ray spectrometer 80W, robotic arm 0W, data transmission 120W." + }, + { + "id": 259, + "scenario_code": "2.6", + "instruction": " When the Chang'e-7 lander conducts exploration in the permanently shadowed region, its Inertial Navigation System (INS) accumulates errors due to long-term operation. Engineers use astronomical navigation to assist in correction: by measuring the azimuth of Vega (α=18h36m, δ=+38°) and Sirius (α=6h45m, δ=-16°) using a star sensor, and combining the precise coordinates of the landing site (85°S, 135°W) and the lunar axis tilt of 1.54°, they establish an observation equation. It is known that the current lunar sidereal time (LST) is 3h20m, and the INS shows an attitude angle error of pitch +0.5°/yaw -0.3°.", + "question": "If the theoretical azimuth value of Vega should be azimuth AZ=142.2°/elevation EL=15.8°, and the actual observed value is AZ=141.7°/EL=16.1°, calculate the calibration correction amount for the INS attitude angle error (considering the weighted average of the two star observation data)?", + "answer": "Calculation steps: 1) The observation error of Vega ΔAZ=-0.5°, ΔEL=+0.3°; 2) Similarly, the observation error of Sirius is assumed to be ΔAZ=-0.4°, ΔEL=+0.2°; 3) Take the average value ΔAZ=(-0.5-0.4)/2=-0.45°, ΔEL=(+0.3+0.2)/2=+0.25°; 4) The INS correction amount is pitch -0.25°/yaw +0.45°" + }, + { + "id": 260, + "scenario_code": "4.9", + "instruction": " The rendezvous and docking phase between the ascender and the lander must meet the following conditions: 1) The internal temperature of the sample container must be maintained at -50±5℃; 2) The relationship between the RFID tag reading success rate and distance is P=100*(1-0.02d)% (d is the distance in meters); 3) The docking mechanism allows a maximum lateral deviation of 0.1 meters. Current telemetry shows the container temperature at -48℃, docking distance at 2.5 meters, and lateral deviation at 0.08 meters. The ascender has 90 seconds remaining for adjustments, the cooling system power is 1℃/min, and the positioning system correction speed is 0.01m/s.", + "question": "Determine if the current status meets the sample transfer conditions? If not, provide the highest priority adjustment measure.", + "answer": "Conditions are not met. Priority adjustment: Reduce the docking distance to 2 meters (takes 50 seconds), at which point the RFID read rate is 96% > 95% requirement; the temperature of -48℃ is already within the range; the lateral deviation of 0.08m < 0.1m does not require adjustment." + }, + { + "id": 261, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the lunar soil in this area are: the top layer 0-30cm is loose fine particles (viscosity coefficient k=0.8), and there are hard basalt fragments (Mohs hardness 6.5) at 30-50cm. The probe carries three sampling tools: ① Rotary impact drill (suitable for hardness >5, power consumption 150W/min) ② Vibration sampling tube (suitable for viscosity k<1, power consumption 80W/min) ③ Adaptive scoop (universal type, power consumption 120W/min). The current remaining energy can support 2000W*min of operation, and a complete rock fragment sample from below 30cm is required.", + "question": "If it is required to retain 50% of the energy redundancy for emergency operations, which sampling tool combination should be chosen to complete the sampling within the energy consumption limit? Please calculate the maximum allowable operation time.", + "answer": "Choose the rotary impact drill. Available energy = 2000*50% = 1000W*min, single tool operation time = 1000/150 ≈ 6.67 minutes" + }, + { + "id": 262, + "scenario_code": "4.9", + "instruction": " During the rendezvous and docking phase of the ascent vehicle with the lander, the transfer of the sealed sample canister must be completed. Known conditions: ① Canister size Φ15cm×25cm ② Manipulator positioning error ±3mm ③ Docking mechanism tolerance ±5mm ④ Lunar surface lighting conditions reduce visual navigation accuracy by 40%. The original design used RFID-guided coarse positioning (accuracy ±10mm) + laser rangefinder fine positioning (accuracy ±1mm), but the laser rangefinder has malfunctioned.", + "question": "When relying solely on RFID guidance, to ensure 100% successful transfer, by how many millimeters at least does the docking mechanism's tolerance need to be increased? ", + "answer": "Required tolerance = positioning error + original tolerance = 10 + 5 = 15mm. Since the decrease in visual navigation accuracy does not affect RFID positioning, the final tolerance needs to be expanded to ±15mm" + }, + { + "id": 263, + "scenario_code": "1.4", + "instruction": " Three scientific instruments (A, B, C) have been deployed in the permanently shadowed regions of the lunar south pole, sharing a lunar surface power grid. Instrument A (seismometer) requires a continuous 10W power, Instrument B (spectrometer) performs a 15-minute high-precision scan every 2 hours with a peak power of 25W. Instrument C (heat flow probe) requires constant temperature control, with a base power consumption of 5W, and when the lunar soil temperature drops below -150°C, the heating module activates, consuming an additional 20W. The power grid consists of solar arrays and batteries, providing a stable 50W output during the day and a maximum discharge power of 30W at night. It is currently in the lunar night phase, and the lunar soil temperature monitoring shows -170°C.", + "question": "If Instrument B initiates a high-precision scan as scheduled at this time, does the system need to trigger power priority management? If so, which instrument's operation should be prioritized first? ", + "answer": "Priority management needs to be triggered. The current total power demand: A(10W) + B(25W) + C(5W+20W) = 60W, exceeding the 30W limit of the night battery. Priority should be given to ensuring the operation of Instrument A (for continuous collection of critical scientific data) and Instrument C (to prevent damage from freezing), and the scanning task of Instrument B should be suspended." + }, + { + "id": 264, + "scenario_code": "1.8", + "instruction": " The Chang'e-7 lander plans to deploy a lunar surface electric field detector at the edge of an impact crater at a latitude of 85°. The measured bearing capacity of the lunar soil in this area is 8kPa (safety factor must be ≥2), the instrument weighs 12kg, and the base contact area is 0.02m². Before deployment, a laser rangefinder detected a 5° slope at the designated location, with the instrument's center of gravity at a height of 0.5m. The known lunar gravitational acceleration is 1.62m/s².", + "question": "Determine if the current site meets the stability requirements? If not, calculate the minimum base area required (assuming a circular contact surface).", + "answer": "Actual bearing capacity requirement: 12*1.62/0.02=972Pa＜8kPa/2=4kPa (statically satisfied). However, the slope causes a tipping moment: 12*1.62*0.5*sin(5°)=0.85Nm; the anti-tipping moment: 12*1.62*√(0.02/π)*cos(5°)=1.54Nm＞0.85Nm (dynamically satisfied). Therefore, the site is qualified, and there is no need to expand the base area." + }, + { + "id": 265, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth, and must communicate through the Queqiao relay satellite. The Queqiao satellite operates in a Halo orbit around the Earth-Moon L2 point, about 65,000 km from the Moon. The average distance from Earth to the Moon is 380,000 km, and the Queqiao satellite uses the X-band (8 GHz) to communicate with the Earth station, with a maximum transmission power of 20 W and an antenna gain of 42 dB. The Earth station antenna gain is 60 dB, and the system noise temperature is 100 K. The communication link margin must be no less than 3 dB.", + "question": "Calculate the maximum free space path loss (FSPL) between the Queqiao satellite and the Earth station in dB? The known free space path loss formula is FSPL = 20 * log10(d) + 20 * log10(f) + 92.45, where d is the distance (km), and f is the frequency (GHz).", + "answer": "FSPL = 20 * log10(384000 + 65000) + 20 * log10(8) + 92.45 ≈ 20 * log10(449000) + 20 * log10(8) + 92.45 ≈ 113.06 + 18.06 + 92.45 = 223.57 dB" + }, + { + "id": 266, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover needs to transmit at least 500 MB of scientific data daily to the Queqiao relay satellite during the lunar day. One day, a solar flare caused the X-band link to be interrupted for 2 hours, and the remaining storage capacity of the rover was only 300 MB. The rover uses two compression modes: lossy compression (compression ratio 1:4) and lossless compression (compression ratio 1:1.5). The time required for lossless compression is 1.2 times that of real-time transmission. The current link rate is 2 Mbps.", + "question": "To ensure data is not lost, which compression mode should be chosen? Provide a calculation to explain the basis for your choice (assuming the compression operation can be completed before the end of the lunar day).", + "answer": "Choose the lossy compression mode. The original 500 MB of data, after lossy compression, becomes 125 MB < 300 MB; after lossless compression, it becomes 333 MB > 300 MB, which would overflow. Additionally, the 2-hour interruption results in a loss of 2*3600*2/8=1800 MB transmission capacity, so the remaining time must prioritize the transmission of critical data." + }, + { + "id": 267, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar regolith samples from the South Pole-Aitken Basin of the Moon. The characteristics of the lunar regolith in this area are as follows: average hardness is 3.5 Mohs (similar to calcite), medium viscosity, and high volatile content (about 1200 ppm). There are three sampling tools available: A-type rotary impact drill (suitable for hardness >4 Mohs), B-type vibratory grab (suitable for viscosity >5 Pa·s), C-type scraper (suitable for volatile content <800 ppm). The power consumption of each tool is: A-type 18W, B-type 12W, C-type 15W. The remaining energy of the probe is 200Wh, and 50Wh needs to be reserved for communication and basic system operation.", + "question": "Based on the characteristics of the lunar regolith and energy constraints, which sampling tool should be chosen? Calculate the maximum available working time after sampling is completed (assuming sampling takes 10 minutes).", + "answer": "Choose the C-type scraper. Sampling energy consumption=15W*(10/60)h=2.5Wh, remaining energy=200-50-2.5=147.5Wh, maximum available working time=147.5Wh/15W=9.83 hours" + }, + { + "id": 268, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration near the Von Kármán crater. According to orbital remote sensing data, the characteristics of three candidate sampling points are as follows: Point 1 (coordinates X12,Y34) has a KREEP rock abundance of 68%±5%, and is 120 meters away from the current position; Point 2 (X15,Y30) has a probability of containing volcanic glass of 82%±3%, and is 80 meters away; Point 3 (X20,Y28) has a breccia coverage area of 55㎡, and is 150 meters away. The rover's movement speed is 0.05m/s, and it can operate for 8 hours per day. The scientific value weight formula is: Priority score = 0.6 * mineral abundance + 0.4 * (100 - distance).", + "question": "Calculate the priority scores for each sampling point and determine the optimal survey path for the day (list reachable points in order of priority).", + "answer": "Score for Point 1 = 0.6 * 68 + 0.4 * (100 - 120) = 32.8; Score for Point 2 = 0.6 * 82 + 0.4 * (100 - 80) = 57.2; Score for Point 3 = 0.6 * 55 + 0.4 * (100 - 150) = 13. Optimal path: Point 2 (movement time = 80 / 0.05 / 3600 ≈ 0.44 hours, can be completed) → Point 1 (cumulative movement time = (80 + 120) / 0.05 / 3600 ≈ 1.11 hours, can be completed)." + }, + { + "id": 269, + "scenario_code": "4.9", + "instruction": " When the ascent vehicle transfers the sample container to the return capsule, the following conditions must be met: 1) The internal temperature of the container must be maintained between -50°C and +10°C; 2) The sealing pressure must be >0.8atm; 3) The RFID tag reading success rate must be ≥99%. Current telemetry data shows: sealing pressure 1.2atm, temperature -35°C, tag read 100 times with 98 successful reads. The transfer procedure takes 15 minutes, during which the temperature may rise by 20°C (due to solar radiation), and the pressure naturally decreases by 0.05atm per hour.", + "question": "Determine whether the current conditions are suitable for immediate transfer? If delayed processing is required, calculate the maximum allowable delay time (considering all constraint critical values).", + "answer": "Current conditions are met (temperature -35°C is within range, pressure 1.2 > 0.8, success rate 98% < 99% not met). The maximum delay time is determined by the RFID, which requires at least one more successful read (overall success rate 99/101 ≈ 98.02% still insufficient), therefore, it cannot be delayed and the RFID system must be immediately repaired." + }, + { + "id": 270, + "scenario_code": "2.7", + "instruction": " While the Chang'e-7 lander is performing exploration tasks at the edge of the Shackleton crater, it suddenly receives a solar proton event warning (lasting 6 hours). The lander is currently in the illuminated area (temperature 127°C) and needs to urgently transfer to the permanent shadow area (-173°C) to avoid danger. It is known that: 1) The maximum allowable slope of the transfer path is 20°; 2) The IMU navigation error accumulation rate is 0.1°/min; 3) The entrance to the shadow area is 300 meters away from the current position in a straight line, but there is a 50-meter diameter impact crater that needs to be bypassed; 4) The emergency movement speed limit is 0.02 m/s.", + "question": "Calculate whether the lander can complete the risk avoidance before the proton event arrives (30-minute warning buffer period + 6-hour event period) under the condition that the IMU error accumulation does not exceed 3°. The key judgment basis needs to be explained.", + "answer": "It cannot be completed. Basis: 1) The maximum allowable operating time for the IMU is t=3°/0.1°/min=30 min <6 hours; 2) The actual travel path is at least 300+50*3.14/2=378.5 meters (half-circle detour), taking 378.5/0.02=18925 seconds≈5.26 hours >30-minute buffer period" + }, + { + "id": 271, + "scenario_code": "2.10", + "instruction": " The lunar rover needs to approach a basaltic outcrop (coordinates X:3541.2 m, Y:2876.8 m) with centimeter-level precision. The parameters of the onboard navigation system are as follows: 1) Visual odometry positioning error ±3 cm/step; 2) UWB beacon network provides absolute positioning accuracy ±5 cm; 3) Wheel odometry calibration error 0.1%; 4) The current straight-line distance to the target point is 20 meters. The control system requires that the final positioning error does not exceed ±10 cm.", + "question": "Design a combined navigation strategy to meet the final error requirement, and calculate the maximum allowable number of visual odometry steps N (assuming each step moves 10 cm). Hint: Total error = √(UWB error² + visual cumulative error² + wheel speed cumulative error²).", + "answer": "Strategy: Correct with UWB once every N steps. Calculation: Visual cumulative error = 3*sqrt(N), wheel speed cumulative error = 20m*0.1% = 2cm. Solve the equation 10 ≥ √(5² + (3√N)² + 2²) → N ≤ ((100-25-4)/9) = 7 steps." + }, + { + "id": 272, + "scenario_code": "5.1", + "instruction": " The Chang'e-6 lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S), and plans to communicate with Earth via the Queqiao-2 relay satellite. It is known that: Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, at an altitude of about 80,000 km above the lunar surface; the lander's transmission power is 10W, with an antenna gain of 5dBi; the relay satellite's receiving antenna gain is 35dBi, and the system noise temperature is 300K; the operating frequency is 2.4GHz (wavelength 0.125m), and the required minimum receive signal-to-noise ratio (SNR) is 6dB. At the current moment, the line connecting Earth and Queqiao-2 intersects the lunar surface at a point 200km from the lander, with the lunar radius being 1737km.", + "question": "Calculate the margin of the Earth-Moon communication link under the current conditions (i.e., the difference between the actual SNR and the minimum requirement), given the free space loss formula L = (4πd/λ)^2, and the Boltzmann constant k = 1.38e-23 J/K.", + "answer": "1. Calculate the communication distance d: d = sqrt(200^2 + 1737^2) - 1737 ≈ 11.5km (line-of-sight distance from the lunar surface to the tangent point) + 80000km = 80115.5km\n2. Free space loss L = (4π*8.01155e7/0.125)^2 ≈ 1.62e21\n3. Received power Pr = Pt*Gt*Gr*λ^2/(4πd)^2 = 10*10^(5/10)*10^(35/10)*0.125^2/(4π*8.01155e7)^2 ≈ 1.58e-13 W\n4. Noise power Pn = kTB = 1.38e-23*300*1e6 ≈ 4.14e-15 W\n5. Actual SNR = Pr/Pn ≈ 38.16 (15.82dB)\n6. Margin = 15.82dB - 6dB = 9.82dB" + }, + { + "id": 273, + "scenario_code": "5.8", + "instruction": " The intelligent data processing system on board the Chang'e-7 orbiter needs to screen the lunar surface mineral spectral data (400MB per orbit, 10 bands) on the satellite. It is known that: the neural network model can identify 5 types of mineral characteristics, and it takes 8 minutes to execute inference for each orbit's data, consuming 15W of power; the X-band downlink rate is 2Mbps, and the orbiter can see the ground station for 10 minutes per orbit; the transmission of raw data requires the full occupation of the link, while after feature extraction, only 20MB of result data needs to be transmitted.", + "question": "Calculate the energy savings per orbit when using the intelligent screening scheme compared to the transmission of raw data (orbiter power supply voltage 28V), and explain whether it meets the real-time downlink requirements.", + "answer": "1. Raw data transmission time: 400MB*8/2Mbps ≈1600s(26.67 minutes)>10-minute window → must be temporarily stored\n2. Intelligent scheme time consumption:\n - Processing time 8 minutes + 20MB transmission time ≈ 80s → total time 9 minutes 20 seconds < 10-minute window\n - Processing energy consumption: 15W*480s=7200J\n - Transmission energy consumption: (20MB*8bits)/2Mbps *28V*1A≈4480J\n3. Raw scheme storage and transmission energy consumption: 400MB write to SSD energy consumption ≈5J/MB*400=2000J\n4. Energy saving value: (2000+4480)-7200≈-720J (more energy consumption)\nConclusion: Not energy-saving but meets real-time downlink requirements" + }, + { + "id": 274, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration within the Von Kármán crater, obtaining the following data: ① Hyperspectral images show that there is a KREEP rock characteristic absorption peak (a sudden drop in reflectivity at a wavelength of 950nm) at coordinates (12.3N, 125.6E); ② The laser radar measures that the horizontal distance from this point to the current position is 83m, with an elevation difference of +1.2m; ③ The navigation camera shows that there are 3 craters with a diameter >1m on the path. The rover's maximum climbing angle is 15°, the average travel speed is 0.05m/s, and the remaining power supports continuous operation for 90 minutes. Scientific priority ranking: KREEP rock (5) > volcanic glass (3) > ordinary lunar soil (1).", + "question": "Determine whether the rover can complete sampling of this KREEP rock point before the power is depleted? Need to calculate the total travel distance and time consumption.", + "answer": "Feasible. The horizontal distance of 83m corresponds to a slope distance = sqrt(83^2 + 1.2^2) = 83.01m; slope angle = arctan(1.2/83) = 0.83° < 15°, meeting the passability requirement; travel time = 83.01/0.05 = 1660s ≈ 27.7 minutes < 90 minutes of remaining power, can complete sampling." + }, + { + "id": 275, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. The characteristics of the soil in this area are: medium hardness (Mohs hardness 4-5), low viscosity, and volatile content of about 120 ppm. There are three sampling tools available: Type A rotary impact drill (suitable for hardness >5), Type B spiral drill (suitable for hardness 3-5), and Type C scraper (suitable for loose surface layers). The maximum output torque of the drill is 50N·m, and the power consumption is related to the sampling depth by the formula P=2.5*d (W, where d is the depth in centimeters). The mission requires collecting at least 15cm of undisturbed samples, and the power consumption for a single operation must not exceed 40W.", + "question": "Based on the characteristics of the lunar soil and the mission constraints, which sampling tool should be chosen? Calculate whether the actual power consumption of the tool meets the requirement when the depth requirement is satisfied.", + "answer": "Choose the Type B spiral drill. The actual power consumption P=2.5*15=37.5W <40W, which meets the requirement." + }, + { + "id": 276, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration near the Von Kármán crater. According to the high-value area priority scoring formula generated from orbital remote sensing data: S=0.3*mineral diversity + 0.2*volatile content + 0.5*terrain flatness (each item is out of 10 points). The data for the current three candidate points are: Point A (8,6,7), Point B (7,9,4), Point C (5,8,9). The remaining power of the rover can support a trip to one point for sampling, and the point with the highest scientific value must be chosen first.", + "question": "Calculate the comprehensive score for each candidate point and determine the optimal sampling point.", + "answer": "Point A S=0.3*8+0.2*6+0.5*7=7.1; Point B S=0.3*7+0.2*9+0.5*4=5.9; Point C S=0.3*5+0.2*8+0.5*9=7.6. The optimal sampling point is Point C." + }, + { + "id": 277, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container transfer must be verified, with the following process requirements: 1) RFID tag reading success rate ≥99%; 2) Pressure in the sealed chamber maintained below 10^-5Pa; 3) 100% completeness of temperature recorder data. Current inspection data: RFID successfully read 9 times out of 10 consecutive attempts, sealed chamber pressure 8×10^-6Pa, temperature recording missing the last 30 seconds of data (total recording duration 2 hours). Container weight 18kg, maximum load capacity of the ascent vehicle's robotic arm 20kg, remaining time window for docking 8 minutes.", + "question": "Determine whether the current sample container meets the transfer standards? If not, identify the specific non-conformities and suggest improvements (known RFID single read time is 5 seconds, temperature data supplementation requires 1 minute).", + "question_answer": "Does not meet transfer standards. Non-conformities: 1) RFID reading success rate 90%<99%; 2) Temperature data completeness 99.58%<100%. Improvement suggestions: 1) Increase the number of RFID reads to 20 times (time required 100 seconds); 2) Supplement temperature data (time required 60 seconds). Total time required 160 seconds < remaining window 480 seconds, robotic arm load margin 2kg meets requirements.", + "answer": "Does not meet transfer standards. Non-conformities: 1) RFID reading success rate 90%<99%; 2) Temperature data completeness 99.58%<100%. Improvement suggestions: 1) Increase the number of RFID reads to 20 times (time required 100 seconds); 2) Supplement temperature data (time required 60 seconds). Total time required 160 seconds < remaining window 480 seconds, robotic arm load margin 2kg meets requirements." + }, + { + "id": 278, + "scenario_code": "5.7", + "instruction": " The 'Chang'e-5' orbiter's SSD uses NAND flash memory chips (single chip capacity 128 GB, P/E cycle 3000 times), with a file system that employs wear-leveling algorithms. The average number of erase/write cycles for each chip is currently 1200, and the number of erase/write cycles generated daily due to data storage is equivalent to 0.3 P/E cycles. The orbiter's design life is 2 years (730 days), with 180 days remaining in the mission.", + "question": "Calculate whether the theoretical remaining life of the SSD under the current usage mode meets the mission requirements, and explain the key basis for judgment.", + "answer": "The number of erase/write cycles generated over the remaining 180 days = 180*0.3=54 cycles; expected total number of erase/write cycles = 1200+54=1254 cycles < 3000 cycle limit. Safety margin = (3000-1254)/3000=58%, far exceeding the engineering redundancy standard (usually required >20%), thus meeting the life requirement." + }, + { + "id": 279, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. Analysis of the soil characteristics in this area shows: the top 0-30cm is loose fine particles (viscosity coefficient k=0.8 Pa·s), and 30-50cm contains high-hardness basalt fragments (Mohs hardness 6.5). The probe is equipped with three sampling tools: a rotary impact drill (suitable for hardness >5), a helical core sampler (suitable for viscosity 0.5-1.2 Pa·s), and an electric shovel (only suitable for loose surface material). The maximum output torque of the drill bit is 8 N·m, and the critical stress for breaking the basalt fragments σ_c=120 MPa, with the drill bit's effective area A=2e-6 m^2.", + "question": "To ensure successful collection of samples from the 30-50cm layer, which sampling tool should be chosen? If the rotary impact drill is selected, please verify whether its output torque meets the breaking requirement (Hint: the required torque T=σ_c*A*r, effective radius r=5mm).", + "answer": "The rotary impact drill should be chosen. Verification calculation: T=120e6*2e-6*0.005=1.2 N·m < 8 N·m, which meets the requirement." + }, + { + "id": 280, + "scenario_code": "4.4", + "instruction": " Yutu-2 is conducting exploration in the Von Kármán crater and has obtained data for three candidate sampling points: Point A (KREEP rock probability 78%, 320 meters from the current location), Point B (volcanic glass probability 65%, 180 meters away), and Point C (breccia probability 92%, 420 meters away). The rover's movement energy consumption model is E=0.12*d+5 (Wh), with a daily available energy limit of 150 Wh. Scientific priority weights: KREEP rock 3 points, volcanic glass 2 points, breccia 1 point.", + "question": "Based on the energy consumption constraints and the principle of maximizing scientific value, please calculate the scientific return per unit of energy consumption (scientific points/Wh) for each candidate point, and determine the optimal sampling route.", + "answer": "Point A return=(78%*3)/(0.12*320+5)=0.052 points/Wh; Point B=(65%*2)/(0.12*180+5)=0.049 points/Wh; Point C=(92%*1)/(0.12*420+5)=0.017 points/Wh. The optimal choice is Point A." + }, + { + "id": 281, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover suddenly experienced a communication interruption during the lunar day. Known facts:\n1. The currently used relay link has experienced a sudden drop in signal-to-noise ratio due to a solar flare;\n2. The backup UHF band can provide a rate of 50kbps but has a higher bit error rate;\n3. The SSD cache has a remaining capacity of 8GB, with a scientific data generation rate of 2MB/min;\n4. It is expected to take 3 hours to restore the X-band main link.", + "question": "To ensure critical data is not lost, how should the transmission strategy be adjusted? Provide specific parameter calculation basis.", + "answer": "1. Prioritize switching to the UHF link to transmit high-priority data (such as status telemetry);\n2. SSD cache duration = (8GB * 1024MB/GB) / (2MB/min) ≈ 4096 minutes > 3 hours (180 minutes);\n3. The amount that can be transmitted via the UHF link in 3 hours = 50kbps * 3600s * 3 ≈ 675MB << 8GB → lossy compression needs to be activated (e.g., reducing image resolution to 70%)" + }, + { + "id": 282, + "scenario_code": "4.9", + "instruction": " The design of the lunar sample return capsule adopts a double-layer sealed structure: the inner layer is a nitrogen environment (maintaining a pressure of 101 kPa±5%), and the outer layer is a vacuum insulation layer that needs to maintain <10^-3 Pa. The seal performance testing standard requires that the pressure change ΔP over 24 hours be <1 kPa. A certain ground test record shows an initial pressure P0=101.3 kPa, which drops to 100.1 kPa after 24 hours, with the ambient temperature being constant at 25±0.5℃. It is known that the container volume V=500 cm^3, and the gas constant R=8.314 J/(mol·K).", + "question": "Please calculate the actual leakage rate Q of the container (unit: mol/s), and determine whether it meets the sealing standard (hint: use the ideal gas state equation PV=nRT, leakage rate Q=Δn/Δt).", + "answer": "Δn=(P0V/RT)-(P1V/RT)=(101300-100100)*5e-4/(8.314*298.15)=2.43e-5 mol; Q=2.43e-5/86400=2.81e-10 mol/s < the allowable leakage rate corresponding to ΔP<1kPa (101000-100000)*5e-4/(8.314*298.15*86400)=2.35e-10 mol/s, thus it does not meet the standard." + }, + { + "id": 283, + "scenario_code": "5.1", + "instruction": " When the Chang'e-6 probe performs sampling tasks on the far side of the moon, it needs to maintain communication with the ground station through the Queqiao-2 relay satellite. It is known that:\n1. Queqiao-2 is located in the Halo orbit at the Earth-Moon L2 point, with an average altitude of about 8000km above the lunar surface;\n2. The maximum transmission power of the probe is 20W, with an antenna gain of 10dBi;\n3. The receiving antenna gain of the relay satellite is 15dBi, and the system noise temperature is 200K;\n4. The operating frequency is 2.4GHz (wavelength 0.125m), and the required minimum receive signal-to-noise ratio is 10dB;\n5. The free space path loss formula: L = 20 * log10(4 * π * d / λ).", + "question": "When the distance between the probe and the relay satellite reaches the farthest 10000km, calculate whether the link margin meets the communication requirements (the specific margin value must be provided)?", + "answer": "1. Calculate the path loss: L = 20 * log10(4 * π * 10000km / 0.125m) ≈ 210dB\n2. Receive power Pr = Pt + Gt + Gr - L = 20W(13dBW) + 10dBi + 15dBi - 210dB = -172dBW\n3. Noise power Pn = kTB = -228.6dBW/Hz + 10*log10(200K) + 10*log10(10MHz) ≈ -150dBW\n4. SNR = Pr - Pn = -172dBW - (-150dBW) = -22dB < 10dB → does not meet, link margin -32dB" + }, + { + "id": 284, + "scenario_code": "2.7", + "instruction": " When the Chang'e-7 lander is working at the edge of the Shackleton crater, it suddenly receives a solar proton event warning (lasting 4 hours) and needs to take immediate shelter. Known: 1) The nearest permanent shadow area shelter is 2km to the northwest; 2) The IMU shows the current speed is 0.05m/s, with a maximum safe speed of 0.1m/s; 3) The terrain slope limit is ≤15°; 4) In emergency mode, energy consumption doubles (original model E=0.2*d). The system needs to plan a sheltering path that meets all constraints within 10 minutes.", + "question": "Calculate the minimum speed required for sheltering and the maximum allowable energy consumption of the corresponding path, and verify whether the current speed meets the timeliness requirement.", + "answer": "Minimum speed v_min = distance / warning response time = 2000 / (4*3600) = 0.139m/s > 0.1m/s; Maximum allowable energy consumption E_max = 0.2*2 = 0.4Wh. The current speed of 0.05m/s requires 400 seconds to complete the journey (about 6.7 minutes), meeting the timeliness but with a risk of overspeed requiring path optimization." + }, + { + "id": 285, + "scenario_code": "4.9", + "instruction": " During the docking phase of the ascent vehicle with the orbiter, it is necessary to ensure that the temperature of the sample container remains stable at -50±5℃. Current monitoring data: initial container temperature -55℃, thermal conductivity of the insulation layer 0.02W/mK, surface area 0.8㎡; lunar daytime environmental temperature 120℃, lunar night -180℃; the temperature control system includes a semiconductor cooling plate (maximum cooling capacity 15W@24V) and an electric heating film (maximum power 20W). The thermocouple measurement shows that the container is warming up at a rate of 0.8℃/min. The heat capacity calculation formula for the container is Q=1200J/℃*ΔT.", + "question": "Calculate the power of the temperature control equipment that needs to be immediately activated and the expected stabilization time (ignoring system response delay).", + "answer": "Heat loss power P=1200J/℃*0.8℃/min≈16W. It is necessary to activate the semiconductor cooling plate at full power (15W), and the remaining 1W temperature difference can be compensated by reducing the heat transfer through the insulation layer. Stabilization time t=ΔT/(heating rate-cooling rate)=5℃/(0.8-15*60/1200)=5/0.05=100 minutes." + }, + { + "id": 286, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the handover of the sample container must be verified. The standard procedure includes: 1) Reading the RFID tag of the container (15s±3s); 2) Sealing pressure test (standard value 1-5Pa, test duration 20s); 3) Temperature record verification (allowable range -50°C to +30°C, duration 10s). If any step exceeds the limit, a retest must be initiated (additional time same as original test). The current communication window has 85s remaining, and the actual parameters of the container are: RFID read 18s, sealing pressure 3Pa, temperature 25°C.", + "question": "Can the entire verification process be completed under the current conditions? If not, which steps can be performed at most under the current conditions? ", + "answer": "It can be completed. Total time = 18(RFID) + 20(pressure) + 10(temperature) = 48s < 85s. All parameters are within the allowable range, no retest is needed." + }, + { + "id": 287, + "scenario_code": "2.9", + "instruction": " The lander deployed a UWB navigation beacon array in the Von Kármán crater (beacon spacing 500±0.1 m). The lunar rover simultaneously receives signals from three beacons: Beacon 1 is 105.3 m away (σ=±0.5 m), Beacon 2 is 201.1 m away (σ=±1.2 m), and Beacon 3 is 150.8 m away (σ=±0.8 m). The coordinates of each beacon are known and there is no multipath interference. The weight coefficient formula in the integrated navigation algorithm is w_i = (1/σ_i^2)/(Σ(1/σ_j^2)).", + "question": "Calculate the weight coefficients w_1, w_2, w_3 of the three beacons (保留3位小数), and explain which beacon's data should be prioritized for high-precision positioning? (保留3位小数 translates to '保留3 decimal places')", + "answer": "w_1 = (1/0.5^2)/(4+0.694+1.5625)=4/6.256≈0.640; w_2=(1/1.44)/6.256≈0.111; w_3=(1/0.64)/6.256≈0.249. The data from Beacon 1 should be prioritized (w_1 is the largest, with the highest ranging accuracy)." + }, + { + "id": 288, + "scenario_code": "1.8", + "instruction": " When deploying the seismometer array, it was found that the bearing capacity of the lunar soil at the predetermined location is only 1.8kPa, while the equipment support requires ≥2.5kPa. The engineering team proposed three adjustment plans:\nA) Expand the support base area to 1.4 times the original design\nB) Reduce the total equipment weight from 42kg to 30kg\nC) Move to a nearby area with a measured bearing capacity of 2.8kPa (requiring an additional 15% energy consumption)\nIt is known that the current energy reserve only allows for one plan to be executed, and the maximum power consumption limit for the relocation operation is 200W.", + "question": "If option A is chosen, please verify whether it meets the bearing capacity requirement (assuming the equipment mass is evenly distributed).", + "answer": "It meets the requirement. Calculation:\nOriginal pressure = 42*9.81/1000 / (original area) = 2.5kPa → original area ≈ 0.164m²\nExpanded area = 0.164*1.4 ≈ 0.23m²\nNew pressure = 42*9.81/1000 / 0.23 ≈ 1.79kPa < 1.8kPa (safety margin about 0.6%)" + }, + { + "id": 289, + "scenario_code": "1.4", + "instruction": " In the permanently shadowed region of the lunar south pole, 3 scientific instruments have been deployed: a seismometer (peak power 120W), an infrared spectrometer (peak power 80W), and a neutron detector (peak power 60W). They share a lunar surface micro-grid powered by a radioisotope thermoelectric generator (RTG), which has a maximum continuous output power of 200W. The instruments use a time-division multiplexing strategy to share power, with each needing at least 50% of its peak power to maintain basic functions. The current mission phase requires the seismometer to operate at full power to monitor seismic activity.", + "question": "Under the premise of ensuring the seismometer operates at full power, how should the remaining power be allocated to the other two devices? Please list the specific allocation plan and verify whether it meets all constraint conditions.", + "answer": "Remaining power = 200W - 120W = 80W; Infrared spectrometer minimum requirement = 80W * 50% = 40W; Neutron detector minimum requirement = 60W * 50% = 30W; Allocation plan: Infrared spectrometer 40W + Neutron detector 40W (or spectrometer 50W + detector 30W, etc.), total power consumption 120+40+40=200W ≤ RTG capacity, and all meet the minimum power constraints." + }, + { + "id": 290, + "scenario_code": "1.8", + "instruction": " The Chang'e-7 lander plans to deploy a 4-node seismometer array at the edge of an impact crater at 85°S latitude. The measured bearing capacity of the lunar soil in the deployment area is 8kPa (dry state) and 5kPa (with volatiles), with each node weighing 15kg and having a base contact area of 0.02m². During deployment, a safety factor of ≥2 (i.e., actual bearing capacity/equipment pressure ≥2) must be ensured, and the distance between adjacent nodes must not be less than 20m to avoid mutual interference.", + "question": "When deploying in the lunar soil area with volatiles, verify whether the stability of a single node meets the requirements? If not, propose two improvement schemes and explain the principles.", + "answer": "Node pressure P=mg/A=15*1.62/0.02=1215Pa=1.215kPa; safety factor=5/1.215≈4.11＞2 (satisfied). If the assumption is not met, improvement schemes: ① Increase the base area to 0.03m² to reduce P to 0.81kPa; ② Reduce the node weight to 10kg to reduce P to 0.81kPa, both can increase the safety factor to 6.17." + }, + { + "id": 291, + "scenario_code": "3.6", + "instruction": " The Yutu-2 rover needs to maintain its core electronic equipment above -40°C during the lunar night. Known: 1) The total thermal dissipation power of the equipment compartment is 8W; 2) The equivalent thermal resistance of the multilayer insulation material R=4 K/W; 3) The rated heat generation power of the isotope heat source is 10W; 4) The electric heater has a backup power of 15W, with a start threshold of -50°C. The lunar night environmental temperature is -180°C, lasting 14 Earth days.", + "question": "Calculate the equilibrium temperature of the equipment compartment relying solely on the isotope heat source, and determine whether the electric heater needs to be activated (ignoring transient thermal capacity processes).", + "answer": "Equilibrium temperature = -180 + (10-8)*4 = -172°C; since -172°C < -50°C threshold, the electric heater needs to be activated." + }, + { + "id": 292, + "scenario_code": "3.8", + "instruction": " The mission cycle of the Chang'e-4 relay satellite is 24 hours, with energy consumption including: 1) X-band communication system power consumption of 80W (6 communication windows per day, each lasting 25 minutes); 2) Attitude control system constant power consumption of 12W; 3) Scientific payload periodic operation power consumption of 20W (3 times per day, each lasting 40 minutes). The total capacity of the lithium-ion battery pack is 480Wh, with a discharge depth limit of 80%. The average daily power generation of the solar panels is 620Wh.", + "question": "Verify whether the energy budget meets the mission requirements (calculate the total energy consumption and available power separately, and provide the surplus percentage).", + "answer": "Total energy consumption = (80*(25*6)/60 + 12*24 + 20*(40*3)/60) = (200 + 288 + 40) = 528 Wh; Available power = min(620, 480*0.8) = 384 Wh; 528 > 384 does not meet the requirement, deficit = (528-384)/384 ≈ 37.5%." + }, + { + "id": 293, + "scenario_code": "3.1", + "instruction": " In the Chang'e-5 mission, the lander is located near the Rümker Mountains at 43.06°N, 51.92°E on the lunar near side. The solar elevation angle in this area varies from 5° to 35° during the lunar day, and the solar panels use two-dimensional tracking (azimuth + pitch). It is known that: 1) The area of a single solar panel is 2 square meters, with a photovoltaic conversion efficiency of 28%; 2) The solar constant on the lunar surface is 1368 W/m^2; 3) Terrain blocking reduces the effective power generation time by 15% daily; 4) Azimuth tracking error is ±3°, pitch tracking error is ±2°.", + "question": "If the current solar elevation angle is 20°, the azimuth tracking error is +2°, and the pitch error is -1°, calculate the actual output power of a single solar panel (considering the cosine loss due to tracking errors and terrain blocking factors).", + "answer": "Actual solar incidence angle = arccos(cos(20°+1°)*cos(2°)) ≈ 20.1°; Effective light intensity = 1368 * cos(20.1°) ≈ 1284 W/m^2; Theoretical output = 2 * 1284 * 0.28 ≈ 719 W; Actual output after considering terrain blocking = 719 * (1-0.15) ≈ 611 W" + }, + { + "id": 294, + "scenario_code": "5.7", + "instruction": " The 128TB solid-state memory of the 'Chang'e-7' orbiter is composed of a RAID5 array of NAND Flash chips. It is known that: 1) the capacity of a single chip is 1TB, with a PE cycle of 3000 times; 2) the current wear-leveling algorithm keeps the write amplification factor of each chip stable at 1:1:1:1:1:1:1:1 (a total of 8 channels); 3) the scientific payload generates 12TB of new data daily that needs to be written to storage.", + "question": "Calculate the theoretical lifespan of the memory (in Earth days) under the current operating mode, and suggest two feasible measures to extend its lifespan.", + "answer": "1) The daily write volume per chip = 12TB / 8 channels = 1:1 allocation → each channel writes 12TB / 8 = 1.5TB per day; 2) The total writable volume per chip = 3000 PE * 1TB = 3000TB; 3) Theoretical lifespan = 3000TB / (1.5TB/day) = 2000 days ≈ 5.48 years. Measures to extend lifespan: ① Enable dynamic wear-leveling algorithm, prioritizing chips with lower PE cycles; ② Implement hierarchical storage for scientific data, compressing low-value data to reduce write volume." + }, + { + "id": 295, + "scenario_code": "1.4", + "instruction": " When deploying a scientific instrument network in the permanently shadowed regions of the lunar south pole, a shared energy grid needs to be established. The current system includes: 1 main solar power station (peak power 1200W, supplying power for 10 hours during the day), 3 radioisotope thermoelectric generators (RTGs, each continuously outputting 200W), and 2 scientific payloads (Payload A has a base power consumption of 80W and a peak of 150W; Payload B has a base power consumption of 50W and a peak of 300W). All devices are connected through a smart power distribution unit, with RTGs prioritizing life support systems (fixed consumption of 100W). The solar power station stops working during the lunar night.", + "question": "If Payloads A and B simultaneously enter peak mode operation during the lunar night, and it is necessary to ensure at least 30 minutes of emergency communication (consuming 60W), will there be a power deficit in the energy system? What is the deficit amount if any existent? ", + "answer": "There will be a power deficit, the deficit is 90W. Calculation process: Total RTG output = 3 * 200 = 600W, life support consumes 100W, leaving 500W; A + B peak load = 150 + 300 = 450W; Emergency communication 60W; Total demand = 450 + 60 = 510W; Deficit = 510 - 500 = 10W" + }, + { + "id": 296, + "scenario_code": "1.5", + "instruction": " The Yutu-2 rover needs to remotely control the robotic arm to collect lunar rocks with a communication delay of 1.3 seconds. The end-effector positioning accuracy of the robotic arm is required to be ±5mm, with a maximum movement speed of 0.1m/s. After the ground control station sends a movement command, it must wait for the image to be transmitted back for confirmation before proceeding to the next operation. The current link bandwidth limitation means that a 2000x1500 pixel color image (approximately 3MB after compression) can only be transmitted back every 5 seconds.", + "question": "If the sampling point is 0.8 meters away from the current position, and a 'move-wait for confirmation' segmented control strategy is adopted, theoretically, how much time is required to complete the approach action at least? (Do not consider actual lunar surface terrain obstacles.)", + "answer": "At least 21.6 seconds. Calculation process: Segment movement time = 0.8/0.1 = 8 seconds; Image transmission time required after each move = 5 seconds; Communication delay compensation times = ceil(0.8/(0.1*5)) = 2 times; Total time = 8 + 5*2 + 1.3*2 = 21.6 seconds" + }, + { + "id": 297, + "scenario_code": "1.8", + "instruction": " The Chang'e-7 lander is equipped with 4 independently adjustable support legs, each equipped with a real-time pressure sensor and a lunar soil mechanics properties analyzer. It is known that the bearing capacity of the lunar soil in the landing area is 15kPa, with a safety factor of 2. The contact area of a single leg is 0.02m², and the current sensor readings are: Leg 1 - 280N, Leg 2 - 310N, Leg 3 - 295N, Leg 4 - 265N. The total mass of the lander (including payload) is 240kg.", + "question": "Based on real-time monitoring data, determine whether the leg distribution needs to be adjusted? If adjustment is needed, indicate which leg should reduce its load to meet safety requirements? (Lunar gravitational acceleration is 1.62m/s².)", + "answer": "Adjustment is needed, Leg 2 should reduce its load. Calculation process: Total weight = 240*1.62 = 388.8N; Maximum allowable force per leg = 15kPa*0.02m²/2 = 150N; Current load on Leg 2 310N > 150N" + }, + { + "id": 298, + "scenario_code": "5.1", + "instruction": " Chang'e-6 lander is located in the South Pole-Aitken Basin on the far side of the Moon (180°E longitude, 45°S latitude), and plans to communicate with the ground station through Queqiao-2 relay satellite. Known: 1) Queqiao-2 operates in the Halo orbit at the Earth-Moon L2 point, with an average altitude of 8000km above the lunar surface; 2) The lander's antenna gain is 10dBi, and the transmission power is 5W; 3) The relay satellite's receiving antenna gain is 20dBi, and the system noise temperature is 300K; 4) The operating frequency is 2.4GHz, and the free space path loss formula is L = 92.4 + 20log10(d) + 20log10(f), where d is the distance (km), and f is the frequency (GHz); 5) The required signal-to-noise ratio at the receiving end is no less than 10dB.", + "question": "Calculate whether the current link margin meets the communication requirements (specific calculation steps are required)?", + "answer": "1) Calculate the distance: The distance from the lunar surface to the L2 point is about 8000km; 2) Free space loss L = 92.4 + 20log10(8000) + 20log10(2.4) ≈ 92.4 + 78.06 + 7.6 = 178.06dB; 3) EIRP = 10log10(5W) + 10dBi ≈ 7 + 10 = 17dBW; 4) Gr/T = 20dBi - (-228.6 + 10log10(300)) ≈ 20 - (-228.6 +24.77) = 223.83dB/K; 5) C/N0 = EIRP - L + Gr/T - k ≈ 17 - 178.06 + 223.83 - (-228.6) = 291.37dBHz; 6) C/N = C/N0 - 10log10(100kHz bandwidth) = 291.37 - 50 = 241.37dB > 10dB requirement. Conclusion: The link margin is sufficient." + }, + { + "id": 299, + "scenario_code": "5.4", + "instruction": " Yutu-2 rover encountered a sudden solar proton event during the lunar day, causing the X-band direct-to-Earth communication to be interrupted. Current status: 1) Remaining power supports continuous operation for 8 hours; 2) There are 2GB of untransmitted scientific data in the cache (priority: 0.8GB terrain data - high priority, 1.2GB spectral data - medium priority); 3) The nearest relay node 'Queqiao-3' will enter the visible window in 30 minutes, with a maximum transmission rate of 512kbps. System strategy: High-priority data must be completely transmitted, and medium-priority data can be lossily compressed to 60% of its original size.", + "question": "Please formulate the optimal data transmission plan to ensure the complete transmission of key data and prevent the loss of data due to power failure.", + "answer": "1) High-priority data transmission time = 0.8GB * 1024MB/GB * 8Mb/MB / 512kbps = 8192Mb / 512kbps = 16000 seconds ≈ 4.44 hours; 2) Compressed size of medium-priority data = 1.2GB * 0.6 = 0.72GB, transmission time = 0.72 * 1024 * 8 / 512 ≈ 11.52 hours; 3) Total required time = 4.44 + 11.52 = 15.96 hours > remaining 8 hours; Plan: Prioritize the complete transmission of 0.8GB high-priority data (using 4.44 hours), and in the remaining 3.56 hours, the amount of medium-priority data that can be transmitted = 512kbps * 3.56 * 3600 seconds ≈ 6,400Mb = 800MB (65% of the original data), and 550MB of the lowest value spectral data must be discarded." + }, + { + "id": 300, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container transfer must be inspected. It is known that:\n- The container seal pressure should be maintained at the 10^−4 Pa level\n- The success rate of RFID tag reading is related to the distance as P=1−0.2*d (d in meters)\n- The mechanical arm docking accuracy error follows a normal distribution N(μ=3mm, σ=1mm)\nThe docking process must meet the following requirements simultaneously:\n1) RFID reading success rate ≥95%\n2) The probability of docking error ≤5mm >99.7%\n3) The fluctuation of sealing pressure does not exceed ±5%.", + "question": "Calculate the maximum allowable installation distance of the RFID reader and the corresponding mechanical arm docking pass rate.", + "answer": "The maximum distance for RFID is d=0.25 meters (solved from 0.95≤1−0.2*d). Docking pass rate: 5mm error corresponds to μ+2σ=5mm, according to the properties of the normal distribution P(μ−3σ99.7%." + }, + { + "id": 301, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is carrying out a patrol mission from point A (coordinates [10,20]) to point B (coordinates [30,40]). It is known that the terrain data indicates that there are two optional paths between the two points: Path 1 is a straight-line distance of 35 meters with an average slope of 5 degrees; Path 2 is a zigzag distance of 40 meters with an average slope of 2 degrees. The motor efficiency model of the lunar rover is: the energy consumption coefficient for climbing is 0.15*slope (degrees)*distance (meters), and the basic energy consumption coefficient for flat roads is 0.1*distance (meters). The current battery remaining energy is 8 joules, and at least 1 joule must be reserved for emergency use.", + "question": "Please calculate the total energy consumption of the two paths and determine whether Yutu-2's current power can safely complete the travel of either path.", + "answer": "Total energy consumption for Path 1 = 0.15*5*35 + 0.1*35 = 26.25 + 3.5 = 29.75 joules; Total energy consumption for Path 2 = 0.15*2*40 + 0.1*40 = 12 + 4 = 16 joules. Available energy 8-1=7 joules is less than the energy consumption of both paths, so it cannot be safely completed." + }, + { + "id": 302, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. Analysis of the soil characteristics in this area shows: the surface layer 0-30cm consists of loose fine particles (viscosity coefficient η=0.8 Pa·s), 30-50cm contains high-hardness basalt fragments (Mohs hardness 6.5), and below 50cm, there may be volatiles (estimated water ice content 2-5%). There are three sampling tools with the following parameters:\n- Rotary Percussion Drill: maximum torque 15N·m, suitable for hardness ≤7, sensitive to volatiles\n- Vibratory Grab: gripping force 200N, suitable for viscosity η≤1.2 Pa·s, no volatile restrictions\n- Helical Core Sampler: shape retention sampling rate >90%, suitable for loose media, high power consumption", + "question": "If a complete core sample is needed at a depth of 40cm while avoiding volatile loss, which tool should be chosen? Provide a comparison of the key parameters for the selection.", + "answer": "The rotary percussion drill should be chosen. Justification: 1) At 40cm, it is in the high-hardness basalt layer (Mohs hardness 6.5 ≤ tool limit 7); 2) The vibratory grab cannot ensure the integrity of the core; 3) The helical core sampler can retain the shape but has high power consumption and no mention of hardness adaptability; 4) At this depth, it has not reached the volatile layer, so no special protection is needed." + }, + { + "id": 303, + "scenario_code": "2.7", + "instruction": " When the lunar rover is working near the terminator and suddenly encounters a solar proton event warning, it needs to reach an emergency shelter 3 kilometers away within 15 minutes. It is known that: the maximum safe speed on the lunar surface is 0.1m/s, the maximum visible distance of the current navigation camera is 200 meters, and the obstacle detection reaction time needs to reserve 5 seconds per detection. On average, there is one rock that needs to be avoided every 50 meters on the lunar surface.", + "question": "Verify whether it can arrive on time by traveling in a straight line at the maximum speed? If not, propose a solution that meets safety constraints (quantitative explanation required).", + "answer": "Straight-line travel time = 3000 / 0.1 = 30000 seconds > 900 seconds, not feasible. Solution: Reduce the detection distance to 150 meters to increase the speed to 150 / (5 + 150 / 0.1) = 0.15m/s, then the new travel time = 3000 / 0.15 + 3000 / 50 * 5 = 20000 + 300 = 20300 seconds, still exceeding the limit, so it is necessary to find a temporary shelter nearby or activate the radiation shielding mode." + }, + { + "id": 304, + "scenario_code": "1.4", + "instruction": " When deploying scientific payloads in the permanently shadowed regions of the lunar south pole, it is necessary to allocate shared energy to 3 devices (seismometer, heat flow probe, neutron spectrometer). The total power budget of the system is 120W, and the basic power consumption of each device is as follows: seismometer 15W (must run continuously), heat flow probe peak 45W (operating cycle 30%), neutron spectrometer peak 60W (operating cycle 50%). The energy scheduling algorithm must ensure: 1) the seismometer never loses power; 2) when the heat flow probe is operating, the neutron spectrometer must be on standby; 3) the total instantaneous power of all devices must not exceed 120W.", + "question": "What is the percentage of time when the heat flow probe and the neutron spectrometer enter their operating cycles simultaneously? Does the system meet the total power constraint at this time? ", + "answer": "The simultaneous operation time ratio is 15% (0.3*0.5), at this time the total power = 15+45+60=120W, just meeting the constraint." + }, + { + "id": 305, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover for rock sampling, the ground command transmission delay is 1.3 seconds. The current speed of the rover is 0.2m/s, and a target rock is found 3 meters ahead. The control system uses a predictive algorithm to compensate for the delay: 1) If an immediate stop command is sent, the actual stopping position of the vehicle = current speed * (command delay + braking response time of 0.5 seconds); 2) The braking process is a uniformly decelerated motion.", + "question": "To ensure that the stopping distance from the rock is no less than 0.5 meters, at what distance from the rock should the stop command be issued at the latest? ", + "answer": "Minimum safe distance = 0.2 * (1.3 + 0.5) + 0.5 = 0.86 meters, therefore the command should be issued at the latest when the distance from the rock is 3 - 0.86 = 2.14 meters." + }, + { + "id": 306, + "scenario_code": "3.6", + "instruction": " The Queqiao relay satellite of Chang'e-4 needs to maintain a constant temperature environment of -40°C to +10°C during the lunar night. Its insulation system uses three layers of thermal insulation materials (thermal conductivity of 0.02W/mK, 0.015W/mK, 0.03W/mK) and 2 10W isotopic heat sources. The external temperature is known to be -180°C, and the equipment heat dissipation power is 8W. It is required to calculate the total thermal resistance through the thermal balance equation Q_out = k*A*ΔT/d (where k is the equivalent thermal conductivity, A=2m² is the surface area, d=0.1m is the total thickness).", + "question": "Calculate the equivalent thermal conductivity k required for the system to reach thermal equilibrium (unit: W/mK, retain four decimal places).", + "answer": "0.0089W/mK" + }, + { + "id": 307, + "scenario_code": "1.4", + "instruction": " Three scientific instruments (A, B, C) have been deployed in the permanently shadowed regions of the Moon's south pole, sharing a solar power network. Instrument A is a seismometer (peak power 30W, continuous operation), Instrument B is a drill (peak power 200W, operates 2 hours daily), and Instrument C is a spectrometer (peak power 50W, intermittent operation). The solar array has a maximum output of 180W, and the storage battery has a capacity of 500Wh. During the lunar day, the solar array can provide full power, while during the lunar night, only the battery can be used. It is currently the 3rd hour of the lunar day, with 400Wh remaining in the battery.", + "question": "If Instrument B is scheduled to start a 2-hour operation at the 5th hour of the lunar day, and Instrument C needs to operate continuously for 4 hours (starting from the current time), please determine if this power scheduling plan is feasible? If not, how should the start time of Instrument B be adjusted to make it feasible? ", + "answer": "Not feasible. Current total demand: Instrument C 50W*4h=200Wh + Instrument B 200W*2h=400Wh =600Wh > available energy (solar 180W*2h=360Wh + battery 400Wh=760Wh), but when Instrument B operates, it will exceed the real-time power supply capacity of the solar array (200W+50W=250W>180W), requiring 70W*2h=140Wh from the battery. Adjustment plan: Delay the start time of Instrument B to the 7th hour of the lunar day, at which point the solar array can independently meet its 200W requirement (180W solar + 20W battery)." + }, + { + "id": 308, + "scenario_code": "3.3", + "instruction": " Yutu-2 measured the battery temperature at +80°C during the lunar day, and it is expected to enter the lunar night phase in 2 hours, with the temperature dropping sharply to -150°C. The thermal control system needs to maintain the battery within the operating range of -20°C to +50°C. It is known that the battery mass is 5kg, specific heat capacity is 800 J/(kg·K), the electric heater power is 20W, and the radiator's maximum cooling power is 15W. Currently, the battery temperature needs to be reduced to below 50°C within 1 hour.", + "question": "Calculate how long the electric heater needs to be turned off to achieve the target temperature drop (ignoring the effect of the radiator).", + "answer": "(80°C -50°C)*5kg*800J/(kg·K) / (20W*3600s/h) = 1.67 hours" + }, + { + "id": 309, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. The characteristics of the lunar soil in this area are: medium hardness (Mohs hardness 4-5), high viscosity (cohesion about 1.5kPa), and volatile content 3-5%. There are three sampling tools available: 1) Diamond-coated rotary drill (suitable for hardness >6, power consumption 120W); 2) Titanium alloy grab (suitable for viscosity <1kPa, power consumption 80W); 3) Ultrasonic scraper (suitable for medium viscosity, power consumption 60W). The maximum allowable power consumption of the sampling system is 100W, and it must ensure a sampling efficiency of ≥90%.", + "question": "Based on the given parameters, which sampling tool should be selected? Please list the key calculation steps for the selection criteria.", + "answer": "Select the ultrasonic scraper. Basis: 1) Hardness match: Lunar soil hardness 4-5 is below the drill's applicable standard; 2) Viscosity match: The scraper is suitable for medium viscosity (1.5kPa is within the range); 3) Power consumption limit: 60W < 100W; 4) Efficiency requirement: The scraper's efficiency for medium viscosity lunar soil is 95% > 90%." + }, + { + "id": 310, + "scenario_code": "4.9", + "instruction": " When the ascent vehicle hands over the sample container, the following conditions must be met: 1) Temperature must be maintained at -50±5°C; 2) Sealing pressure <10^-3Pa; 3) RFID read success rate ≥99%. Current telemetry data: Temperature -48°C, pressure 5*10^-4Pa, RFID signal strength -65dBm (threshold -70dBm). The handover process takes 180 seconds, with RFID verification needing to last for 20 seconds. It is known that the signal attenuation model is: signal attenuation = initial strength + 10*log10(time).", + "question": "Determine whether the current conditions meet the handover requirements and calculate the minimum initial signal strength for the RFID verification phase.", + "answer": "Requirements are met. Justification: 1) Temperature -48°C is within range; 2) Pressure is within standard; 3) Current RFID signal strength is acceptable. Minimum initial strength calculation: -70 = x + 10*log10(20) → x = -70 -13 = -83dBm." + }, + { + "id": 311, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. Based on preliminary remote sensing data analysis, the target area has two typical types of lunar soil: Class A is loose, dry fine-grained lunar soil (hardness 2MPa, viscosity 0.5Pa·s), and Class B is sticky lunar soil containing volatiles (hardness 5MPa, viscosity 8Pa·s). The engineering team is equipped with three sampling tools: a rotary impact drill (suitable for hardness >3MPa), an electric grab (suitable for viscosity <5Pa·s), and a screw sampler (universal but less efficient). The maximum power consumption limit of the sampling system is 150W, with the rotary impact drill operating at 120W, the electric grab at 80W, and the screw sampler at 60W.", + "question": "If it is necessary to collect samples of both Class A and Class B in a single operation without exceeding the power consumption limit, how should the sampling tools be combined? Provide specific tool selection and operation sequence.", + "answer": "First, use the electric grab to collect Class A samples (80W), then use the rotary impact drill to collect Class B samples (120W), the total power consumption of 200W exceeds the limit; or first use the screw sampler to collect Class A samples (60W), then use the rotary impact drill to collect Class B samples (120W), the total power consumption of 180W still exceeds the limit; the only feasible solution is to use the screw sampler to collect both types of samples in sequence (60W*2=120W<150W)." + }, + { + "id": 312, + "scenario_code": "4.9", + "instruction": " The lunar sample return capsule is designed with a double-layer sealed structure: the inner layer is an aluminum alloy container with a nitrogen environment (leakage rate <1e-7 Pa·m³/s), and the outer layer is a titanium alloy protective shell. When the ascent vehicle docks with the return capsule, the following conditions must be met: ① Temperature difference at the docking interface <50K; ② Relative velocity <0.05m/s; ③ Attitude angle deviation <3°. Current telemetry data shows: the surface temperature of the return capsule is 110K, the temperature of the ascent vehicle's docking ring is 170K; the relative velocity is 0.03m/s; the pitch angle deviation is 2°, and the yaw angle deviation is 4°.", + "question": "Can the sample container transfer be executed directly under the current conditions? If not, which parameter needs to be adjusted?)", + "answer": "The transfer cannot be executed directly. The temperature difference of 60K > 50K and the yaw angle deviation of 4° > 3° both exceed the limits. The attitude of the ascent vehicle must be adjusted to ensure the yaw angle is ≤3°, and active temperature control must be applied to the return capsule to reduce the temperature difference to within 50K." + }, + { + "id": 313, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. It is known that: the container seal pressure should be maintained at 10±0.5kPa, the temperature recorder shows the data for the past 3 hours as -60℃, -55℃, -58℃ (the allowable range is -70℃ to -40℃), and the RFID tag read success rate is 99.7% (>99% is qualified). The handover agreement stipulates that if any two of the three indicators are abnormal, a second review will be triggered.", + "question": "Based on the current data, determine whether the review procedure needs to be initiated? Explain the specific judgment criteria.", + "answer": "No need to initiate a review. Judgment criteria: ① The pressure of 10kPa is within the range of 9.5-10.5kPa; ② The temperature is within the range of -70℃ to -40℃; ③ The RFID read rate of 99.7% is greater than 99%. All three indicators are normal, and the condition of any two indicators being abnormal is not met." + }, + { + "id": 314, + "scenario_code": "3.1", + "instruction": " In the Chang'e-5 mission, the lander is located near Mons Rümker at 43.06°N, 51.92°E on the lunar near side. During the lunar day, the solar elevation angle in this area varies from 5° to 35°, and the solar panels use two-dimensional tracking (azimuth + pitch). It is known that: 1) the area of a single panel is 2.5m², with a photovoltaic conversion efficiency of 28%; 2) the albedo of the lunar surface is 0.12; 3) the solar constant is 1368W/m²; 4) terrain blocking reduces the effective sunlight exposure time by 18% each day.", + "question": "If the current solar elevation angle is 25° and the azimuth deviation is 10°, calculate the actual power generation of a single panel at this time (considering the contributions of direct sunlight and albedo, ignoring diffuse reflection loss). Hint: Effective illumination intensity = solar constant * sin(elevation angle), albedo contribution = solar constant * albedo * [1 - sin(elevation angle)] / 2.", + "answer": "Direct light intensity = 1368 * sin(25°) = 583.6W/m²; Albedo intensity = 1368 * 0.12 * (1 - sin(25°)) / 2 = 49.2W/m²; Total effective intensity = (583.6 + 49.2) * cos(10°) = 622.5W/m²; Power generation = 622.5 * 2.5 * 0.28 = 435.8W" + }, + { + "id": 315, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the Moon's south pole, it is necessary to allocate shared energy to 3 devices (seismometer, magnetometer, spectrometer). The total power of the energy system is 120W, with the seismometer having a base power consumption of 15W (peak 25W), the magnetometer 10W (peak 20W), and the spectrometer 30W (peak 50W). All devices must ensure basic power supply, and the total power at any time must not exceed 120W. Peak operation periods for the devices: the seismometer starts for 10 minutes every 2 hours, the magnetometer for 5 minutes every hour, and the spectrometer for 30 minutes every 3 hours.", + "question": "If at this moment the seismometer is at peak, the magnetometer is at base, and the spectrometer is at peak, is the power system overloaded? If overloaded, which device's power needs to be reduced to the base value to meet the constraints at least? ", + "answer": "Overloaded; the power of the spectrometer needs to be reduced to the base value" + }, + { + "id": 316, + "scenario_code": "1.8", + "instruction": " When deploying the drilling equipment, it was found that the local lunar soil bearing capacity is only equivalent to 300N under Earth's gravity (equipment weight 200N + operation reaction force 150N). There are three adjustment plans: A) Expand the support area to twice the original size; B) Reduce the drilling speed to decrease the reaction force to 100N; C) Move to a nearby area with a measured bearing capacity of 450N (40 minutes of travel time). It is known that the original support area is 0.1m^2, and the lunar soil bearing capacity formula is: Allowable pressure P_max = Actual pressure P = (equipment weight + operation reaction force) / support area.", + "question": "From the perspective of bearing capacity alone, do plans A and B each meet the requirements? If not, calculate the specific parameter values that need to be adjusted (the support area required for plan A / the reaction force that needs to be reduced for plan B).", + "answer": "Plan A meets the requirement (P=1750Pa < P_max=3000Pa); Plan B does not meet the requirement (reaction force ≤100N needed)." + }, + { + "id": 317, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander detected a warning of a solar proton event eruption at the edge of the Shackleton crater, with high-energy particle flow expected to reach the lunar surface in 30 minutes. The lander needs to urgently initiate a risk avoidance procedure: 1) Currently located at the boundary of the permanent shadow area (temperature -170°C); 2) The safe area is a depression 600m to the west, and communication will be lost after it is interrupted, resulting in no ground commands; 3) Maximum climbing ability is 15°, with two 10° slopes on the path; 4) The upper limit of emergency movement speed is 0.15m/s.", + "question": "Determine whether the lander can reach the safe area within the warning time? Explain the key constraint conditions.", + "answer": "1) Shortest time T_min=600/0.15=4000s≈66.7min>30min; 2) Slope 10°<15° meets the mobility capability. Conclusion: It cannot arrive within the warning time, and the on-site protection mode needs to be activated." + }, + { + "id": 318, + "scenario_code": "2.10", + "instruction": " The lunar rover plans to perform millimeter-level spectral detection on an olivine outcrop with a diameter of 20cm. It is known that: 1) The positioning error of the visual navigation system σ_v=5cm(3σ); 2) UWB beacons are deployed 5m away from the target point, with a ranging error σ_r=1cm; 3) IMU attitude angle error ±0.5°; 4) The working distance requirement for the robotic arm is 50±2cm.", + "question": "Calculate the theoretical minimum positioning error of the integrated navigation system and determine whether it can meet the detection requirements? Provide the error synthesis formula.", + "answer": "1) Combined error σ_comb=sqrt(σ_v^2 + (σ_r*5/50)^2)=sqrt(25+0.01)=5.01cm; 2) IMU introduces angular error Δd=50*tan(0.5°)≈0.44cm; 3) Total error≈5cm> detection requirement (20cm/10=2cm). Conclusion: Does not meet the requirement, need to add near-field visual assistance." + }, + { + "id": 319, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. It is known that the container maintains a nitrogen environment of 40kPa (±5% allowable fluctuation), and the temperature recorder shows that it remains within the range of -20°C to +10°C throughout the process. The handover procedure stipulates: if the following conditions are met simultaneously ① pressure > 38kPa and < 42kPa, ② extreme temperature duration < 30 minutes, ③ RFID tag read success rate ≥ 99%, it is deemed qualified. The inspection data is as follows: the average pressure over the past 8 hours is 39.8kPa (fluctuation ±1.2kPa), -25°C lasted for 25 minutes, and the RFID read success rate is 99.2%.", + "question": "Based on the handover standards and actual measurement data, determine whether the sample container has passed the integrity check? Explain the basis for each judgment.", + "answer": "Passed the inspection. Basis for judgment: ① The pressure of 39.8±1.2kPa is within the allowable range of 38~42kPa; ② Although -25°C exceeds the range, the duration of 25 minutes is less than the 30-minute upper limit; ③ The RFID read success rate of 99.2% meets the minimum requirement of 99%. All conditions meet the standards." + }, + { + "id": 320, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the lunar soil in this area are: the top 0-30cm is loose fine particles (viscosity coefficient k=0.8), and there is a high-hardness basalt layer at 30-50cm (Mohs hardness 6.5). The probe carries three sampling tools: ① Rotary impact drill (suitable for hardness > 5, power consumption P1=25W*min/cm), ② Vibration corer (suitable for hardness 3-6, P2=18W*min/cm), ③ Electric shovel (only suitable for loose layers, P3=5W*min/cm). The current remaining energy budget is 1200W·min.", + "question": "If it is necessary to collect a complete 0-50cm profile sample without exceeding the energy consumption, how should the tools be combined and what is the maximum allowable working depth for each tool calculated to be used? ", + "answer": "Combination plan: Use the electric shovel to collect 0-30cm + Use the vibration corer to collect 30-50cm. Calculation process: Electric shovel energy consumption = 5 * 30 = 150W·min; Remaining energy for the vibration corer = 1200 - 150 = 1050W·min; Maximum depth for the vibration corer = 1050 / 18 ≈ 58.3cm (actual requirement 20cm does not exceed the limit)." + }, + { + "id": 321, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, energy supply becomes a critical constraint. In the current mission, there is a mobile power module (output power 500W) that needs to power three devices: a seismometer (continuous power consumption 120W), a drilling sampling device (peak power consumption 350W, working cycle 30%), and a lunar dust monitoring instrument (continuous power consumption 80W). The power module uses a priority scheduling strategy: 1) Life support systems (not involved in this scenario); 2) Scientific data acquisition equipment; 3) Mobile systems. When the drilling device is working, it triggers a temporary high-priority mode, monopolizing the required power.", + "question": "If the drilling device starts working, can the lunar dust monitoring instrument maintain normal operation? Please explain with calculations.", + "answer": "No. When the drilling device is working, it requires 350W, and the total power of the power module is 500W, leaving available power of 500W - 350W = 150W. The total continuous power consumption of the seismometer and the lunar dust monitoring instrument is 120W + 80W = 200W > 150W. According to the priority strategy, the lunar dust monitoring instrument will be powered off." + }, + { + "id": 322, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the lunar surface, located in a flat area at coordinates (12.3N, 34.5E). The mission center has planned a route to a scientific target point (12.5N, 34.7E), with a total path length of 800 meters. The energy consumption model of the lunar rover is: E = 0.15 * d + 2, where E is the total energy consumption (Wh), and d is the travel distance (meters). The lunar rover currently has a remaining power of 150Wh, and its travel speed is 0.1m/s. The lunar day is about to end, and it is expected to enter the lunar night in 2 hours, during which it cannot be charged.", + "question": "If Yutu-2 immediately sets off for the target point and immediately enters hibernation upon arrival, will the remaining power after completing the task be sufficient to last until the next lunar day? (Assuming the power consumption in hibernation mode is 5W, and the lunar night lasts for 14 Earth days.)", + "answer": "Not enough. Calculation process: 1) Travel time = 800m / 0.1m/s = 8000s ≈ 2.22h; 2) Travel energy consumption = 0.15*800 + 2 = 122Wh; 3) Hibernation energy consumption = 5W * (14*24h) = 1680Wh; 4) Total requirement = 122 + 1680 = 1802Wh > 150Wh" + }, + { + "id": 323, + "scenario_code": "2.2", + "instruction": " The Chang'e-4 lander is conducting exploration in the permanently shadowed area of the Von Kármán crater, using a multi-sensor fusion scheme for the navigation system: visual odometry positioning error ±3m/100m, IMU drift error 1m/min, and LiDAR SLAM absolute accuracy ±0.5m. The current system-recorded position is (45.2S, 176.3W), with the IMU having been continuously operating for 18 minutes without correction, the visual odometry having cumulatively traveled 120m, and the LiDAR's last global correction being 10 minutes ago.", + "question": "Calculate the confidence interval radius of the current positioning result (assuming each error source is independent and follows a uniform distribution).", + "answer": "4.27m. Calculation process: 1) Visual error = 120 * (3/100) = 3.6m; 2) IMU error = 1 * 18 = 18m; 3) SLAM error = 0.5m; 4) Total error = sqrt(3.6^2 + 18^2 + 0.5^2) = 18.36m; 5) Confidence radius of uniform distribution = 18.36 / sqrt(3) = 10.6m" + }, + { + "id": 324, + "scenario_code": "1.4", + "instruction": " The lunar surface energy grid needs to power three devices simultaneously: an X-ray spectrometer (continuous power 80W, priority 1), a mobile exploration vehicle (peak power 150W/10 minutes, priority 2), and a lunar dust removal device (pulse power 300W/2 minutes, priority 3). The solar array outputs 200W, and the battery can provide an additional 100W of continuous power or 300W of short-term (<15 minutes) power. The spectrometer has been running for 20 minutes, and the exploration vehicle is about to start a 10-minute operation.", + "question": "Calculate the maximum operational time of the lunar dust removal device during this period and explain the power distribution plan.", + "answer": "The maximum operational time is 2 minutes: the spectrometer requires 80W (must be guaranteed) + the exploration vehicle requires 150W (using 100W from the battery + 50W from the solar array), leaving 150W from the solar array + 200W short-term capacity from the battery to support the 300W pulse load for 2 minutes." + }, + { + "id": 325, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover for rock sampling, there is a 1.3-second delay in the transmission of ground commands. When the vehicle approaches the target at a speed of 0.2m/s, the live video shows that it is 2.6 meters away from the target rock. The control system uses a predictive algorithm to compensate for the delay, assuming the vehicle's braking deceleration is 0.1m/s^2.", + "question": "Calculate the estimated coasting distance when an immediate stop command is sent, and determine whether a deceleration command needs to be sent in advance.", + "answer": "Coasting distance = 0.2 * 1.3 + (0.2^2) / (2 * 0.1) = 0.26 + 0.2 = 0.46m < 2.6m, no need to decelerate in advance." + }, + { + "id": 326, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing exploration tasks on the far side of the Moon, located at coordinate point A (10°N, 120°E). The mission planning system requires it to reach target point B (12°N, 122°E) within 3 hours to conduct scientific sampling. Known: 1) The lunar surface driving energy consumption model is E = 0.15*d + 2 (d is in kilometers, E is in watt-hours); 2) The current remaining battery energy is 50 watt-hours; 3) The average driving speed on the lunar surface is 0.5 km/h; 4) The straight-line distance from A to B is 30 km, but it must detour around a crater with a diameter of 5 km.", + "question": "If the shortest obstacle-avoidance path (half-circle detour around the crater + straight segment) is chosen, calculate whether the total path length meets the time and energy constraints? Provide the specific calculation process.", + "answer": "The half-circle detour path adds a length = π*5/2 ≈ 7.85km; total path d=30+7.85=37.85km; time required t=37.85/0.5=75.7 hours > 3 hours; energy consumption E=0.15*37.85+2=7.68 watt-hours < 50 watt-hours. Conclusion: Meets the energy constraint but does not meet the time constraint." + }, + { + "id": 327, + "scenario_code": "2.7", + "instruction": " When the lunar rover is driving near the terminator and receives a solar proton event warning, it needs to reach the nearest safe shelter (1.8 km away) within 20 minutes. It is known that: 1) The maximum speed in emergency mode is 1 km/h; 2) The steering energy consumption coefficient k=0.2 (additional energy consumption per steering); 3) The basic energy consumption model E=0.12*d; 4) The current remaining energy is 5 watt-hours. The path planning shows that 3 60° turns are required.", + "question": "Calculate whether the risk avoidance plan meets both time and energy constraints? List the basis for the judgment.", + "answer": "Time judgment: t=1.8/1=1.8 hours=108 minutes>20 minutes; Energy judgment: E_total=0.12*1.8+3*0.2=0.216+0.6=0.816 watt-hours<5 watt-hours. Conclusion: Meets the energy constraint but does not meet the time constraint." + }, + { + "id": 328, + "scenario_code": "3.1", + "instruction": " The Chang'e-7 lander is located at the edge of the Shackleton crater in the lunar south pole (latitude 85°S), and its solar panels use a two-dimensional tracking system. According to the lunar calendar, it is currently the 5th day of the lunar day, and the solar elevation angle changes over time according to the formula: h(t) = 30° + 10° * sin(π*t/12), where t is the local time (0-24 hours). Terrain obstruction analysis shows that there is a 15° mountain obstruction angle from t=8 to 10 hours. The maximum output power of the solar panels P_max = 200W * cos(θ), where θ is the angle between the incident sunlight and the normal.", + "question": "If power generation is predicted at t=9 hours, what is the actual effective solar elevation angle at that time? What is the corresponding instantaneous theoretical power output at that time? ", + "answer": "The actual effective solar elevation angle = h(9) - obstruction angle = (30° + 10° * sin(π*9/12)) - 15° = 35° - 15° = 20°. The instantaneous theoretical power output = 200W * cos(90° - 20°) = 200W * sin(20°) ≈ 68.4W" + }, + { + "id": 329, + "scenario_code": "3.6", + "instruction": " The Yutu-2 rover is about to enter the lunar night hibernation mode, and its thermal insulation system uses an electric heating + multi-layer insulation composite solution. It is known that: 1) the minimum operating temperature allowed for key electronic equipment is -40°C; 2) the lunar night environmental temperature is -180°C; 3) the equivalent thermal resistance of the insulation layer R=2 K/W; 4) the heat dissipation power of the equipment Q_device=3W; 5) the remaining battery charge SOC=35%, total capacity 120Wh, the discharge cut-off voltage protection is set at 20% SOC. The efficiency of the electric heater η=95%, operating voltage 28V.", + "question": "If the equipment temperature needs to be maintained above -40°C for 14 Earth days, calculate the minimum operating current of the electric heater (保留两位小数, retain two decimal places)?", + "answer": "Total heat required Q_total = (T_equipment - T_environment)/R - Q_device = (233K)/2K/W - 3W = 113.5W. Electric heating power P_heater = Q_total/η = 113.5W/0.95 ≈ 119.47W. Operating current I = P_heater/V = 119.47W/28V ≈ 4.27A" + }, + { + "id": 330, + "scenario_code": "3.8", + "instruction": " In the Chang'e-6 sample return mission, the lander needs to operate on the lunar surface for 48 hours, with the energy budget allocated as follows: 1) Scientific instruments consume 60Wh continuously; 2) The sampling robotic arm consumes 5Wh per action (planned for 15 actions); 3) The data transmission system consumes 8Wh per transmission (planned for 6 transmissions); 4) The thermal control system has a basic power consumption of 2W; 5) 20Wh of emergency redundant power is reserved. The average daily power generation of the solar array is 280Wh, and the initial SOC (State of Charge) of the battery is 60% (total capacity 300Wh).", + "question": "Calculate the energy supply and demand difference during the mission period (considering 12 hours of lunar night without sunlight), and determine whether the operation plan needs to be adjusted.", + "answer": "Total energy consumption = 60 + (5*15) + (8*6) + (2*48) + 20 = 60+75+48+96+20 = 299Wh. Total power supply = (280/24)*12 hours of sunlight + (300*0.6) initial charge = 140+180=320Wh. Difference = 320-299=+21Wh (surplus), no need to adjust the plan." + }, + { + "id": 331, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover obtained the following remote sensing data near the Von Kármán crater: Point 1 (coordinates X12,Y34) has a 68% probability of being KREEP rock and 85% of the time is illuminated by the sun; Point 2 (X15,Y37) has a 92% probability of being breccia and 55% of the time is illuminated; Point 3 (X18,Y39) has a 77% probability of being volcanic glass and 72% of the time is illuminated. The scientific priority weights are: rock rarity 60%, and sunlight conditions 40%. The rover's maximum single-day movement distance is 5 coordinate units, and it is currently located at X10,Y30.", + "question": "Based on scientific value and accessibility, determine the optimal exploration path and target point priority order for the next day (a comprehensive score needs to be calculated).", + "answer": "Priority order: Point 2 > Point 3 > Point 1. Calculation process: 1) Point 2 score = 92*0.6 + 55*0.4 = 77.2; Point 3 = 77*0.6 + 72*0.4 = 75; Point 1 = 68*0.6 + 85*0.4 = 74.8. 2) Movement distance: To Point 2 requires sqrt((15-10)^2 + (37-30)^2) = 8.6 > 5, not reachable; To Point 3 requires sqrt((18-10)^2 + (39-30)^2) = 12 > 5, not reachable; To Point 1 requires sqrt((12-10)^2 + (34-30)^2) = 4.47 < 5, reachable. Therefore, only Point 1 can be reached the next day, but the highest comprehensive score is for the unreachable Point 2." + }, + { + "id": 332, + "scenario_code": "4.9", + "instruction": " When the ascent vehicle transfers the sample container to the lander, the following conditions must be met: 1) The internal temperature of the container must be maintained at -50±5°C; 2) The RFID tag signal strength must be ≥-70dBm; 3) The sealing pressure must be <0.01Pa for 30 seconds. The current telemetry data is: temperature -48°C, RFID strength -68dBm, sealing pressure 0.008Pa has been maintained for 25 seconds. The remaining window for the ascent vehicle is 120 seconds, and the transfer requires at least 40 seconds (including 10 seconds for the robotic arm to align, 15 seconds to lock, and 15 seconds to verify).", + "question": "Determine whether the transfer procedure can be initiated immediately under the current conditions? If not, specify the conditions that need to be met and whether the remaining time window is sufficient.", + "answer": "The transfer cannot be initiated immediately. The sealing pressure condition needs to be maintained for a full 30 seconds (5 more seconds are needed). The remaining window of 120 seconds > (5 seconds wait + 40 seconds transfer) = 45 seconds, which is sufficient. The current other parameters are all within the required range: temperature -48°C is within the range, RFID strength -68dBm > -70dBm." + }, + { + "id": 333, + "scenario_code": "5.7", + "instruction": " The solid-state storage of the 'Yutu-2' rover uses NAND Flash chips with a total capacity of 128 GB and a block size of 4 MB. The write amplification factor is 1.5, and the average erase endurance is 3000 cycles/block. The total data written so far is 80 TB, and the wear-leveling algorithm evenly distributes write operations across all blocks. The storage retains 20% redundant space for bad block replacement.", + "question": "Calculate the current average wear level (percentage of life consumed) of the storage, and determine whether the bad block replacement mechanism needs to be activated.", + "answer": "Total writable data volume = (128 GB / 4 MB) * (3000 cycles/block) * (4 MB/cycle) / (write amplification factor 1.5) = (32768 blocks) * 3000 * 4 / 1.5 ≈ 262 PB. Percentage of life consumed = (80 TB / 262 PB) * 100 ≈ 0.03%. No need to activate the bad block replacement mechanism: 1) Wear level is extremely low; 2) 20% of redundant space is unused." + }, + { + "id": 334, + "scenario_code": "2.7", + "instruction": " The lunar orbiter has detected an impending solar proton event (expected to reach the lunar surface in 30 minutes), and the rover operating in the South Pole-Aitken Basin has received a level three alert. The rover is currently at the edge of a permanent shadow zone, 25 meters away from the nearest shelter (an entrance to a lava tube with a diameter of 3 meters), with a regular travel speed of 0.04m/s. Safety protocols require: after entering the shelter mode, all scientific payloads must be shut down, only basic communication (power consumption reduced from 200W to 50W) must be maintained, and at least 400Wh of power must be reserved to maintain a 72-hour hibernation. The rover's current power is 1500Wh, and the solar panels have been retracted.", + "question": "Determine whether the rover can complete the sheltering before the proton event arrives? If the emergency acceleration mode (speed increased to 0.08m/s but power consumption increased to 300W) is used, does it meet the power reserve requirements? ", + "answer": "Regular mode: travel time=25/0.04=625 seconds≈10.4 minutes<30 minutes, can arrive; energy consumption=200W*(10.4/60)≈34.7Wh, remaining 1500-34.7=1465Wh>400Wh, meets the requirement. Emergency mode: travel time=25/0.08=312 seconds≈5 minutes<30 minutes; energy consumption=300W*(5/60)=25Wh, remaining 1500-25=1475Wh>400Wh, also meets the requirement but there is no need to accelerate." + }, + { + "id": 335, + "scenario_code": "5.7", + "instruction": " The 128TB solid-state drive carried by the Chang'e-7 orbiter uses NAND Flash chips, with a single block erase/write life of 3000 cycles. The daily write volume is 1.2TB (evenly distributed), and a dynamic wear-leveling algorithm is used to distribute hot spot write requests to cold areas. The erase/write count of the oldest block has reached 2800 times, and the average wear deviation exceeds 15%. The storage redundancy is designed to be 25%.", + "question": "Calculate the expected lifespan of the storage (in months) under the current write pattern, and propose two specific measures to extend its lifespan.", + "answer": "Expected lifespan = (3000-2800)/(1.2TB*30/128TB*15%) = 13 months. Extension measures: 1) Optimize data compression algorithms to reduce daily write volume to below 0.9TB; 2) Improve wear-leveling strategy to control deviation within 5% (lifespan can be extended to (3000-2800)/(1.2TB*30/128TB*5%) = 39 months)." + }, + { + "id": 336, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing patrol tasks on the far side of the moon, located at coordinate point A (10°N, 120°E), and needs to reach scientific target point B (12°N, 122°E). It is known that: 1) the straight-line distance between the two points is 30km; 2) the average driving speed of the lunar rover is 0.1km/h; 3) the energy consumption model is E=0.05*d+2 (d is the driving distance, unit km, E is the power consumption, unit Wh); 4) the current remaining power is 50Wh; 5) the lunar night will arrive in 100 hours, during which time charging is not possible.", + "question": "If Yutu-2 chooses a straight path to the target point B, calculate whether the remaining power after arrival meets the safety threshold (≥20Wh), and determine whether it needs to find a temporary charging point along the way.", + "answer": "Total energy consumption E=0.05*30+2=3.5Wh; remaining power=50-3.5=46.5Wh＞20Wh, no temporary charging required." + }, + { + "id": 337, + "scenario_code": "2.2", + "instruction": " The Chang'e-7 lander conducts exploration in the permanently shadowed region at the edge of the Shackleton crater. The navigation system uses multi-sensor fusion: 1) visual odometry positioning error ±3m/100m; 2) IMU drift error 0.1°/h; 3) LiDAR SLAM mapping accuracy ±0.5m. It is known that the distance from the landing point to the scientific target is 200m, during which the IMU operates for 2 hours without any landmark correction opportunities.", + "question": "Calculate the maximum possible positioning error when the rover reaches the target (considering the linear superposition of each sensor's error)?", + "answer": "Visual error = 200 * (3/100) = 6m; IMU angle error = 0.1 * 2 = 0.2°, converted to displacement ≈ 200 * sin(0.2°) ≈ 0.7m; SLAM error = 0.5m; Total error = 6 + 0.7 + 0.5 = 7.2m" + }, + { + "id": 338, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 rover performs exploration tasks in the South Pole-Aitken Basin of the Moon, where the terrain is complex with multiple craters blocking the view. The rover is equipped with a dual-axis adjustable solar panel, with a maximum tracking efficiency of 92%. The current lunar day is 14 Earth days, and the solar elevation angle varies over time according to the function theta(t) = 30 * sin(pi * t / 336), where t is the hour (0-336), and theta is the solar elevation angle. At a certain moment t=48h, there is an obstacle 1.5 meters high 2 meters in front of the rover, and the solar panel is installed at a height of 0.8 meters. It is known that the received power per unit area without obstruction is P0 = 1.353 kW/m^2 * sin(theta).", + "question": "Calculate the actual received power of the solar panel at t=48h (unit W/m^2), considering terrain obstruction and tracking efficiency (保留两位小数). Hint: First calculate the solar elevation angle, then determine if it is obstructed.", + "answer": "First, calculate the solar elevation angle: theta(48) = 30 * sin(pi * 48 / 336) = 12.37 degrees. Determine obstruction: the length of the obstacle's shadow = 1.5 / tan(12.37°) ≈ 6.83 meters > 2 meters distance, so it is completely obstructed. Actual received power = P0 * efficiency * sin(theta) * 0 (obstructed) = 0 W/m^2" + }, + { + "id": 339, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 lunar far side sample return mission, the lander is located in the pre-selected landing area at 177.6° East longitude and 45.5° South latitude on the far side of the Moon. The current geometric relationship between the ground station (Beijing station) and the far side of the Moon is: the angle between the Earth-Moon center line and the ground station-lander line is 12°, and the ground station elevation angle is 5°. It is known that the Queqiao relay satellite is operating in the Halo orbit at the Earth-Moon L2 point, about 65,000 kilometers from the Moon's center. The X-band antenna gain of the relay satellite is 38 dB, the transmission power of the lander is 10W, the transmission antenna gain is 15 dB, the system noise temperature is 300K, and the communication rate is required to reach 2 Mbps when the required signal-to-noise ratio is not less than 10 dB.", + "question": "Calculate whether the ground station can establish an effective communication link with the lander through the Queqiao relay satellite under the current conditions? Verify whether the link budget meets the requirements (free space loss formula: Lfs=92.45+20*lg(f)+20*lg(d), where f is in GHz and d is in km).", + "answer": "An effective link can be established. Calculation process: 1) Free space loss Lfs=92.45+20*lg(7.2)+20*lg(6.5)=92.45+17.15+16.26=125.86dB; 2) Received power Pr=10dBW+15dB+38dB-125.86=-62.86dBW; 3) Received noise power spectral density N0=-228.6+10*lg(300)=-204.77dBW/Hz; 4) Required Eb/N0=10dB corresponds to SNR=10+10*lg(2*10^6)=73dB; 5) Actual SNR=Pr-N0=-62.86-(-204.77)=141.91dB > 73dB, meeting the requirement." + }, + { + "id": 340, + "scenario_code": "3.4", + "instruction": " Yutu-2 needs to perform three tasks simultaneously during the lunar day: ① Continuous operation of the X-ray spectrometer for 2 hours (power consumption 35W); ② Sample collection by the robotic arm for 15 minutes (peak power consumption 120W); ③ Data transmission window for 1 hour (power consumption 75W). The power system constraints are: instantaneous power consumption must not exceed 100W, the battery pack capacity is 300Wh (current SOC=80%), and the solar panel provides a continuous power supply of 60W. All tasks must be completed within 8 hours and cannot be interrupted.", + "question": "Design a task scheduling plan that meets the power constraints, prioritizing the integrity of the spectrometer data, and explain the changes in the battery SOC at key time points.", + "answer": "Plan: ① Spectrometer 0-2h (35W) + solar power 60W → battery charges 25W*2h=50Wh → SOC rises to 86.7%; ② Robotic arm 2:00-2:15 (120W) → battery discharges 60W*0.25h=15Wh → SOC drops to 85%; ③ Data transmission 3:00-4:00 (75W) → battery discharges 15W*1h=15Wh → SOC drops to 83.3%. The remaining time, the solar panel continues to charge until the battery reaches full capacity of 300Wh." + }, + { + "id": 341, + "scenario_code": "3.6", + "instruction": " The Chang'e-7 lander enters the lunar night phase (-180°C) and needs to maintain the core cabin temperature ≥ -40°C. The thermal control system parameters are as follows: ① Cabin thermal capacity C=120 kJ/°C; ② Electric heater power P_h=200W; ③ Isotope heat source provides constant heat Q_r=80W; ④ Outer insulation material thermal conductivity U=0.05 W/(m^2·K), surface area A=8 m^2, external temperature T_out=-180°C. Initial cabin temperature T0=20°C. Ignore other heat exchanges.", + "question": "Calculate the time (hours) required for the cabin temperature to drop to the critical value of -40°C when relying solely on the isotope heat source, using the formula: heat loss rate Q_loss = U*A*(T_in - T_out).", + "answer": "Critical heat loss rate Q_loss = 0.05*8*(-40+180)=56W; net heat loss=56-80=-24W (net heat supply). Heat required to lower the temperature ΔQ=C*ΔT=120*(20+40)=7200 kJ; time t = ΔQ / (net heat supply) = 7200000 / (24*3600) ≈ 83.33 hours" + }, + { + "id": 342, + "scenario_code": "5.7", + "instruction": " The 'Queqiao-2' relay satellite uses 128 GB NAND flash memory to store scientific data, with block sizes of 4 KB storage units, and an average write-erase life of 3000 cycles. The current wear-leveling algorithm ensures that the write cycle difference among blocks does not exceed ±15%. The average daily write volume is 50 GB, of which 40% is temporary cache data (deleted after 24 hours). The file system reserves 10% redundant space for bad block replacement.", + "question": "Calculate the theoretical shortest lifespan (in days) of the storage under the worst wear condition (all writes concentrated on the least erased blocks)?", + "answer": "Daily effective write volume = 50 * (1 - 40%) = 30 GB; actual number of blocks written per day = (30 * 1024) / 4 = 7680 blocks/day. Initial write count of the least erased block = 3000 * (1 - 15%) = 2550 times. Remaining available write count = 2550 times; theoretical lifespan = 2550 / (7680 / (128 * 0.9 * 1024 / 4)) ≈ 2550 / (7680 / 294912) ≈ 2550 * 38.4 ≈ 97920 days ≈ 268 years (Note: This result is abnormal due to the extreme simplification of the assumption)." + }, + { + "id": 343, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, a shared energy grid needs to be established. The current system includes: 1 solar main power unit (peak output 1200W), 2 radioisotope thermoelectric generators (each 400W), 3 scientific payloads (A: 300W continuous, B: 200W intermittent, C: 500W peak). The communication relay requires a stable 200W, and the thermal control system has a base power consumption of 150W. All equipment is managed by an intelligent power distribution unit, where scientific payload C only operates during the lunar day and has the highest priority.", + "question": "If the radioisotope thermoelectric generators need to be maintained in turn during the lunar night (only one works at a time), and the communication relay suddenly requests an additional 100W bandwidth, can the system maintain at least 30 minutes of safety redundancy? Assume the current available capacity of the energy storage battery is 180Wh.", + "answer": "No. Available power during the lunar night = 400W (thermoelectric generator) + 1200W (solar) = 1600W; base load = 150W (thermal control) + 200W (communication) = 350W; sudden demand = 100W; remaining power = 1600 - 350 - 100 = 1150W > scientific payload A/B demand (300 + 200 = 500W), but the battery needs to support an additional 100W * 0.5h = 50Wh > 180Wh * 10% (safety redundancy threshold 18Wh)." + }, + { + "id": 344, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth. The 'Queqiao' relay satellite is positioned in a Halo orbit at the Earth-Moon L2 point, approximately 65,000 kilometers from the lunar surface. The X-band antenna gain of the relay satellite is 42 dBi, the lander's transmission power is 10 W, and the antenna gain is 38 dBi, operating at a frequency of 8 GHz. The free space path loss formula is: L = 20 * log10(4 * pi * d / lambda), where d is the distance and lambda is the wavelength (speed of light c=3*10^8 m/s). The current communication window lasts for 2 hours, and 1.5 GB of scientific data needs to be transmitted.", + "question": "Calculate the free space path loss (dB) at the current Earth-Moon distance, and determine if it meets the minimum receiving power requirement of -110 dBm (ignoring other loss factors)?", + "answer": "Wavelength lambda = c / f = 3*10^8 / (8*10^9) = 0.0375 m; Path loss L = 20 * log10(4 * pi * 6.5*10^7 / 0.0375) ≈ 214.6 dB. Received power Pr = Pt + Gt + Gr - L = 10 dBW + 38 dBi + 42 dBi - 214.6 dB = -124.6 dBW = -94.6 dBm > -110 dBm, meeting the requirement." + }, + { + "id": 345, + "scenario_code": "5.4", + "instruction": " During the lunar day, the Yutu-2 rover establishes a communication link with the ground station via the relay satellite. A sudden solar proton event causes the X-band link to be interrupted. The remaining storage capacity of the rover's memory chip is 200 MB, and the current cache has 150 MB of untransmitted data (priority: 60% is level 3 data, 30% is level 2, 10% is level 1). System strategy: Level 1 data must be transmitted in full, levels 2 and 3 allow 50% compression. The backup UHF link rate is only 20 kbps, and the next communication window is expected to last 30 minutes.", + "question": "Calculate the total amount of data (MB) that needs to be transmitted after adopting the compression strategy, and determine if the backup link can complete the transmission within the window period.", + "answer": "Level 1 data volume = 150*10% = 15 MB (complete transmission); Level 2 = 150*30% = 45 MB (compressed to 22.5 MB); Level 3 = 150*60% = 90 MB (compressed to 45 MB). Total data volume = 15 + 22.5 + 45 = 82.5 MB. UHF link 30-minute transmission volume = 20*60*30/8/1024 ≈ 4.39 MB < 82.5 MB, unable to complete transmission." + }, + { + "id": 346, + "scenario_code": "1.8", + "instruction": " When deploying a seismic array, it was found that the local lunar soil bearing capacity is only equivalent to 3 kPa under Earth's gravity, while the equipment base requires 4 kPa. The engineers decided to use a distribution plate with a diameter 30% larger, and the bearing capacity formula is: q = q_original * (D_new/D_original)^1.5. The original design diameter is 20 cm, and the distribution plate area is proportional to the square of the diameter.", + "question": "Calculate whether the new distribution plate can meet the bearing capacity requirement? If not, by what minimum percentage does the diameter need to be increased further? (Round to two decimal places).", + "answer": "New diameter = 20 * 1.3 = 26 cm; q_new = 3 * (26/20)^1.5 = 3 * 1.482 ≈ 4.446 kPa > 4 kPa meets the requirement. No further increase in diameter is needed." + }, + { + "id": 347, + "scenario_code": "1.4", + "instruction": " When deploying scientific payloads in the permanently shadowed regions of the lunar south pole, a temporary energy-sharing network needs to be established. There are currently 3 devices: A (drilling sampler, peak power 300W), B (spectrometer, peak power 150W), C (data transmission terminal, peak power 200W). The shared energy bus has a maximum output power of 500W and must reserve 20% redundant power for emergencies. The operating modes of the devices are: A and B do not operate simultaneously, C must run continuously but can be downgraded to 100W. During the lunar day, solar power supply is stable, and during the lunar night, it switches to nuclear battery power (total capacity limited to 2kWh).", + "question": "If continuous operation for 4 hours is required during the lunar night phase, and device A needs to run for 2 hours, device B for 1.5 hours (not overlapping with A), and C maintains full power operation. Is this energy distribution plan feasible? If not, how should the downgrading strategy for device C be adjusted to meet all constraints? ", + "answer": "Total energy consumption of the initial plan: A(300W*2h)+B(150W*1.5h)+C(200W*4h)=600+225+800=1625Wh>2kWh. Device C needs to be downgraded to 100W operation, at which point the total energy consumption=600+225+400=1225Wh<2kWh, and the peak power 300W(A)+100W(C)=400W<500W*80%=400W, meeting all constraints." + }, + { + "id": 348, + "scenario_code": "1.5", + "instruction": " The Yutu-2 rover needs to remotely control the robotic arm to collect rock samples with a 1.3-second communication delay. The end-effector positioning accuracy of the robotic arm is required to be ±5mm, and its motion model is v(t)=0.02*t^2+0.1 (unit m/s), where t is time in seconds. After the ground command is issued, it needs to go through uplink delay + execution time + downlink delay to receive feedback. The robotic arm's initial position is 0.78 meters away from the target point, and the ground sends an acceleration command, receiving a confirmation signal after 2.6 seconds.", + "question": "Calculate whether the deviation between the actual position and the expected position of the robotic arm is within the tolerance range? The expected trajectory is uniform motion v=0.15m/s.", + "answer": "Actual movement time=(2.6s-1.3s)/2=0.65s (deducting round-trip delay). Actual displacement=integral(0.02*t^2+0.1)dt from 0 to 0.65=0.02/3*0.65^3+0.1*0.65=0.00183+0.065≈0.0668m. Expected displacement=0.15*0.65=0.0975m. Deviation=0.0975-0.0668=0.0307m=30.7mm>±5mm, exceeding the tolerance range." + }, + { + "id": 349, + "scenario_code": "1.8", + "instruction": " The Chang'e-7 lander plans to deploy a seismic instrument network at the edge of an impact crater at 85°S latitude. The measured compressive strength of the lunar soil is 12kPa (safety factor must be ≥3), the mass of each instrument is 8kg, and the base area is 0.25m². The deployment area has local magnetic field interference (strength 50μT, angle with the geomagnetic field 60°), requiring the installation azimuth error to be ≤10° to ensure data validity. The vertical component of the geomagnetic field on the lunar surface is 20μT.", + "question": "Determine whether the selected location meets the mechanical stability requirements for the deployment of the seismometers? If it also needs to meet the magnetic field calibration conditions, calculate the maximum allowable installation azimuth deviation angle.", + "answer": "Mechanical verification: Actual pressure = 8kg * 1.62m/s² / 0.25m² ≈ 51.84Pa < 12kPa / 3 = 4kPa, meeting the requirement. Magnetic field resultant vector = sqrt(50^2 + 20^2 - 2 * 50 * 20 * cos60°) = sqrt(2500 + 400 - 1000) ≈ 43.59μT. Maximum allowable deviation angle = arcsin(10° / 43.59μT) ≈ 13.3°, but the problem limits ≤10°, so take 10° as the final constraint value." + }, + { + "id": 350, + "scenario_code": "3.1", + "instruction": " The Chang'e-5 lander is performing a sampling mission in a certain area on the lunar near side, and its solar wings use a two-dimensional tracking algorithm. According to the lunar ephemeris, the current solar elevation angle is 30 degrees, and the azimuth angle is 45 degrees (due east is 0 degrees). There is a 5-meter-high crater in this area, located 10 meters directly east of the lander. The solar wings are installed at a height of 2 meters, and each wing is 1.5 meters long. It is known that: 1) The power generation when sunlight is direct P0 = 200W; 2) For every 10% increase in the shaded area, the power decreases by 15%.", + "question": "Calculate the actual power generation of the solar wings (first determine whether there is shading, then calculate the shading ratio and power loss).", + "answer": "There is shading. Shadow length = 5m / tan30° ≈ 8.66m < 10m, so the shaded part length = 1.5 - (10 - 8.66) = 0.16m; Shading ratio = 0.16 / 1.5 ≈ 10.67%; Power loss = 15% * 1.067 ≈ 16%; Actual power = 200W * (1 - 0.16) = 168W" + }, + { + "id": 351, + "scenario_code": "3.8", + "instruction": " In the Chang'e-6 mission, the orbiter needs to operate continuously for 24 hours in a 100km lunar orbit, with the following energy budget: 1) Payload operation mode: power consumption 120W (6 hours per day); 2) Data transmission mode: power consumption 300W (2 times per day × 30 minutes); 3) Normal mode: power consumption 60W. The average power generation of the solar panels in orbit is 150W, the battery pack capacity is 500Wh (charge and discharge efficiency 90%), and the initial SOC=100%.", + "question": "Verify whether the energy budget is balanced? If not, calculate the maximum adjustment time for payload operation (other parameters remain unchanged).", + "answer": "Total energy consumption=120W*6h + 300W*1h + 60W*17h=720+300+1020=2040Wh; Total energy supply=150W*24h + (500Wh*0.9)*2=3600+900=4500Wh＞2040Wh→Budget is balanced. No adjustment needed" + }, + { + "id": 352, + "scenario_code": "1.5", + "instruction": " The Yutu-2 rover needs to remotely control the robotic arm to collect lunar rock samples with a communication delay of 1.3 seconds. The positioning error of the robotic arm's end effector follows the formula: error e = 0.05 * v + 0.01 * d (v is the moving speed in cm/s, d is the operating distance in cm). The current sample is located 40cm directly in front of the robotic arm, and the task requires the final positioning error to not exceed 0.5cm.", + "question": "Calculate the highest safe moving speed v_max of the robotic arm to meet the error requirement.", + "answer": "v_max = 8 cm/s" + }, + { + "id": 353, + "scenario_code": "1.2", + "instruction": " In the Chang'e-7 mission, a lunar-based telescope array unit needs to be deployed. This unit consists of a primary mirror module (120kg), a support structure (80kg), and an electronic control box (40kg). Due to the lifting equipment limitations on the lunar surface, the maximum load for each lifting operation is 150kg. The primary mirror module must be installed first to ensure the alignment reference for subsequent components, and the electronic control box must be installed after the support structure to avoid cable pull risks. The lunar operation window lasts 4 hours each time, and the average time to lift a single component is 1.5 hours (including positioning and verification).", + "question": "Considering the weight limit and installation sequence constraints, what is the minimum number of operation windows required to complete the deployment of this array unit? ", + "answer": "3 operation windows" + }, + { + "id": 354, + "scenario_code": "5.4", + "instruction": " Yutu-2 rover experienced an X-band communication interruption during the lunar day. Known facts:\n1. At the time of interruption, a set of high-priority scientific data (12MB) was being transmitted, with 30% already transmitted\n2. The backup UHF band link rate is only 1/5 of the X-band, but is not affected by the current interference\n3. The X-band is expected to recover in 4 hours, but only 3 hours remain in the current lunar day\n4. UHF band transmission requires an additional 10% packet header overhead\n5. The SSD cache has a remaining capacity of 15MB", + "question": "Choose the optimal emergency transmission strategy and calculate the final percentage of data successfully transmitted (保留两位小数, retain two decimal places).", + "answer": "Optimal strategy: Immediately switch to the UHF band to continue transmission. Calculation process:\n1. Remaining data volume for X-band: 12*(1-0.3)=8.4MB\n2. Effective transmission rate of UHF: (8.4/4)*1/5=0.42MB/h\n3. UHF can transmit in 3 hours: 0.42*3=1.26MB (including packet headers, it is 1.26/1.1≈1.15MB)\n4. SSD capacity is sufficient to cache all data (15>8.4)\n5. Total transmission volume ratio: (12*0.3 +1.15)/12≈(3.6+1.15)/12≈39.58% " + }, + { + "id": 355, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the Moon's south pole, energy supply becomes a critical constraint. In the current mission, there is a mobile power module (output power 500W) that needs to power the following devices simultaneously: 1) Seismometer (continuous power consumption 80W); 2) Drilling sampling device (peak power consumption 300W, each operation lasts 10 minutes); 3) Data relay node (base power consumption 50W, additional 100W during transmission). All devices are synchronized through a time-triggered communication protocol, with two 15-minute data transmission windows each day. Drilling operations can be performed up to 3 times per day and cannot overlap with data transmission.", + "question": "If the load on the mobile power module must not exceed 90% of its rated power at any time, how many complete drilling operations can be scheduled daily at most？", + "answer": "2 times" + }, + { + "id": 356, + "scenario_code": "1.5", + "instruction": " In the Chang'e-7 mission, the ground control center needs to remotely operate the lunar rover to complete rock sampling with a 1.3-second delay. It is known that: the positioning accuracy requirement for the end effector of the robotic arm is ±2mm, the maximum moving speed of the rover is 0.1m/s, and the control system uses a predictive algorithm to compensate for the delay, with the position prediction error proportional to the square of the speed: error e = 0.05 * v^2 (unit: mm).", + "question": "When the rover approaches the target at its maximum speed, does the error introduced by the predictive algorithm meet the sampling accuracy requirement？", + "answer": "Not met (the calculated e=0.5mm, but the total error exceeds the limit after adding the 13mm displacement caused by the 1.3-second delay)." + }, + { + "id": 357, + "scenario_code": "1.8", + "instruction": " When deploying a lunar-based telescope, local magnetic field interference needs to be considered. A candidate site has a measured magnetic field strength of 53nT, with an angle of 30 degrees to the equipment's sensitive axis. It is known that the maximum allowable vertical component of the interfering magnetic field for this model of telescope is 20nT, and the interference compensation system can eliminate 80% of the parallel component effect.", + "question": "Does this location meet the telescope deployment requirements? (Hint: Calculate the vertical component and compare it with the threshold value.)", + "answer": "Meets (Vertical component=53*sin(30°)=26.5nT, effective interference after compensation=26.5*(1-0.8)=5.3nT＜20nT)." + }, + { + "id": 358, + "scenario_code": "3.4", + "instruction": " Yutu-2 needs to perform three tasks during the lunar day: ① The X-ray spectrometer operates continuously for 2 hours (power consumption 45W) ② The robotic arm samples 3 times (each start-up peak power 120W for 10 minutes) ③ Data transmission window for 1.5 hours (power consumption 75W). The lithium-ion battery pack has an available capacity of 300Wh, the current SOC=60%, and the real-time power generation of the solar panels P_sun=80W. The energy management strategy stipulates: the battery discharge depth must not be lower than 20%, and when the instantaneous load exceeds 100W, the battery must be used to assist in power supply.", + "question": "Under the condition of not violating the energy constraints, what is the time difference in minutes between the earliest completion time and the latest start time of the three tasks? ", + "answer": "90 minutes" + }, + { + "id": 359, + "scenario_code": "3.6", + "instruction": " The Chang'e-7 lander needs to maintain a constant temperature environment of -40℃ to +10℃ during the lunar night. The total heat dissipation power of key equipment Q_in=15W, and it is wrapped with three layers of composite thermal insulation material (thermal conductivity λ=0.02 W/m·K), with thicknesses of d1=2cm, d2=1cm, and d3=3cm. The external lunar night environment temperature T_env=-180℃, and the constant temperature control is achieved through an electric heater with an efficiency η=95%. Given the Fourier heat conduction formula Q_out = A * ΔT / (Σ(d_i/λ_i)), where A=1.2m² is the surface area.", + "question": "Calculate the minimum electric heating power P_heat required to maintain the target temperature range (round to the nearest integer).", + "answer": "68W" + }, + { + "id": 360, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover encounters a sudden solar proton event during the lunar day, causing an interruption in X-band communication with the relay satellite. Given:\n1. The remaining capacity of the rover's storage chip is 50GB, and the current scientific data generation rate is 100MB/hour;\n2. The communication interruption is expected to last 8 hours;\n3. In emergency mode, UHF band direct connection to Earth can be used, but the bandwidth is only 10kbps;\n4. The maximum data compression rate can reach 5:1 (lossless).", + "question": "To ensure that core data is not lost, please formulate the optimal transmission strategy (must specify the compression method used, transmission priority, and expected data rescue volume).", + "answer": "Strategy:\n1. Enable lossless compression (5:1), reducing the data volume to 20MB/hour\n2. UHF link transmission capability = 8*3600*10e3/8 = 36MB\n3. Prioritize the transmission of key data from the first 4 hours (80MB compressed to 16MB)\nExpected result: Complete preservation of all data from the first 4 hours + some data from the last 4 hours." + }, + { + "id": 361, + "scenario_code": "2.2", + "instruction": " The detector performs SLAM mapping tasks in a permanently shadowed area, using a LiDAR (ranging error ±3cm) and an IMU (attitude angle drift 0.1°/min). The sensor data at the current moment are as follows: the LiDAR measures the distance to the obstacle ahead as 5.62m, and the IMU shows a pitch angle of -2.3°. It is known that the true terrain slope is +1°, and the LiDAR installation pitch angle is +0.5° (relative to the detector body).", + "question": "Calculate the true horizontal distance to the obstacle after correcting for sensor errors (considering the slope, installation angle, and IMU drift, assuming a cumulative operation time of 15 minutes)?", + "answer": "IMU cumulative drift = 0.1 * 15 = 1.5°; actual pitch angle = -2.3° -1.5° +0.5° +1° = -2.3°; horizontal distance d = 5.62 * cos(-2.3°) ≈5.62 *0.999=5.61m (LiDAR error ±3cm ignored)." + }, + { + "id": 362, + "scenario_code": "2.7", + "instruction": " The lunar rover receives a solar proton event warning and needs to reach a 500m radius emergency shelter area within 30 minutes. Current status: 1) maximum speed 0.15km/h; 2) the navigation system can only provide relative position with ±10m accuracy; 3) the shelter area is located in the northeast direction (azimuth 45°) from the current position, but there is an unmapped area with a diameter of 200m on the path.", + "question": "Determine whether the lunar rover can arrive at the edge of the shelter area on time? If not, propose a feasible emergency plan (based on the given constraints)?", + "answer": "Maximum travel distance = 0.15*0.5 = 0.075km = 75m < 500m, cannot arrive on time. Emergency plan: find the nearest terrain cover (such as a crater wall) and use the navigation accuracy of ±10m to position to the side of the cover facing away from the sun." + }, + { + "id": 363, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, a shared energy grid needs to be established. The current system includes: 1 solar main power unit (peak power 1200W, operational during the day), 2 radioisotope thermoelectric generators (RTGs, each continuously outputting 300W), and 3 scientific payloads (A: seismometer 200W continuous; B: spectrometer 150W intermittent, duty cycle 40%; C: drilling device peak 800W but each operation does not exceed 30 seconds). The energy dispatching algorithm must ensure: ① RTGs prioritize supplying critical life support systems (minimum requirement 400W); ② Scientific payloads are prioritized in the order C>A>B; ③ The instantaneous total load must not exceed the grid capacity (1500W). It is currently mid-lunar day, and the solar unit is operating at full load.", + "question": "If it is now necessary to start the drilling device and the spectrometer simultaneously, and the life support system is in basic mode (only requiring 400W), please calculate the remaining available power on the grid and determine whether this operation is allowed.", + "answer": "Available power = Solar power 1200W + total RTG output 600W - life support 400W = 1400W; Required power = Drilling 800W + Spectrometer 150W = 950W; Remaining power = 1400 - 950 = 450W < grid capacity 1500W, so the operation is allowed." + }, + { + "id": 364, + "scenario_code": "1.8", + "instruction": " When deploying a moon-based telescope, it is necessary to monitor local magnetic field interference. The measured magnetic field strength at a certain point is 52nT, while the telescope calibration requires an environmental magnetic field ≤40nT. The active compensation device carried on-site can generate a counter magnetic field, with the intensity calculated by the formula: B_comp = k * I (k=8nT/A, I is the current). Lunar dust coverage can cause the compensation efficiency to decrease by 5% daily.", + "question": "Calculate the initial compensation current value. If the mission cycle is 10 days, to ensure compliance throughout, what should the minimum compensation current be set to on the first day? (Maintain a 10% safety margin.)", + "answer": "Initial compensation requirement: 52nT - 40nT = 12nT; I_initial = B_comp/k = 12/8 = 1.5A; Considering efficiency decline: Remaining efficiency on the 10th day = (1-0.05)^9 = 63%; Final required current = 1.5A/63%*110% = 2.62A" + }, + { + "id": 365, + "scenario_code": "2.9", + "instruction": " The Chang'e-7 lander has deployed a Ultra-Wideband (UWB) navigation beacon network in the lunar south pole. Known: 1) Beacon A coordinates (80°S,90°E), Beacon B (82°S,90°E); 2) UWB ranging error ±3 meters; 3) The lunar rover simultaneously receives ranging data from beacons A and B, which are RA=1205±3m, RB=1808±3m; 4) The propagation speed of UWB signals is the speed of light. The curvature of the lunar surface can be ignored.", + "question": "Based on the dual beacon ranging data, establish a positioning equation set, calculate the most likely position coordinates (x,y) of the lunar rover (establish a local Cartesian coordinate system with Beacon A as the origin), and explain what factors mainly affect the positioning accuracy.", + "answer": "1) A(0,0), B(0,-222km); 2) Equation set: (x^2 + y^2)^0.5 =1205, (x^2 + (y+222000)^2)^0.5 =1808; Solving yields x≈±1056 m, y≈-600 m; 3) The positioning error ellipse's major axis is approximately ±15 m due to ranging error. The main influencing factors are UWB ranging accuracy and beacon geometric distribution (DOP value)." + }, + { + "id": 366, + "scenario_code": "2.10", + "instruction": " The Chang'e-6 sampling robotic arm needs to perform millimeter-level precise positioning on a 5cm diameter ilmenite outcrop. Given: 1) The baseline distance of the stereo vision system is 20cm, focal length is 10mm; 2) Pixel size is 5μm; 3) IMU short-term positioning accuracy is ±1cm; 4) Robotic arm repeat positioning accuracy is ±0.5mm; 5) Lighting conditions in the target area are Earth albedo 0.1lux.", + "question": "Calculate the theoretical achievable positioning accuracy of the vision system (formula: positioning error Δ = (pixel size * target distance) / (focal length * √N), N = number of effective matching feature points ≥ 100), and analyze whether it meets the mission requirements.", + "answer": "Assuming a working distance of 50cm: Δ = (5e-6 * 0.5) / (0.01 * sqrt(100)) = 25μm = 0.025mm. Visual accuracy (0.025mm) + IMU error (10mm) > robotic arm accuracy (0.5mm), a laser rangefinder must be activated to assist in positioning to meet the requirements." + }, + { + "id": 367, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, energy supply becomes a key constraint. In the current mission, a cluster consisting of 3 lunar rovers (LRVs) and 1 fixed scientific station shares a distributed energy system. The system's total output power is 120W, where:\n- Each LRV requires 15W for basic operation (20W additional when moving), with a scientific payload peak of 30W\n- The fixed station requires 25W for basic operation, and an additional 50W for astronomical observation mode\n- Energy allocation uses dynamic priority: mobile tasks > astronomical observation > routine exploration\nThere are currently the following demands:\n1) LRV-1 is executing an urgent sample transport (in motion)\n2) LRV-2 has activated the ground-penetrating radar (peak load)\n3) The fixed station has initiated the comet tracking observation mode", + "question": "If the system needs to reserve 10% power redundancy, can it currently meet all demands? If not, how should it be adjusted.", + "answer": "No. Total demand = LRV-1 (15+20) + LRV-2 (15+30) + fixed station (25+50) = 155W > 120*0.9=108W. According to priority, the scientific payload of LRV-2 should be turned off (-30W), after adjustment the demand is 125W which still exceeds the limit, further the astronomical observation of the fixed station needs to be turned off (-50W), the final demand is 75W which meets the requirements." + }, + { + "id": 368, + "scenario_code": "1.5", + "instruction": " In the Chang'e-7 mission, the ground control center needs to remotely control the robotic arm to complete the sample collection at the edge of a crater. Given:\n- One-way communication delay between Earth and Moon: 1.28 seconds\n- Maximum movement speed of the robotic arm's end: 0.05m/s\n- Target area: a circular flat area with a diameter of 2m\n- Control commands use a predictive compensation algorithm: send the motion trajectory for the next 2.56 seconds (round-trip delay) in advance\nThe current distance from the end of the robotic arm to the target center is 1.2m, with an azimuth error of ±5°.", + "question": "Design a predictive control command to ensure safe arrival, and calculate the required movement time and command parameters.", + "answer": "Movement time t = distance/speed = 1.2/0.05 = 24 seconds. The command should include: start time t0, a 24-second uniform linear motion (speed 0.05m/s), ending 0.12m (0.05*2.56) before the target center, reserving the last 2.56 seconds for actual position correction allowance." + }, + { + "id": 369, + "scenario_code": "1.8", + "instruction": " When deploying the seismometer array, it was found that the Young's modulus of the lunar soil at the designated location is only 3MPa (lower than the design requirement of 5MPa), which may affect the stability of the equipment. Emergency solutions proposed:\nA) Use a triangular support base (increase contact area by 40%)\nB) Move to a backup point 200m away (bearing capacity meets standards but extends wiring by 12m)\nC) Reinforce on-site (takes 6 hours and consumes 15% of mission energy)\nGiven:\n- The original design safety factor must be ≥2\n- Current bearing capacity calculation value = lunar soil strength * original contact area = 3MPa * 0.01m² = 30kN\n- Equipment weight + operational load = 18kN", + "question": "Choose the optimal solution and verify its safety.", + "answer": "Choose option A. New contact area = 0.01 * 1.4 = 0.014m², new bearing capacity = 3 * 0.014 = 42kN, safety factor = 42/18 = 2.33 > 2, meeting the standard; compared to option B, it saves wiring loss, and compared to option C, it is more time and energy efficient." + }, + { + "id": 370, + "scenario_code": "2.9", + "instruction": " The lunar orbit navigation satellite LBNSS-1 establishes a two-way ranging link with Yutu-3. Given: 1) satellite orbit height 200km; 2) ranging signal frequency f=2GHz; 3) ionospheric delay error δion=0.03*(f/1GHz)^-2 meters; 4) equipment clock error δclock=±1 microsecond (speed of light c=3e8m/s). The current pseudo-range value measured is 200123 meters.", + "question": "Calculate the true geometric distance after eliminating the effects of ionospheric delay and clock error (round to the nearest integer)?", + "answer": "Ionospheric correction δion=0.03*(2)^-2=0.0075 meters; Clock error correction δclock=c*1e-6=300 meters; True distance=200123-0.0075-300≈199823 meters" + }, + { + "id": 371, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the moon, located at coordinate point A (10°N, 120°E). The science team requires it to travel to target point B (12°N, 122°E) to collect basalt samples. It is known that: 1) the straight-line distance d (km) between two points on the lunar surface = 111.3 * the square root of the sum of the squares of the latitude and longitude differences; 2) the energy consumption model is E = 0.15 * d + 5 (unit: Wh), where 0.15 is the base energy consumption coefficient per kilometer, and 5 is the fixed energy consumption for instrument preheating; 3) the current remaining power of the solar battery is 80Wh.", + "question": "If a straight-line path is chosen, calculate the theoretical total energy consumption for this movement and determine if the current power is sufficient to meet the demand.", + "answer": "Latitude and longitude differences Δlat = 2°, Δlon = 2°; distance d = 111.3 * sqrt(2^2 + 2^2) = 314.8km; total energy consumption E = 0.15 * 314.8 + 5 = 52.22Wh. 80Wh > 52.22Wh, the power is sufficient." + }, + { + "id": 372, + "scenario_code": "1.4", + "instruction": " The lunar base energy grid needs to power three devices simultaneously: an X-ray spectrometer (peak power 200W), a lunar soil analyzer (150W), and a robotic arm (300W). The grid adopts a priority power supply strategy: 1) The robotic arm has the highest priority during movement; 2) Scientific instruments share the remaining power and must not exceed 80% of their rated power. The current total power output of the solar array is 400W, and the robotic arm is performing a sample transfer task.", + "question": "Calculate the maximum power allocation for the two scientific instruments at this time, and explain the allocation basis.", + "answer": "After the robotic arm uses 300W, 100W remains. According to the constraints: the X-ray spectrometer has a maximum of 160W (200*0.8), and the lunar soil analyzer has a maximum of 120W (150*0.8). The actual allocation must satisfy x+y≤100 and x≤160, y≤120, so the maximum combination is x=80W, y=120W (reversely taking the limit)." + }, + { + "id": 373, + "scenario_code": "5.4", + "instruction": " Yutu-2 rover encountered a sudden solar proton event during the lunar day, causing the X-band communication to be interrupted. The system initiated an emergency plan:\n1. Switch to UHF band to communicate with the relay node 50km away\n2. The maximum transmission distance of the UHF link is 60km, with the path loss model: Lp = 100 + 30log10(d)\n3. The remaining power can only support 15 minutes of continuous transmission (5W power)\n4. The size of the emergency engineering data packet to be transmitted is 50MB, using QPSK modulation (spectral efficiency 2bps/Hz).", + "question": "Calculate the minimum required channel bandwidth (in MHz) to ensure the transmission is completed before the power is depleted. Hint: First calculate the data rate requirement within the available time.", + "answer": "Available time t=15min=900s\nRequired data rate R = 50MB*8/900 ≈ 444.4kbps\nAccording to Shannon's formula R=B*spectral efficiency → B ≥ R/2 = 222.2kHz ≈ 0.23MHz" + }, + { + "id": 374, + "scenario_code": "5.1", + "instruction": " The Chang'e-6 lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S), and plans to communicate with the ground station via the Queqiao-2 relay satellite. It is known that:\n1. Queqiao-2 operates in the Earth-Moon L2 point Halo orbit, approximately 65,000km from the Moon's center\n2. At the current time, the Moon's rotation causes the geometric elevation angle between the lander and the relay satellite to be 12°\n3. The tracking and control station uses the Ka band (26GHz) for communication, with a transmission power of 20W and an antenna gain of 45dBi\n4. The link budget must meet Eb/N0 ≥ 9dB (including a 3dB margin)\n5. The free space loss formula: Lfs = 92.4 + 20log10(f) + 20log10(d), where f is in GHz and d is in km", + "question": "Calculate the maximum allowable receiving system noise temperature (in units of K) under the current conditions, given that the data transmission rate R=1Mbps, the receiving antenna gain is 40dBi, and the total loss is 3dB. Hint: Eb/N0 = (P*Gt*Gr)/(k*T*R*L), where k=1.38e-23 J/K", + "answer": "First, calculate the free space loss: Lfs = 92.4 + 20log10(26) + 20log10(65000) ≈ 220.7dB\nTotal loss L = Lfs + 3 = 223.7dB\nAccording to the Eb/N0 formula, we get: T ≤ (P*Gt*Gr)/(k*R*L*(Eb/N0))\nSubstitute the values: T ≤ (20*10^(45/10)*10^(40/10))/(1.38e-23*1e6*10^(223.7/10)*10^(9/10)) ≈ 186K" + }, + { + "id": 375, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the final status of the sealed sample canister must be confirmed. Known: the canister is designed for a pressure of 10^5Pa, and the current telemetry shows an internal pressure of 8*10^4Pa (with an allowable ±5% deviation); the temperature sensor records a 24-hour average of -60°C (meeting the storage requirement of -80°C to +20°C); the RFID tag read success rate is 99.9%; the capture force of the docking mechanism must remain above 200N to ensure safety. The engineering manual stipulates that any parameter exceeding the threshold must halt the transfer. The current capture force sensor feedback value is 180±15N.", + "question": "Based on the above data, should the sample transfer procedure continue? List specific evaluation items and conclusions.", + "answer": "The transfer should be halted: 1) The capture force of 180N is below the lower limit of 200N, and the lower limit of the error range, 165N, is further below the threshold; 2) All other parameters are within acceptable limits (pressure within the allowable range of 7.6-8.4*10^4Pa, temperature, and RFID are normal). According to the manual, a single parameter failing to meet the standard triggers the halt condition." + }, + { + "id": 376, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 lander is located on the edge of an impact crater at 23.5°E, 12.8°N on the lunar near side, and its solar panels use two-dimensional tracking (azimuth + elevation). According to the lunar calendar, it is the 8th Earth day of the lunar day, with a solar elevation angle of 32° and an azimuth angle of 147°. Topographic mapping shows a 1.2-meter-high rock wall 3 meters to the west, and the maximum deployment height of the solar panels is 1.5 meters. Known: each panel has an area of 2 square meters, with an efficiency of 28% under standard lighting conditions, and a diffuse reflection gain coefficient of 0.15.", + "question": "If the current direct solar power is 1360 W/m², calculate the actual power generation of both panels considering terrain shading and diffuse reflection (round to the nearest integer)?", + "answer": "189 W" + }, + { + "id": 377, + "scenario_code": "3.4", + "instruction": " The Yutu-2 rover plans to execute three tasks simultaneously during the 3rd Earth day of the lunar day: ① Continuous operation of the X-ray spectrometer for 2 hours (peak power consumption 45W) ② Sampling by the robotic arm for 15 minutes (instantaneous power consumption 120W) ③ Transmit data packets to the relay satellite (30 minutes requiring a stable 60W). Energy system configuration: Lithium-ion battery current SOC=65% (total capacity 360Wh), solar array current output power 85W. System requirement: SOC≥40% at the end of the tasks.", + "question": "Please verify whether the task sequence meets the energy safety constraints? If not, propose an adjustment plan (only the start time of a single task can be modified).", + "answer": "Not met, the data transmission should be postponed until after the robotic arm task is completed." + }, + { + "id": 378, + "scenario_code": "3.6", + "instruction": " The Chang'e-7 lander needs to maintain the temperature of key electronic equipment at -180°C during the lunar night (total heat generation 8W). Insulation plan: ① Multi-layer thermal insulation material combination (equivalent thermal resistance 0.25 K/W) ② Isotope heat source providing constant 10W heat supply ③ Electric heating backup system (efficiency 90%). The thermodynamic model shows that the equipment compartment radiates heat to the lunar surface with a power of P_rad=5.67e-8*T^4 (T is absolute temperature), and the requirement is to maintain the temperature inside the compartment above -40°C.", + "question": "Calculate whether the isotope heat source alone can meet the insulation requirements? If not, determine the minimum additional power required from the electric heating system (保留1位小数).", + "answer": "Not possible, an additional 2.7W is required." + }, + { + "id": 379, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. Analysis of the soil characteristics in this area shows: the surface layer 0-30cm consists of loose fine particles (viscosity coefficient k=0.8N·s/m²), and 30-50cm contains high-hardness basalt fragments (Mohs hardness 6.5). The engineering team is equipped with three sampling tools: Type A rotary drill (maximum torque 50N·m, suitable for hardness <5), Type B impact drill (peak force 2000N, suitable for hardness >5 but with high power consumption), and Type C helical core sampler (suitable for continuous sampling of loose layers but unable to handle hard rock). The sampling process must meet the total energy consumption limit of no more than 300Wh.", + "question": "If it is necessary to obtain complete stratigraphic samples within 50cm depth, please select the optimal tool combination and explain the operating sequence and theoretical basis.", + "answer": "First, use the Type C helical core sampler to collect the loose layer from 0-30cm (low energy consumption and high fidelity), then switch to the Type B impact drill to penetrate the hard rock layer from 30-50cm (the only tool that meets the hardness requirement). The Type A drill is excluded due to insufficient torque, and the total energy consumption of the combination is approximately 280Wh (Type C 120Wh + Type B 160Wh), which meets the constraint." + }, + { + "id": 380, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. Analysis of the soil characteristics in this area shows: the surface layer 0-30cm consists of loose fine particles (viscosity coefficient k=0.8 Pa·s), and 30-50cm contains high-hardness basalt fragments (Mohs hardness 6.5). The probe is equipped with three sampling tools: ① Rotary impact drill (suitable for hardness >5, power consumption 300W) ② Vibration sampling tube (suitable for viscosity <1Pa·s, power consumption 150W) ③ Electric shovel (universal type, power consumption 200W). The total power limit of the sampling system is 400W, and sampling must be completed within 10 minutes.", + "question": "Design a combination of sampling tools that meets the power constraint, and calculate the maximum allowable single sampling duration (minutes). Known: Combined power consumption = Tool 1 power consumption + Tool 2 power consumption, total duration = single duration * sampling times ≤ 10 minutes.", + "answer": "Choose the vibration sampling tube (150W) + electric shovel (200W), combined power consumption 350W < 400W. Maximum single duration = 10/(1+1) = 5 minutes" + }, + { + "id": 381, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the lunar soil in this area are as follows: medium hardness (Mohs hardness 4-5), low viscosity, and volatile content of about 120ppm. There are three sampling tools available: 1) Diamond-coated rotary drill bit (suitable for rocks with hardness > 6); 2) Titanium alloy grab (suitable for loose lunar soil, maximum sampling depth 0.5 meters); 3) Tungsten carbide scraper (suitable for medium-hard, viscous materials, sampling efficiency 0.2kg/min). The maximum output torque of the probe's robotic arm is 15Nm, and the sampling time window is 30 minutes.", + "question": "Based on the characteristics of the lunar soil and the parameters of the tools, which sampling tool should be chosen? Please explain the basis for your choice and calculate the maximum sample mass that can be collected using this tool.", + "answer": "The tungsten carbide scraper should be chosen. Basis: 1) The hardness of the lunar soil (4-5) is below the standard suitable for the diamond drill bit; 2) The grab is not suitable for medium-hard materials and the sampling depth is insufficient; 3) The scraper matches the characteristics of the lunar soil. Maximum sample mass = 0.2kg/min * 30min = 6kg." + }, + { + "id": 382, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. Container parameters: internal pressure <10^-5Pa, temperature maintained at -50±5℃, RFID tag frequency 13.56MHz. Fault detection logic: 1) If the pressure >10^-3Pa or the temperature is outside the -60 to -40℃ range, a level one alarm is triggered; 2) If the RFID signal strength is <-70dBm, a level two alarm is triggered. Current telemetry data: pressure 8*10^-6Pa, temperature -48℃, RFID signal -65dBm, container mass is 12g lighter than expected.", + "question": "Based on the detection logic, determine which level of alarm should be triggered? And explain the most likely cause of the fault (it is known that the mass error of each gram of the sample container is allowed to be ±0.5g).", + "answer": "No alarm of any level is triggered. Justification: 1) Pressure 8e-6Pa < threshold; 2) Temperature -48℃ is within the range; 3) RFID signal -65dBm > -70dBm. The mass difference of 12g exceeds the allowable error (12g > 11g * 0.5g), but the mass parameter is not included in the alarm logic." + }, + { + "id": 383, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. Analysis of the soil characteristics in this area shows: the surface layer 0-30cm consists of loose fine particles (viscosity coefficient k=0.8 Pa·s), and 30-50cm contains high-hardness basalt fragments (Mohs hardness 6.5). The probe is equipped with three sampling tools: ① Rotary Percussion Drill (suitable for hardness >5, power consumption 300W) ② Vibration Sampling Tube (suitable for viscosity <1Pa·s, power consumption 150W) ③ Electric Shovel (universal, power consumption 200W). The mission requires prioritizing the success rate of sampling, followed by energy consumption optimization.", + "question": "If a complete stratified sample is needed at a depth of 50cm, how should the sampling tools be combined and what is the total energy consumption calculated to be used for this task？", + "answer": "For 0-30cm, use the Vibration Sampling Tube (150W*30cm), and for 30-50cm, use the Rotary Percussion Drill (300W*20cm), total energy consumption=150*0.3+300*0.2=105Wh" + }, + { + "id": 384, + "scenario_code": "1.5", + "instruction": " The Yutu-2 lunar rover needs to remotely operate its robotic arm to collect rock samples with a communication delay of 1.3 seconds. The maximum movement speed of the robotic arm's end is 0.1 m/s, and the target rock is 0.8 meters away from the current position of the arm. After the ground control center sends a movement command, it must wait for the action completion feedback before sending the next command.", + "question": "What is the shortest theoretical time from sending the movement command to receiving the confirmation information? (Do not consider the time for command processing.)", + "answer": "Shortest time = communication delay * 2 + movement time = 1.3 * 2 + (0.8 / 0.1) = 2.6 + 8 = 10.6 seconds" + }, + { + "id": 385, + "scenario_code": "5.10", + "instruction": " The ground station performs two-way ranging with the lunar rover through the 'Queqiao' relay satellite. The measured pseudo-code round-trip delay is 2.48 seconds, the ionospheric delay correction value is 12 ms, the tropospheric delay is 6 ms, and the equipment delay calibration is 0.8 ms. The speed of light is taken as 299,792 km/s. The clock drift of the lunar rover can be ignored after calibration.", + "question": "Calculate the precise distance between the ground station and the lunar rover (the handling method for each correction term must be explained)?", + "answer": "One-way propagation delay t = (total delay - equipment delay)/2 - ionospheric delay - tropospheric delay = (2480ms - 0.8ms)/2 - 12ms - 6ms = 1239.6ms - 18ms = 1221.6ms = 1.2216s. Distance d = c*t = 299792km/s * 1.2216s ≈ 366,178km (rounded to the nearest integer)." + }, + { + "id": 386, + "scenario_code": "5.1", + "instruction": " The Chang'e-6 probe is performing a sampling mission on the far side of the Moon and needs to maintain communication with the ground station via the Queqiao-2 relay satellite. Given:\n- Average Earth-Moon distance: 384,400 km\n- Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, approximately 65,000 km above the lunar surface\n- X-band communication frequency f = 8 GHz\n- Probe transmission power Pt = 20 W, relay satellite receiving antenna gain Gr = 40 dB\n- Free space path loss formula: L = 20 * log10(4 * π * d / λ), where λ = c / f (c=3e8 m/s)\n- Current communication window probe-relay satellite distance d = 68,000 km", + "question": "Calculate the free space path loss value (in dB) for the current uplink (probe→relay satellite) and determine whether it meets the minimum receiving power threshold of -110 dBm.", + "answer": "Calculation steps:\n1. λ = c / f = 3e8 / 8e9 = 0.0375 m\n2. L = 20 * log10(4 * π * 68e6 / 0.0375) ≈ 20 * log10(2.27e10) ≈ 207.1 dB\n3. Received power Pr = Pt + Gr - L = 10 * log10(20) + 40 - 207.1 ≈ 13 + 40 - 207.1 = -154.1 dBm\nConclusion: -154.1 dBm < -110 dBm, does not meet the requirement" + }, + { + "id": 387, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover experiences a sudden communication interruption during the lunar day. Fault analysis shows:\n1) Current solar activity index KP=6 causing ionospheric disturbance\n2) Direct-to-Earth communication elevation angle is below 5 degrees with terrain obstruction on the lunar surface\n3) SSD cache capacity can only maintain 30 minutes of scientific data storage\nEmergency strategy options:\nA) Immediately switch to low frequency (S-band) anti-interference mode to attempt direct connection to Earth\nB) Enter hibernation to reduce power consumption and wait for KP index to drop below 4 before reconnecting to Queqiao relay\nC) Activate the nearest lander node in the mesh network for data relay transmission", + "question": "Based on the given constraints (ionospheric disturbance, terrain obstruction, cache capacity), select the optimal emergency strategy and explain the reasoning.", + "answer": "Choose strategy C. Reasoning:\n1) Strategy A has a high failure rate: Although low frequency mode is more resistant to interference, it cannot solve the terrain obstruction issue, and the low elevation angle leads to severe atmospheric attenuation.\n2) Strategy B is risky: The time for KP index to drop is uncertain and may exceed the 30-minute cache capacity limit.\n3) Strategy C is optimal: The mesh network can bypass terrain obstruction, is not directly affected by ionospheric disturbance, and can promptly relieve cache pressure." + }, + { + "id": 388, + "scenario_code": "1.5", + "instruction": " The ground control center controls the lunar rover to perform rock sampling through a remote operation link with a delay of 1.3 seconds. The rover's maximum translational speed is 0.1m/s, and the end-effector positioning accuracy of the robotic arm is ±5mm. The target rock is currently 2.4 meters in front of the rover, and the robotic arm needs to contact the rock surface at a speed of 3mm/s and apply a force of 5N. The control system uses a predictive algorithm to compensate for the delay, with the position prediction error increasing with distance as: error (mm) = 0.2 * distance (m)^1.5.", + "question": "Calculate the shortest theoretical time from the start of movement to the completion of sampling, and explain whether the prediction error will affect the success rate of sampling.", + "answer": "Shortest time = movement time + operation time = (2.4m / 0.1m/s) + (5mm / 3mm/s) = 24s + 1.67s ≈ 25.67 seconds. Prediction error = 0.2 * 2.4^1.5 ≈ 0.74mm < 5mm positioning accuracy, so it does not affect the success rate." + }, + { + "id": 389, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth. The Queqiao relay satellite is deployed in a Halo orbit at the Earth-Moon L2 point, about 65,000 kilometers from the Moon. Given:\n1. The relay satellite's X-band antenna gain is 38dBi, the lander's transmission power is 10W, and the antenna gain is 15dBi\n2. Free space loss formula: L = 20log10(4πd/λ), where d is the distance, λ=0.0375m (X-band)\n3. Receiver sensitivity -110dBm\n4. The current communication window forms an isosceles triangle between Earth-Moon-relay satellite-lander, with a single-hop distance of 78,000 kilometers", + "question": "Calculate whether the current link margin meets the communication requirements (consider a 3dB system margin)? Provide key numerical steps", + "answer": "1. Free space loss: L=20log10(4π*7.8e7/0.0375)=214.3dB\n2. EIRP of transmission=10log10(10)+15=25dBm\n3. Received power=25+38-214.3=-151.3dBm\n4. Link margin=-110-(-151.3)-3=38.3dB>0, meets requirements" + }, + { + "id": 390, + "scenario_code": "5.7", + "instruction": " The lunar research station needs to store scientific data long-term in an environment of -180°C. Using radiation-resistant SSDs, the parameters are as follows:\n1. Total capacity 1TB, using NAND flash block size of 128KB\n2. Write amplification factor 1.2, average erase cycles 3000 times\n3. Daily write volume fluctuation: 20-50GB (average 35GB)\n4. Required 5-year lifespan with 20% redundant space", + "question": "Verify if the current SSD configuration meets the lifespan requirement (provide complete judgment basis).", + "answer": "1. Total write volume over five years = 35 * 365 * 5 = 63,875GB\n2. Total writable volume of SSD = (3000 * 1024GB) / (1.2 * 128KB/block) = 24,000,000 blocks * 128KB = 3840TB\n3. Wear = (63,875 / 3840) * 100% = 1.66% << 100% (meets requirement)\n4. Redundant space check: When the actual usage peak is 50GB/day, the occupancy rate = (50 * 365 * 5) / 1024TB = 89TB < 800TB (80%)" + }, + { + "id": 391, + "scenario_code": "4.9", + "instruction": " Lunar sample return capsule design parameters: inner diameter of the sealed container is 20cm, using dual O-ring sealing (single O-ring leakage rate ≤1×10^-7 Pa·m^3/s). Maximum acceleration during ascent is 12g, temperature cycle range is -180°C to +80°C. Handover process requirements: ① Complete 3 pressure retention tests before ascent (pressure drop <50Pa within 1 hour) ② RFID tag reading success rate ≥99.9% ③ Docking error with the orbiter <5cm. Current telemetry data shows a pressure drop of 65Pa in the second pressure test within 1 hour.", + "question": "Determine whether the current sealing system meets the launch requirements? If not, what measures need to be taken? ", + "answer": "Does not meet requirements. Basis: Measured pressure drop 65Pa > standard value 50Pa. Measures: ① Check the installation status of the O-ring and replace damaged sealing components; ② Reconduct 3 complete pressure tests until all are qualified; ③ Add helium mass spectrometry leak detection to confirm the leakage rate <1×10^-7 Pa·m^3/s." + }, + { + "id": 392, + "scenario_code": "3.1", + "instruction": " The Chang'e-5 lander is executing a sampling mission in the area at 43.06°N, 51.92°W on the near side of the Moon. During the lunar day, the solar elevation angle in this region varies from 5° to 35°, and the solar panels use a two-dimensional tracking method (azimuth + elevation). It is known that: 1) the area of a single panel is 2.5m², with a photovoltaic conversion efficiency of 28%; 2) the albedo of the lunar surface is 0.12; 3) the solar constant is 1368W/m²; 4) terrain obstruction reduces the effective sunlight hours by 15% compared to the theoretical value.", + "question": "If the current solar elevation angle is 25°, and the azimuth tracking error is ±3°, calculate the actual power generation of a single panel at this time (considering both direct and reflected light contributions, ignoring atmospheric loss).", + "answer": "Direct light power = 1368 * sin(25°) * 2.5 * 0.28 * cos(3°) ≈ 403.6W; Reflected light power = 1368 * 0.12 * (1-sin(25°))/2 * 2.5 * 0.28 ≈ 16.2W; Total power = 403.6 + 16.2 ≈ 419.8W" + }, + { + "id": 393, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration in the Von Kármán crater, obtaining multispectral data from three candidate sampling points: Point 1 has distinct KREEP rock characteristics but is 2.1 kilometers away; Point 2 has clear breccia outcrops but is located on a 15° slope; Point 3 has a volcanic glass abundance of 35% but the communication window is only 40 minutes. The rover's movement speed is 0.05m/s, a single spectral analysis requires 8 minutes, and an additional 10 minutes of safety time is required for operations on the slope. The scientific priority weights are: KREEP rock > volcanic glass > breccia.", + "question": "Based on a comprehensive evaluation of scientific value and engineering constraints, which sampling point should be prioritized? Calculate whether the total time for movement + analysis under this choice meets the communication window limit.", + "answer": "Point 1 KREEP rock should be prioritized. Movement time = 2100m / 0.05m/s = 42000 seconds = 700 minutes, far exceeding the communication window, so in practice, Point 3 volcanic glass should be chosen. Movement time = 800m / 0.05m/s = 16000 seconds ≈ 267 minutes + 8 minutes analysis = 275 minutes < 40 minutes communication window, thus no feasible option is available and the plan needs to be adjusted." + }, + { + "id": 394, + "scenario_code": "4.9", + "instruction": " The sample container transfer process between the ascent vehicle and the lander requires: ① Container temperature must be maintained at -50±5℃; ② Sealing pressure test value > 0.1MPa; ③ 100% success rate for RFID tag reading. Current data: temperature -48℃, pressure 0.12MPa, RFID read success rate 98% over three attempts. Transferring the container from the lander to the ascent vehicle takes 6 minutes, during which the temperature rises by 1℃ per minute. The transfer protocol stipulates that the process will be aborted if any condition is not met.", + "question": "Determine if the current status allows the start of the transfer process? If the temperature change rate remains constant after the start, calculate whether the final temperature upon completion of the transfer still meets the requirements.", + "answer": "The start is allowed (all current conditions are met). Final temperature = -48℃ + (6min * 1℃/min) = -42℃, which is still within the -45±5℃ range and meets the requirements." + }, + { + "id": 395, + "scenario_code": "3.6", + "instruction": " The relay satellite of Chang'e-4 needs to maintain a constant temperature above -40°C during the lunar night. It is known that: 1) the equipment heat dissipation power is 2W; 2) the equivalent thermal resistance of the multi-layer insulation material is 8K/W; 3) the rated output power of the radioisotope heat source (RHU) is 3W; 4) the lunar night environmental temperature is -180°C; 5) the electric heater has a backup power of 5W but will consume battery energy.", + "question": "Calculate the internal equilibrium temperature relying solely on RHU + insulation layer, and determine whether the electric heater needs to be activated (require calculation process).", + "answer": "Thermal balance equation: (T_in +180)=(3+2)*8 → T_in=-140°C＜-40°C, the electric heater needs to be activated. Additional heating power requirement: (-40+180)/8 -5=15W, actually need to turn on 5W electric heater to make the total heat supply reach 10W" + }, + { + "id": 396, + "scenario_code": "3.1", + "instruction": " The Chang'e-7 lander is located at the edge of the Shackleton crater in the lunar south pole (latitude 88.5°S), and its solar panels use a three-dimensional tracking algorithm. According to the lunar ephemeris, the current solar elevation angle is 5°, and the azimuth angle is 45° (due east is 0°). Terrain obstruction analysis shows that the western crater wall causes a 10% power generation loss in the azimuth range of 30°-60°. It is known that the standard operating condition output power of the solar panel is P_std=200W/m², and the actual output power formula is: P_act = P_std * cos(θ) * (1 - L), where θ is the solar incidence angle, and L is the obstruction loss ratio.", + "question": "If the normal vector of the solar panel is currently adjusted to an angle θ=8° with the solar vector, calculate the actual output power per square meter of the solar panel at this time (保留两位小数).", + "answer": "187.60W" + }, + { + "id": 397, + "scenario_code": "3.8", + "instruction": " In the Chang'e-6 sample return mission, the lander needs to complete the following tasks during the lunar day: 1) drilling and sampling for 2 hours, power consumption 150W; 2) spectral analysis for 1.5 hours, power consumption 80W; 3) data transmission for 0.5 hours, power consumption 200W. System energy constraints: available lithium-ion battery capacity E_batt=500Wh, real-time charging power of solar panels P_solar=120W (continuous charging during tasks). Energy balance formula: remaining power = E_batt + ∫(P_solar - P_load)dt.", + "question": "Verify whether the task sequence is within the energy safety range (require final remaining power ≥100Wh). If not, provide the maximum allowable adjustment for the drilling time (other task durations remain unchanged).", + "answer": "Insufficient, the maximum drilling time needs to be reduced to 1.08 hours" + }, + { + "id": 398, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, energy supply becomes a critical constraint. In the current mission, three devices are deployed: A (seismometer, peak power 50W), B (infrared spectrometer, peak power 120W), C (neutron detector, peak power 80W). They share a lunar surface mini nuclear battery power supply system with a maximum instantaneous output power of 200W. The operating cycle of the devices is: A works for 10 minutes every 2 hours, B works for 15 minutes every 3 hours, C works for 20 minutes every 1.5 hours. All devices start their first operating cycle simultaneously at 08:00 UTC+0.", + "question": "At 09:30 UTC+0, if all devices operate according to the preset cycle and startup delays are not considered, will the total power demand of the system exceed the power supply capability? If it exceeds, which device needs to be shut down at a minimum to meet the power supply constraint? ", + "answer": "Exceeds power supply capability, device B needs to be shut down" + }, + { + "id": 399, + "scenario_code": "5.4", + "instruction": " During the lunar day, the Yutu-2 rover suddenly encounters a solar conjunction causing a communication interruption. It is known that: 1) The remaining capacity of the SSD cache is 50GB; 2) The data generation rate of the panoramic camera is 200MB/hour; 3) The spectrometer data has a higher priority (must ensure complete transmission), with a generation rate of 80MB/hour; 4) The solar conjunction is expected to last for 8 hours; 5) After the interruption, the link rate stabilizes at 2Mbps.", + "question": "Design a cache management strategy to ensure that all high-priority data is completely saved and transmitted first. Explain the basis for data volume calculations at each stage.", + "answer": "1) Total amount of high-priority data: 80MB/h * 8h = 640MB; 2) Low-priority data can be partially discarded: total generated 1600MB, available cache 50GB - 640MB = 49.36GB >> demand → all saved; 3) Transmission order after recovery: first transmit 640MB of spectrometer data (takes 640*8/2=2560 seconds ≈ 42.7 minutes), then transmit panoramic data" + }, + { + "id": 400, + "scenario_code": "5.7", + "instruction": " The main control computer of the lunar scientific research station uses a 128TB radiation-resistant SSD to store scientific data. Technical parameters: 1) Uses 3D TLC NAND flash memory, with a PE cycle of 3000 times; 2) Wear leveling algorithm controls the write amplification factor to 1.2; 3) Average daily write volume is 500GB; 4) LDPC error correction can tolerate ≤8% bad block rate.", + "question": "Calculate the theoretical service life of the SSD before reaching the bad block rate threshold (based on 365 days/year). List the formula for calculating the lifespan.", + "answer": "1) Total writable volume = 128TB * 3000 / 1.2 = 320PB; 2) Annual write volume = 500GB * 365 ≈ 178.75TB; 3) Theoretical lifespan = 320PB / 178.75TB ≈ 1791 years (Note: Actual lifespan is significantly shortened by radiation and other factors)." + }, + { + "id": 401, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, a temporary power grid needs to be established. Currently, there are three devices: a drilling machine (peak power 200W), a spectrometer (150W), and a communication relay (100W). The solar panel array has a maximum output power of 300W, and the battery pack can provide an additional 100W of continuous power. All devices must operate simultaneously, but the power distribution ratio of each device can be dynamically adjusted.", + "question": "If it is necessary to ensure that the drilling machine runs at full load, what is the maximum power that can be allocated to the spectrometer and the communication relay, respectively? List the calculation steps.", + "answer": "Total available power = Solar 300W + Battery 100W = 400W; After the drilling machine occupies 200W, the remaining power = 400 - 200 = 200W; The upper limit of power allocation for the spectrometer and the communication relay is 150W and 100W (rated value), respectively, but is limited by the total remaining power of 200W. The actual maximum allocation plan is: Spectrometer 150W + Communication Relay 50W, or Spectrometer 100W + Communication Relay 100W." + }, + { + "id": 402, + "scenario_code": "1.8", + "instruction": " Before deploying a seismometer, the bearing capacity of the lunar soil must be tested. The static bearing limit of the area is measured to be 8kPa. The contact area of the seismometer base is 0.25m², its own weight is 20kg, and the additional equipment weighs 10kg. The gravitational acceleration on the Moon is 1.62m/s².", + "question": "Determine whether the lunar soil can directly support the deployment of the seismometer. Provide the pressure calculation formula and the specific numerical comparison process.", + "answer": "Total mass = 20kg + 10kg = 30kg; Force F = m * g = 30 * 1.62 = 48.6N; Pressure P = F / A = 48.6 / 0.25 = 194.4Pa = 0.1944kPa < 8kPa, therefore it can be safely deployed." + }, + { + "id": 403, + "scenario_code": "1.4", + "instruction": " Three scientific instruments have been deployed in the permanently shadowed region of the lunar south pole: a seismometer (peak power 120W), an infrared spectrometer (peak power 80W), and a neutron detector (peak power 60W). They share a lunar surface power grid, which consists of a solar array and a battery, with a maximum continuous power supply of 200W. The priority order of the devices is: seismometer > infrared spectrometer > neutron detector. The current battery charge is 500Wh, and it is expected to enter the lunar night period (lasting 14 days) in 2 hours.", + "question": "If all devices operate simultaneously at peak power, how should the power grid dynamically adjust the power supply strategy to meet the priority and maximize scientific output? Calculate the sustainable operation time of the system at this time.", + "answer": "Turn off the neutron detector (60W) according to priority, the remaining total power is 120+80=200W, which exactly meets the upper limit of the power grid. Sustainable operation time = battery charge / (total power consumption - solar power supply) = 500Wh / (200W - 0W) = 2.5 hours" + }, + { + "id": 404, + "scenario_code": "1.8", + "instruction": " The Chang'e-7 lander plans to deploy an array of 4 seismometers on the edge of an impact crater at a latitude of 85°. Field measurements show that the bearing capacity of the lunar soil in this area is 8kPa (safety factor must be ≥2), and the local magnetic field disturbance is ±200nT. Each seismometer weighs 15kg, with a base contact area of 0.02m² and a magnetic field sensitivity of ≤50nT. The spacing between deployment points must meet: minimum 20m (to avoid mutual interference), maximum 100m (to ensure time synchronization accuracy). The current measured magnetic field values at each candidate point are: A(+180nT), B(-30nT), C(+90nT), D(-150nT).", + "question": "Analyze feasible deployment schemes from the perspectives of mechanics and electromagnetic compatibility, list all 4-point combinations that meet the constraints, and explain the reasons for the optimal point selection.", + "answer": "Mechanical verification: single unit pressure=15*9.8/0.02/1000=7.35kPa<8kPa/2; qualified magnetic field points: B(-30nT) and C(+90nT). Feasible combinations: ①B1-B2-C1-C2 (need to select two points each near B/C with a spacing of 20-100m); the optimal selection is two points in the B area and two points in the C area, because the magnetic field disturbance is minimal and the spacing constraints are met." + }, + { + "id": 405, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, a temporary energy-sharing network needs to be established. There are currently 3 devices: A (seismometer, peak power demand 50W), B (spectrometer, peak power demand 120W), C (drilling device, peak power demand 200W). The power module has a maximum output power of 300W and must reserve 20% redundant power to ensure system safety. All devices can dynamically adjust their operating modes (sleep/low power/full power), but at least one device must be in full power mode to maintain basic scientific tasks.", + "question": "If the current power module output has reached the critical value, and device C must switch to full power mode due to sampling needs, please provide a device operating mode adjustment plan that meets all constraints (the final state of each device must be explained).", + "answer": "Device C switches to full power (200W), device B switches to low power (60W), device A switches to sleep (0W). Total power = 200 + 60 + 0 = 260W > 300 * 0.8 = 240W, which does not meet the requirement; therefore, the adjustment is: device C full power (200W), device B sleep (0W), device A low power (25W), total power = 200 + 0 + 25 = 225W ≤ 240W and meets the requirement of at least one device in full power." + }, + { + "id": 406, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform rock sampling, the one-way communication delay between Earth and the Moon is 1.3 seconds. The current speed of the lunar rover is 0.2m/s, and the emergency braking distance is 0.15m. The operator sends a braking command immediately upon discovering a hazardous terrain 1.8 meters ahead through real-time video. Video transmission and command processing take a total of 0.4 seconds.", + "question": "Calculate the total movement distance from the discovery of the hazardous terrain to the complete stop of the lunar rover, and determine whether a hazard will occur (the calculation steps must be listed).", + "answer": "Total delay = communication delay * 2 + processing time = 1.3 * 2 + 0.4 = 3 seconds; Braking distance = speed * total delay + emergency braking distance = 0.2 * 3 + 0.15 = 0.75m; 1.8m > 0.75m, no hazard will occur." + }, + { + "id": 407, + "scenario_code": "2.2", + "instruction": " The Chang'e-7 lander releases a rover at the edge of the Shackleton crater (a permanently shadowed area). Navigation system configuration: 1) IMU drift error 1°/h; 2) Stereo visual odometry positioning error under low light is 3% of the travel distance; 3) LiDAR SLAM absolute accuracy ±0.1m/100m. The rover travels in a straight line at a speed of 0.1m/s for 200 seconds, after which the IMU measures a heading change of +5°, the visual odometry records a displacement of 19.4m, and the LiDAR mapping shows an actual displacement of 20.1m.", + "question": "According to the principle of multi-sensor data fusion, calculate the optimal estimated value of the actual travel distance of the rover (the basis for weighting must be explained)?", + "answer": "Optimal estimated value = (LiDAR weight 1/0.1^2 * 20.1 + Visual weight 1/(0.03*20)^2 * 19.4 + IMU weight 0) / (1/0.01 + 1/0.36 + 0) ≈ (20100*20.1 + 77*19.4) / 20177 ≈ 20.08m (the highest precision of LiDAR is given the maximum weight, and the IMU has no displacement measurement capability, so its weight is 0)." + }, + { + "id": 408, + "scenario_code": "2.2", + "instruction": " The Chang'e-7 lander is conducting exploration at the edge of the Shackleton crater in a permanently shadowed area. The navigation system uses a multi-sensor fusion approach: 1) IMU drift error is 0.1°/h; 2) Visual Odometry (VO) positioning error under low light conditions is ±3 cm/s; 3) LiDAR SLAM absolute accuracy is ±5 cm. It is known that the distance from the landing point to the scientific target area is 50 m, and the mission allows a maximum cumulative positioning error of no more than 15 cm.", + "question": "If only relying on IMU+VO combined navigation and moving at a speed of 2 cm/s, does it meet the final positioning accuracy requirements? What additional correction methods are needed to supplement this approach? ", + "answer": "Travel time = 50 m / (2 cm/s) = 2500 s ≈ 0.694 h; IMU angle error = 0.1 * 0.694 ≈ 0.0694°; position error ≈ tan(0.0694°) * 50m ≈ 6 cm; VO error = 3 cm/s * (2500 s)^(1/2) ≈ 47 cm (random walk); total error ≈ sqrt(6^2 + 47^2) > 47 cm >> 15 cm. Additional correction methods such as LiDAR SLAM or celestial navigation are required." + }, + { + "id": 409, + "scenario_code": "3.4", + "instruction": " During the lunar day, the Yutu-2 rover needs to simultaneously perform: ① Continuous operation of the X-ray spectrometer for 20 minutes (peak power consumption 80W); ② Sampling by the robotic arm for 10 minutes (peak power consumption 120W); ③ Data transmission for 15 minutes (peak power consumption 60W). The power system has a maximum output power limit of 150W, and the battery can currently provide an additional 50W buffer power. Task priorities: ②>③>①.", + "question": "Design a task scheduling plan that meets the power constraints, ensuring that high-priority tasks are executed continuously, and calculate the total task completion time.", + "answer": "Plan: First execute ② for 10 minutes (120W), while executing the first 10 minutes of ③ (60W), totaling 180W, exceeding the limit by 130W (150+50-70 buffer), so ① needs to be postponed; then execute the remaining 5 minutes of ③ alone; finally, execute ① for 20 minutes. Total time = 10 + 5 + 20 = 35 minutes." + }, + { + "id": 410, + "scenario_code": "2.4", + "instruction": " The Yutu-2 rover is currently conducting a patrol and exploration on the far side of the moon, located at coordinate point A (10°N, 120°E). The mission control center has planned two scientific target points: Point B (10.5°N, 120.2°E) is 3.2 kilometers away from point A in a straight line, with flat terrain; Point C (9.8°N, 120.5°E) is 4.1 kilometers away from point A, passing through the edge of an impact crater with a slope of 15°. The energy consumption model of the rover is: energy consumption rate on flat ground is 0.1kWh/km, and the energy consumption rate when climbing increases to 0.15kWh/km * slope (°). The current remaining power is 0.5kWh, and 0.1kWh needs to be reserved for emergency power.", + "question": "Considering only the energy constraints, which target point should Yutu-2 prioritize for exploration? Please calculate and explain.", + "answer": "Point B. Calculation process: 1) Total energy consumption for Point B = 3.2km * 0.1kWh/km = 0.32kWh; 2) Energy consumption for the uphill section of Point C = 4.1km * 0.15kWh/km * 15° = 9.225kWh (exceeding the total), and the uphill section alone has already exceeded the available power of 0.4kWh (0.5 - 0.1)." + }, + { + "id": 411, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander, while conducting exploration at the edge of the Shackleton crater, suddenly receives a solar proton event warning (lasting 4 hours). The lander needs to transfer to the nearest permanent shadow area for shelter (point D, azimuth 45°, 800 meters away) within 30 minutes. There are two options for the shelter path: Path 1 is a straight-line crossing of the loose lunar soil area (speed limit 0.05m/s), and Path 2 is a detour through a hardened lava tube (total length 1200 meters, speed up to 0.12m/s). Safety regulations require that the power consumption during the transfer process does not exceed 200W·h. It is known that the power consumption model of the moving system is: P=150+10*v (W), where v is the speed (m/s).", + "question": "Please determine through calculation which transfer path the lander should choose to meet both time and energy consumption requirements.", + "answer": "Path 2. Calculation process: 1) Path 1 time consumption = 800/0.05 = 16000s > 30min (1800s), directly excluded; 2) Path 2 time consumption = 1200/0.12 = 10000s < 1800s; 3) Path 2 power consumption = (150+10*0.12)*10000/3600 = 420W·h > 200W·h. However, only Path 2 meets the time requirement in the question, implying that parameters need to be revised or there is a priority setting." + }, + { + "id": 412, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover encountered an emergency while working near the terminator on the near side of the Moon:\n1. Direct Earth communication is currently experiencing a 50% drop in SNR due to a solar flare\n2. The backup relay link (Queqiao-3) requires 15 minutes to establish a connection\n3. The SSD cache has 8GB of remaining capacity, and the scientific data generation rate is 50MB/min\n4. The maximum number of retransmissions for the DTN protocol is 3 times, with a single transmission success rate of 80%.", + "question": " ", + "answer": "1. SSD available time = (8GB-2GB)/(50MB/min) ≈ (6*1024)/50 ≈122 minutes >15 minutes → can fully cache critical data\n2. DTN transmission success probability =1-(1-0.8)^3=99.2% " + }, + { + "id": 413, + "scenario_code": "5.9", + "instruction": " Chang'e-7 orbiter needs to update its flight control software via the telemetry and control link:\n1. S-band uplink rate 4kbps, downlink rate 16kbps\n2. Update package size 48MB, using RS(255,223) encoding\n3. If CRC check fails, the entire data block (block size 512B) needs to be retransmitted\n4. Each communication window lasts 20 minutes", + "question": "Calculate the minimum number of communication windows required to complete the update in the worst case (each transmission needs to be retransmitted once).", + "answer": "1. Data volume after RS encoding = 48*(255/223) ≈ 54.9MB\n2. Number of CRC blocks = 54.9MB/512B ≈ 112,400 blocks\n3. Time per block transmission = 512*8/(4*1024) = 1 second → total uplink time ≈ 112,400 seconds ≈ 31 hours\n4. Effective time per window = 20*60*(4/(4+16)) = 240 seconds → minimum number of windows needed 112400/240 ≈ 469 windows" + }, + { + "id": 414, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the moon, located at coordinate point A(10,20), and needs to reach scientific target point B(50,60). Terrain data indicates there are three optional paths between the two points: Path 1 is a straight-line distance of 60 meters with a slope of 8°; Path 2 is a zigzag distance of 75 meters with a slope of 3°; Path 3 is a detour distance of 90 meters with a slope of 1°. It is known that the motor efficiency model of the lunar rover is: slope climbing energy consumption E_slope=0.2*slope(°)*distance(m), flat driving energy consumption E_flat=0.1*distance(m). The remaining battery power can only support a maximum energy consumption of 12 joules.", + "question": "Please calculate the total energy consumption of the three paths and determine whether Yutu-2 can safely reach target point B under the current power level? If not, which path should be chosen to drive to the farthest position possible under the current power level? ", + "answer": "Total energy consumption for Path 1 = 0.2*8*60 + 0.1*60 = 96 + 6 = 102J; Total energy consumption for Path 2 = 0.2*3*75 + 0.1*75 = 45 + 7.5 = 52.5J; Total energy consumption for Path 3 = 0.2*1*90 + 0.1*90 = 18 + 9 = 27J. The current power level of only 12J is insufficient for any path, Path 3 should be chosen to drive to a distance d satisfying 0.2*1*d + 0.1*d = 12 → d = 40 meters." + }, + { + "id": 415, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the far side of the Moon. Analysis of the soil characteristics in this area shows: the top layer 0-30cm is loose fine particles (viscosity coefficient k=0.8 Pa·s), and 30-50cm contains high-hardness basalt fragments (Mohs hardness 6.5). The probe is equipped with three sampling tools: a rotary impact drill (suitable for hardness >5), a helical core sampler (suitable for viscosity 0.5-1.2 Pa·s), and an electric shovel (only suitable for the top layer <20cm). The maximum output torque of the sampling system is 15N·m, and the drill bit diameter is limited to ≤3cm.", + "question": "If a complete sample at a depth of 40cm is required without damaging the equipment, which tool should be chosen? Provide the key parameter verification process.", + "answer": "Choose the rotary impact drill. Reasons: 1) The 40cm depth involves high-hardness basalt (6.5>5), which fits within the range suitable for the rotary impact drill; 2) Although the helical core sampler is suitable for the viscosity, it cannot handle high-hardness rocks; 3) The electric shovel is insufficient in depth. Key verification: The drill bit diameter of 3cm meets the restriction, and the torque required to break the basalt σ=8N·m <15N·m safety threshold." + }, + { + "id": 416, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform rock sampling, the one-way communication delay between Earth and the Moon is 1.3 seconds. The control system uses a predictive algorithm to compensate for the delay: ① Upload path correction commands every 5 seconds; ② The vehicle's motion model is v(t) = 0.5*t^2 (0≤t≤4), with a maximum speed limit of 8cm/s; ③ The allowable error threshold between the actual position and the predicted position is ±15cm. At the current time t=0, the vehicle is stationary at the origin, and receives a sequence of commands: [t=1s: accelerate to 4cm/s], [t=6s: turn right 30°].", + "question": "Calculate whether the maximum possible error between the predicted position and the actual position exceeds the threshold before sending the next command at t=5s (assuming no slipping or turning errors)?", + "answer": "Predicted position: Move at a constant speed of v=4cm/s, distance moved in 5 seconds = 4*5 = 20cm; Actual position: v(t)=0.5*t^2 reaches a maximum speed of 8cm/s at t=4s, distance moved from 0-4 seconds = integral(0.5*t^2) = 0.5/3*4^3 ≈ 10.67cm, distance moved from 4-5 seconds = 8cm, total = 18.67cm; Error = 20-18.67 = 1.33cm < 15cm, does not exceed the threshold." + }, + { + "id": 417, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the soil in this area are: medium hardness (Mohs hardness 4-5), low viscosity, and high volatile content (about 500 ppm). There are three sampling tools available: A. Diamond-coated rotary drill (suitable for rocks with hardness >6); B. Titanium alloy scoop (suitable for loose lunar soil); C. Scraping tool with heating function (suitable for samples containing volatiles). The working power consumption of each tool is: A=120W, B=80W, C=100W. The remaining energy of the probe is 1500Wh, and 300Wh needs to be reserved for return communication.", + "question": "According to the characteristics of the lunar soil and energy constraints, which sampling tool should be chosen? Calculate whether the remaining available energy meets the requirement for 2 hours of continuous sampling.", + "answer": "Choose tool C (scraping tool with heating function). Reasons: 1) Hardness is suitable (Mohs 4-5 < 6, no need for diamond drill); 2) Volatile processing requirement; 3) Energy consumption calculation: 100W*2h=200Wh < (1500-300)Wh=1200Wh, meeting the requirement." + }, + { + "id": 418, + "scenario_code": "4.4", + "instruction": " Yutu-2 is conducting exploration in the Von Kármán crater and has obtained the following data: 1) Orbital remote sensing shows 3 candidate points: Point A (KREEP rock probability 70%, distance 1.2km), Point B (volcanic glass probability 85%, distance 2.3km), Point C (breccia probability 60%, distance 0.8km); 2) The rover's average daily travel capacity is 500m; 3) Scientific priority weight: KREEP rock=3, volcanic glass=2, breccia=1; 4) One day needs to be reserved for sampling operations. The remaining mission cycle is 5 days.", + "question": "Please calculate the comprehensive value index (probability*weight/distance) of each candidate point and determine the optimal path planning scheme (including reachable sampling points and day allocation).", + "answer": "Value index: A=70*3/1.2=175; B=85*2/2.3≈73.9; C=60*1/0.8=75. Optimal plan: Day 1 travel 0.8km to point C → Day 2 sampling → Days 3-4 travel 1.2km to point A (cumulative 2km < 2.5km limit) → Day 5 sampling. Point B is not reachable due to excessive distance." + }, + { + "id": 419, + "scenario_code": "2.9", + "instruction": " The Lunar Navigation Satellite System (LBNSS-1) establishes a two-way ranging link with Yutu-3. Given: 1) Satellite orbit height 100km (Lunar radius 1737km); 2) Ranging signal frequency 2GHz; 3) Receiver signal-to-noise ratio threshold 10dB; 4) Satellite transmission power 20W, antenna gain 26dB; 5) Lunar rover reception antenna gain 18dB; 6) System loss 3dB. The signal propagation speed equals the speed of light c.", + "question": "Calculate whether the maximum theoretical ranging distance meets the current Earth-Moon distance requirement? Consider the free space path loss formula: Lfs=32.45+20log10(d)+20log10(f), where d is in kilometers, and f is in MHz.", + "answer": "Actual distance d=sqrt((1737+100)^2-1737^2)=597km. Lfs=32.45+20log10(597)+20log10(2000)=32.45+55.52+66=154dB; Received power Pr=Pt+Gt+Gr-Lfs-Lsys=20dBW+26dB+18dB-154dB-3dB=-93dBW>-100dBW (threshold 10dB corresponds to 1e-10W). Conclusion: The theoretical maximum ranging distance far exceeds 597km and the received power meets the requirement." + }, + { + "id": 420, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently conducting a patrol exploration on the far side of the moon, located at coordinate point A (10°N, 20°E). The mission center has planned two scientific target points: Point B (10.5°N, 20.2°E) has a special basalt outcrop that needs to be sampled, and Point C (10.3°N, 19.8°E) has a suspected lava tube entrance that needs to be surveyed. It is known that: 1) 1 degree of latitude and longitude on the lunar surface corresponds to about 30 kilometers; 2) The energy consumption model is E = 0.12*d + 2.5 (where d is in kilometers and E is in watt-hours); 3) The current remaining power is 80 watt-hours; 4) Completing a single sampling or survey requires a fixed energy consumption of 15 watt-hours.", + "question": "If at least one target point must be investigated before returning to recharge, please calculate the path combinations Yutu-2 can choose and the corresponding total energy consumption, and determine whether it can complete the tasks at both B and C points simultaneously.", + "answer": "Distance AB = sqrt((0.5*30)^2 + (0.2*30)^2) = 16.16km, energy consumption = 0.12*16.16 + 2.5 = 4.44 watt-hours; Distance AC = sqrt((0.3*30)^2 + (0.2*30)^2) = 10.82km, energy consumption = 0.12*10.82 + 2.5 = 3.8 watt-hours; Distance BC = sqrt((0.2*30)^2 + (0.4*30)^2) = 13.42km. Path combinations: 1) A→B→A total energy consumption = (4.44 + 15)*2 = 38.88 watt-hours; 2) A→C→A total energy consumption = (3.8 + 15)*2 = 37.6 watt-hours; 3) A→B→C→A total energy consumption = 4.44 + 15 + 0.12*13.42 + 15 + 3.8 = 39 > 80 - 38 = 42 watt-hours (not feasible). Conclusion: It can complete the task at point B or C alone, but the remaining power is insufficient to complete the tasks at both points simultaneously." + }, + { + "id": 421, + "scenario_code": "3.1", + "instruction": " Chang'e-6 lander is conducting exploration tasks near the lunar south pole, where the terrain is complex with many craters blocking the view. The solar panels use a two-dimensional tracking algorithm, adjusting the angle every 30 minutes to maximize power generation efficiency. Given that the current solar elevation angle is 15 degrees, and the azimuth angle is 45 degrees; the maximum output power of the solar panels is 200W (when unobstructed), and the current terrain obstruction reduces the effective illuminated area by 40%. The albedo of the lunar surface is 0.12, and the contribution coefficient of diffuse reflection to power generation is 0.2.", + "question": "Calculate the actual output power of the solar panels under the current conditions (consider both direct and diffuse reflection contributions)?", + "answer": "Actual output power = Direct part + Diffuse reflection part = 200W * (1-0.4) * sin(15°) + 200W * 0.12 * 0.2 = 200*0.6*0.2588 + 4.8 ≈ 31.06W + 4.8W = 35.86W" + }, + { + "id": 422, + "scenario_code": "3.6", + "instruction": " The X-band communication equipment of the Chang'e-7 lander needs to maintain a working temperature range of -20°C to +30°C during the lunar night. The equipment's heat dissipation power is 5W, the thermal resistance of the outer insulation material is 2K/W, and the isotope heat source can provide a constant 10W of thermal power. The lunar night environmental temperature is stable at -180°C, and the heat exchange between the equipment and the outside world follows the formula: heat flow Q=(T_in - T_out)/R_total, where R_total=thermal resistance of the insulation layer + radiation thermal resistance (negligible).", + "question": "Calculate whether the isotope heat source alone can keep the equipment within the permissible temperature range? If not, how much additional electrical heating power is needed? ", + "answer": "At equilibrium Q_heat = Q_loss → 10W + P_elec = (T_in +180)/2; the lower limit of the permissible temperature requires: 10W + P_elec ≥ (-20+180)/2=80 → P_elec≥70W (when only the isotope heat source is used, T_in=10*2-180=-160°C, exceeding the lower limit)." + }, + { + "id": 423, + "scenario_code": "1.4", + "instruction": " The lunar base energy grid needs to support mobile exploration vehicles (peak demand 180W), life support systems (constant 120W), and scientific payloads (adjustable 50-100W). The total capacity of the power grid is 300W, with the life support system having the highest priority. Currently, the mobile vehicle is performing a critical sampling task requiring full power operation, and the scientific payload was originally running at 80W. A lunar dust storm warning has triggered an additional 30W heating load for the life support system.", + "question": "To ensure the power grid does not overload and to follow the priority rules, to what power should the scientific payload be adjusted? List the power allocation for each device after adjustment.", + "answer": "Adjust the scientific payload to 50W; Allocation: Life support 150W + Mobile vehicle 180W + Scientific payload 50W = 380W (overload, no solution, the problem setup is contradictory)." + }, + { + "id": 424, + "scenario_code": "1.5", + "instruction": " In the remote operation of Yutu-2, the uplink command delay is 1.3 seconds, and the downlink video delay is 1.25 seconds. When the vehicle travels at a constant speed of 0.1m/s, an emergency stop command must take effect within 0.5 meters of an obstacle. The braking response time is known to be 0.8 seconds (from command reception to complete stop).", + "question": "Calculate the maximum allowable decision-making time from when the ground station detects an obstacle to when the stop command is issued, ensuring the vehicle does not collide. Formula: Safe distance ≥ v*(total delay + braking time) + decision time * v", + "answer": "Decision time ≤ (0.5 - 0.1*(1.3 + 0.8))/0.1 = 2.9 seconds" + }, + { + "id": 425, + "scenario_code": "4.9", + "instruction": " The lunar sample return capsule is designed with a triple-seal structure: ① The main container is made of Ti-6Al-4V alloy (leakage rate < 1×10^-9 Pa·m^3/s) ② The middle layer is pressurized with nitrogen (standard pressure 101kPa) ③ The outer layer is a carbon fiber protective shell. During the ascent phase, three key parameters need to be monitored: seal pressure (normal range 100-105kPa), temperature (-20°C to +50°C), and acceleration (≤15g). The data recording frequency is 10Hz.", + "question": "If the telemetry data from the ascent vehicle shows that the outer layer temperature suddenly rises to 65°C at a certain moment while other parameters are normal, determine whether the sample container integrity alarm should be triggered? Explain the basis.", + "answer": "Trigger the alarm. Basis: The temperature parameter exceeds the upper limit of the normal range (65°C > 50°C). Although other parameters are normal, according to the design specifications, any parameter exceeding the limit should trigger the integrity check procedure." + }, + { + "id": 426, + "scenario_code": "5.7", + "instruction": " The Chang'e-7 orbiter SSD uses NAND Flash storage chips with the following characteristics: 1) Total capacity 1TB, block size 128KB; 2) PE cycle 3000 times, write amplification factor WA=1.5; 3) Average daily write volume 20GB (including scientific data and engineering telemetry); 4) Wear-leveling algorithm uses dynamic cold-hot partitioning strategy, with 15% reserved OP space. The controller needs to monitor the remaining life and issue warnings.", + "question": "Calculate the theoretical service life (in days) of the SSD under the condition of ensuring wear leveling, rounding the result.", + "answer": "1) Actual usable capacity = 1TB * (1-15%) = 850GB; 2) Daily actual write volume to NAND = 20GB * WA = 30GB; 3) Total writable data volume = 850GB * 3000 = 2550TB; 4) Theoretical service life in days = (2550 * 1024) / 30 ≈ 87,040 days (about 238 years). Note: In actual engineering, a more conservative life estimation factor would be considered." + }, + { + "id": 427, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. Analysis of the characteristics of the lunar soil in this area shows: the surface layer 0-30cm is loose fine particles (viscosity coefficient k=0.8 N·s/m^2), and there are hard basalt fragments (Mohs hardness 6.5) at 30-50cm. The probe carries three sampling tools: ① Rotary impact drill (suitable for hardness >5, power consumption 300W) ② Vibration sampling tube (suitable for viscosity <1, power consumption 150W) ③ Electric shovel (universal type, power consumption 200W). The mission requires prioritizing the success rate of sampling, followed by optimizing power consumption.", + "question": "If a complete core sample is needed at a depth of 45cm, which tool should be selected? Provide the key parameter comparison process for the selection.", + "answer": "Select the rotary impact drill. Key parameter comparison: ① The target depth of 45cm is in the high-hardness basalt layer (Mohs hardness 6.5), and the vibration sampling tube and electric shovel do not meet the hardness requirements; ② Although the rotary impact drill has the highest power consumption (300W), it meets the mission requirement of 'prioritizing success rate'." + }, + { + "id": 428, + "scenario_code": "5.1", + "instruction": " Chang'e-6 lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S), and plans to communicate with the ground station through the Queqiao-2 relay satellite. It is known that: 1) Queqiao-2 operates in the Halo orbit around the Earth-Moon L2 point, about 65,000 kilometers from the Moon's center; 2) The lander's transmission power is 10W, with an antenna gain of 5dBi; 3) The relay satellite's receiving system G/T value is 2dB/K; 4) The operating frequency is 2.4GHz, and the free space loss formula is Lfs = 92.45 + 20*lg(d_km) + 20*lg(f_GHz); 5) The required receiving end signal-to-noise ratio Eb/N0 ≥ 10dB, and the data transmission rate is 1Mbps.", + "question": "Calculate whether the current link margin meets the requirements (considering a 3dB polarization loss and a 2dB equipment margin)?", + "answer": "1) Calculate the distance: the distance from the Moon's center to the lander is 1738km, the distance from the Moon's center to the relay satellite is 65000km, and the Earth-Moon distance is 384400km. According to the cosine theorem, the communication distance d = sqrt(1738^2 + 65000^2 - 2*1738*65000*cos(45.5°)) = 64789km; 2) Free space loss Lfs = 92.45 + 20*lg(64789) + 20*lg(2.4) = 214.7dB; 3) EIRP = 10log10(10) + 5 = 15dBW; 4) The receiving power Pr = EIRP - Lfs + Gr/T - Lp - Lm = 15 - 214.7 + 2 - 3 - 2 = -202.7dBW; 5) The required Eb/N0 is converted to the receiving sensitivity Ps = -228.6 + 10log10(1e6) + 10 = -168.6dBW; 6) Margin = Pr - Ps = -202.7 - (-168.6) = -34.1dB, which does not meet the requirements." + }, + { + "id": 429, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth. The 'Queqiao' relay satellite is deployed in a Halo orbit at the Earth-Moon L2 point, about 65,000 kilometers from the Moon. The X-band antenna gain of the relay satellite is 42 dBi, the transmission power of the lander is 10 W, the antenna gain is 6 dBi, and the operating frequency is 8 GHz. The free space path loss formula is: L = 20 * log10(4 * π * d / λ), where d is the distance, and λ is the wavelength (speed of light c = 3 * 10^8 m/s).", + "question": "Calculate the free space path loss of the uplink from the lander to the 'Queqiao' relay satellite (round the answer to the nearest integer).", + "answer": "214" + }, + { + "id": 430, + "scenario_code": "1.2", + "instruction": " When deploying an integrated drilling and sampling device on the edge of a crater in the lunar south pole, the geometric constraints for equipment installation must be considered: the main drill tower unfolds to a height of 2.8 meters (including a 0.5-meter buffer), and the solar panel unfolds to a span of 4.2 meters. The actual measured slope of the landing area is 8°, with local lunar rock obstacles with a diameter of 1.5 meters. The device's electrical interface requirements are: the distance between the drill tower and the power module ≤3 meters (cable length limit), and the distance between the drill tower and the communication module ≤5 meters (signal attenuation threshold). The current candidate installation point coordinates are: Point A (slope 6°, 2.1 meters from the lunar rock), Point B (slope 9°, 3.0 meters from the lunar rock).", + "question": "Based on geometric and electrical constraints, determine which installation point meets all deployment requirements? List the key parameter comparisons.", + "answer": "Point A meets the requirements: 1) Slope 6°<8° is satisfied; 2) Distance from the lunar rock 2.1m>1.5m is satisfied; 3) The equipment orientation can be adjusted so that the distance between the drill tower and the power source is ≤3m and the distance between the drill tower and the communication module is ≤5m. Point B is excluded due to the slope 9°>8°." + }, + { + "id": 431, + "scenario_code": "3.4", + "instruction": " Yutu-2 rover is performing three tasks simultaneously on the 3rd day of the lunar day: ① Continuous sampling by the X-ray spectrometer (power consumption 25W, high priority); ② Panoramic camera shooting (instantaneous peak 50W, lasting 10 minutes, medium priority); ③ Drilling lunar soil with the robotic arm (instantaneous start 120W, stable at 40W, low priority). The power system uses a lithium-ion battery (current available capacity 800Wh) and a PCU with a peak power of 150W. The thermal control system requires reserving at least 200Wh for heating. There are 4 hours of remaining sunlight during the lunar day, with an expected subsequent power generation of 300Wh.", + "question": "Design the task execution order and time allocation plan to ensure that the system overload protection is not triggered and the total energy consumption does not exceed the safety margin. Explain the start time of each task and the power consumption control measures.", + "answer": "Execution order: ①→②→③. Specific plan: 1) Immediately start the X-ray spectrometer; 2) Start the panoramic camera 2 hours later and limit the frame rate to ensure the peak ≤50W; 3) Start the drill in the last hour and load it in stages (run at half power for 5 minutes first, then full power). Total energy consumption = 25W*4h + 50W*0.167h + (60W*0.083h+40W*0.917h) = 100+8.35+40.02 = 148.37Wh < (800+300-200) = 900Wh safety margin" + }, + { + "id": 432, + "scenario_code": "3.6", + "instruction": " Chang'e-6 lander is about to enter the lunar night phase (lasting 14 Earth days), and it is necessary to keep key equipment warm: ① Computer (operating temperature -40°C~+85°C) consumes 5W; ② Battery (optimal temperature -20°C~+30°C) self-heats 2W; ③ Laser rangefinder (only allowed -10°C~+50°C) consumes 0W when not working. The heating system includes: electric heater (100% efficiency), multi-layer thermal insulation material (equivalent thermal resistance R=2K/W), and isotope heat source (constant output 8W). The lunar night environmental temperature is -180°C, and the equipment is coupled through heat-conducting plates (neglecting temperature difference). The current temperature of each device is +10°C.", + "question": "Calculate the minimum power (unit: W) of the electric heater that needs to be turned on to meet the lower temperature requirements of all equipment. Hint: Total heat loss = ΔT/R, required total heating power = heat loss - isotope heat source - battery self-heating.", + "answer": "The most stringent requirement comes from the laser rangefinder (-10°C). Total heat loss = (10 - (-180)) / 2 = 95W; Required additional heating power = 95 - 8 - 2 = 85W; The computer's requirement (5W) is already included in the operating power consumption." + }, + { + "id": 433, + "scenario_code": "3.1", + "instruction": " The Chang'e-5 lander is located near the Mons Rümker mountain at 43.06°N, 51.92°E on the near side of the Moon. During the lunar day, the solar elevation angle in this area varies from 5° to 35°, and the solar panels use two-dimensional tracking (azimuth + elevation). Given: 1) Each solar panel has an area of 1.5m² and an efficiency of 28% under standard sunlight; 2) The current solar elevation angle is 22°, and the azimuth angle is 120°; 3) Due to terrain obstruction, the actual effective sunlight time is 80% of the theoretical value; 4) The solar constant on the lunar surface is 1368W/m².", + "question": "If the solar panels are fully aligned with the sun, the output power is the theoretical maximum. Please calculate the actual power generation at the current moment (considering the impact of terrain obstruction).", + "answer": "Theoretical maximum power = 1368 * 1.5 * 0.28 = 574.56W; Actual power = 574.56 * 0.8 = 459.65W" + }, + { + "id": 434, + "scenario_code": "3.4", + "instruction": " The Yutu-2 rover plans to perform the following tasks on the third day of the lunar day: 1) Move to a new exploration point (80 meters away, 120W for 2 hours); 2) Start the particle-induced X-ray spectrometer (instantaneous peak 300W for 15 minutes); 3) Transmit data via a directional antenna (peak power consumption 200W for 45 minutes). Energy system constraints: The instantaneous total power consumption must not exceed 350W, and the available capacity of the lithium-ion battery pack is 1800Wh.", + "question": "To avoid exceeding the limit, how should the start sequence of the three tasks be arranged? Provide at least one feasible solution that meets the constraints.", + "answer": "Solution 1: First execute the movement task (120W), then sequentially execute the X-ray spectrometer (300W) and data transmission (200W), with the three tasks executed in series. Or Solution 2: Execute the movement and data transmission in parallel (120+200=320W<350W), then separately execute the X-ray spectrometer." + }, + { + "id": 435, + "scenario_code": "3.6", + "instruction": " The relay satellite of Chang'e-4 is about to enter the lunar night phase, and it needs to maintain a constant temperature box between -20°C and +40°C to protect precision instruments. It is known that: 1) The heat capacity of the constant temperature box is 1500J/°C; 2) The lunar night environmental temperature is -180°C; 3) The equivalent thermal resistance of the insulation layer is 0.25°C/W; 4) The rated heat dissipation power of the isotope heat source is 8W; 5) The maximum power of the electric heater is 15W but can only be used intermittently due to the remaining power.", + "question": "Calculate whether the equilibrium temperature of the constant temperature box relying solely on the isotope heat source meets the standard? If the electric heater needs to be activated to make up for the temperature difference, what should its minimum operating power be set to be? ", + "answer": "Equilibrium temperature = -180 + (8 * 0.25) = -178°C (not up to standard); need to make up for ΔT=198°C, electric heating power ≥ ΔT / R = 198 / 0.25 = 792W (exceeds capability, need to optimize insulation or adjust temperature control range)." + }, + { + "id": 436, + "scenario_code": "4.9", + "instruction": " During the handover phase between the ascent vehicle and the sample container, the following conditions must be met: 1) The internal temperature of the container is maintained at -50±5°C; 2) The RFID tag read success rate is ≥99.9%; 3) The docking impact force is <50N. The current telemetry data shows: temperature -48°C, RFID read 10 consecutive successes, the damping coefficient of the docking mechanism buffer is preset to 80N*s/m, and the expected contact speed is 0.6m/s. The impact force calculation formula is F = damping coefficient * contact speed.", + "question": "Determine whether the current handover conditions meet all requirements? Provide the impact force calculation result.", + "answer": "All requirements are met. Calculation process: 1) Temperature -48°C is within the range of -55 to -45°C; 2) RFID read success rate 100% > 99.9%; 3) Impact force F = 80 * 0.6 = 48N < 50N." + }, + { + "id": 437, + "scenario_code": "1.8", + "instruction": " When deploying the seismometer on the lunar rover, it is necessary to monitor the bearing capacity of the lunar soil in real time. It is known that: ① The seismometer bracket needs to withstand a vertical load of 10kg after deployment; ② The actual measured compressive strength of the lunar soil in the current area is 45kPa; ③ The bracket has three legs, each with a circular pressure pad with a diameter of 8cm; ④ The safety factor requirement is ≥2. During the deployment process, an alarm occurs: one leg sinks into the lunar soil to a depth of 3cm (at this time, the actual measured load on a single leg is 4kg), while the other two legs each bear 3kg. The compression characteristics of the lunar soil conform to the formula: compressive stress σ(kPa) = 30 * (compression δ/cm)^0.6.", + "question": "Based on real-time data, determine: ① Whether the actual stress on the current single leg that has sunk exceeds the limit? ② Does the system need to immediately terminate the deployment? (Please write out the comparison formula.)", + "answer": "① The stress on the sunken leg σ = 30*(3)^0.6 ≈58kPa >45kPa (exceeds the limit); ② The safety factor for a single leg = 45/(4*9.8/(π*0.04^2))≈1.13<2; Total load = 4+3+3=10kg = design value but unevenly distributed. Conclusion: Due to local exceedance and insufficient safety factor, immediate termination and adjustment of the leg distribution are required." + }, + { + "id": 438, + "scenario_code": "1.2", + "instruction": " When deploying an array of lunar-based telescopes at the edge of a crater in the lunar south pole, it is necessary to consider the geometric obstruction and electrical interface limitations between devices. The array consists of three main mirror units (A/B/C), and the installation sequence must meet the following conditions: ① Mirror A must be installed first to provide a reference for positioning; ② The installation interval between Mirror B and Mirror C must not exceed 2 hours (to prevent the thermal control system from overloading); ③ The power interface of Mirror C depends on the activation of the power distribution unit of Mirror B. The current ground control center has received the status of each mirror: Mirror A is in place, the transport vehicle for Mirror B is 300 meters from the deployment point (speed 0.05m/s), and Mirror C is on standby (startup time 30 minutes). There are 4 hours of sunlight left on the lunar surface.", + "question": "To ensure the complete deployment of the array, calculate the latest time by which the transport vehicle for Mirror B must arrive at the deployment point. List the key constraints and calculation steps.", + "answer": "The latest arrival time must meet: Mirror B must be installed and completed within 2 hours after Mirror C is installed, and the total time must not exceed the remaining 4 hours of sunlight. Calculation steps: ① The startup time for Mirror C is 30 minutes; ② The installation interval between B and C ≤ 2 hours ⇒ The completion time for installing Mirror B ≤ 4h-0.5h-2h=1.5h; ③ The transportation time for Mirror B = 300m/0.05m/s=6000 seconds=100 minutes≈1.67 hours > 1.5 hours ⇒ The constraint cannot be met. The transportation speed must be adjusted to ≥300m/(1.5*3600)s≈0.0556m/s." + }, + { + "id": 439, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, energy management becomes a key challenge. In the current mission, a network consisting of 3 lunar rovers (LRVs) and 1 fixed scientific station shares a nuclear battery system with a peak power of 1200W. Each LRV consumes 350W continuously (including movement, robotic arm operation, and basic communication) when performing sampling tasks, the scientific station consumes 200W in night maintenance mode, and requires an additional 300W for full-function mode (such as laser ranging and high-frequency data transmission). System settings: ① The total power consumption at any time must not exceed the peak power; ② The full-function mode of the scientific station can last a maximum of 10 minutes each time; ③ At least 100W of redundant power must be reserved to cope with emergencies. At this moment: LRV-1/2 are performing sampling, LRV-3 is on standby (only 50W sleep power consumption), and the scientific station is in night maintenance mode.", + "question": "If the scientific station now requests to activate the full-function mode for 10 minutes, and it must ensure that the tasks of LRV-1/2 are not interrupted, how should the system adjust the power consumption of LRV-3 to meet all the constraints? (Provide specific numerical calculation process.)", + "answer": "Current total power consumption = LRV-1/2 (350*2) + scientific station maintenance (200) + LRV-3 sleep (50) = 1050W. Activating the full function requires an additional 300W to 1350W, exceeding the peak of 1200W and lacking redundancy. The maximum allowable additional power = 1200 - 1050 - 100 = 50W, so the sleep power consumption of LRV-3 must be reduced from 50W to 0 (complete shutdown). After adjustment, the total power consumption = 700 + 500 + 0 = 1200W, meeting all constraints." + }, + { + "id": 440, + "scenario_code": "1.4", + "instruction": " The lunar base energy grid powers three scientific instruments: a seismometer (continuous power consumption of 20W), a spectrometer (peak 80W, operational cycle 40%), and a drill (pulsed load, each start consumes 150J, can be triggered up to 3 times per hour). The grid's output power is limited to 100W, and the storage battery capacity is 500Wh. The current battery charge is 300Wh, and the lunar night is about to last 14 Earth days.", + "question": "Under the premise of ensuring the continuous operation of the seismometer, how should the working modes of the spectrometer and the drill be adjusted to make the system last through the entire lunar night? Provide the maximum allowable trigger frequency of the drill.", + "answer": "Available total energy = 300Wh + 100W * 14 * 24h = 33600Wh. Seismometer energy consumption = 20W * 14 * 24h = 6720Wh => 26880Wh remaining for the spectrometer and the drill. Let the drill trigger x times/hour, then the total energy consumption = 80W * 0.4 * 336h + 150J * x * 336h / 3600s/h ≤ 26880Wh -> 10752Wh + 14x Wh ≤ 26880Wh => x ≤ (26880-10752)/14 ≈ 1152 times/336h ≈ 3.43 times/h => Maximum trigger frequency 3 times/h (not exceeding the hardware limit)." + }, + { + "id": 441, + "scenario_code": "1.5", + "instruction": " When remotely controlling the lunar rover to perform rock sampling, the one-way communication delay between Earth and Moon is 1.3 seconds. The current speed of the lunar rover is 0.2m/s, and there is an obstacle 10 meters ahead. It takes 0.5 seconds to generate control commands, and the braking system responds with a delay of 0.8 seconds before decelerating at an acceleration of -0.15m/s². The autonomous braking distance threshold of the onboard safety system is 3 meters.", + "question": "Determine whether the ground control personnel need to immediately issue an emergency braking command? List the complete sequence analysis and distance calculation process.", + "answer": "Total delay = command transmission 1.3s + generation 0.5s + response 0.8s = 2.6s. During this period, the lunar rover moves a distance of 0.2m/s * 2.6s = 0.52m; the remaining distance is 10m - 0.52m = 9.48m. The braking distance required v²/(2a) = (0.2)²/(2*0.15) ≈ 0.133m < 3m autonomous threshold => No emergency braking is needed, the safety system can handle it. However, if the initial distance ≤ (3m + 0.52m) = 3.52m, intervention is required." + }, + { + "id": 442, + "scenario_code": "2.9", + "instruction": " The Lunar Beacon Navigation Satellite System (LBNSS) operates in a circular orbit 100 km above the lunar surface, with an orbital period of 120 minutes. At a certain moment, the geometric relationship between the beacon and the lunar rover is as follows: the satellite elevation angle is 60°, the Doppler frequency shift measurement indicates a rate of distance change of +15 m/s, and the UWB beacon ranging accuracy is ±3 m (1σ). It is known that: 1) the radial velocity component of the satellite Vr = Vorb * sin(θ), where Vorb = 1.64 km/s; 2) the current inertial navigation system (INS) positioning error ellipse major axis is 50 m (3σ).", + "question": "Determine whether the theoretical positioning accuracy of the current integrated navigation system is better than that of the pure INS? Please provide the key comparison parameters.", + "answer": "1) The radial velocity component of the satellite Vr = 1640 * sin(60°) ≈ 1420 m/s; 2) Doppler velocity measurement error = 15 / 1420 ≈ 1% corresponding to a position error of ±14.2 m; 3) Combined error = sqrt(3^2 + 14.2^2) ≈ 14.5 m < 50 m / 3 ≈ 16.7 m. Conclusion: The integrated navigation accuracy (14.5 m @ 1σ) is better than the pure INS (16.7 m @ 1σ)." + }, + { + "id": 443, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 rover is conducting exploration tasks in the lunar south pole, and its solar panels use a two-dimensional tracking algorithm. At the current moment, the solar altitude angle is 15 degrees, and the azimuth angle is 30 degrees (with north as 0 degrees). The rover's location is obstructed by a crater on the east side, preventing power generation when the solar azimuth angle is between 60 and 120 degrees. The maximum output power of the solar panels is 200W (when unobstructed), and the power drops to 50W when obstructed. The lunar day lasts 14 Earth days, and it is currently the 3rd day of the lunar day.", + "question": "If the rover maintains its current orientation, calculate the total power generation of the solar panels over the next 24 hours (assuming the solar altitude angle and azimuth angle changes can be ignored).", + "answer": "Since the solar azimuth angle of 30 degrees is not within the obstructed range (60-120 degrees), the solar panels will operate at maximum power of 200W for 24 hours, with a total power generation of 200W * 24h = 4800Wh." + }, + { + "id": 444, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing patrol tasks on the far side of the moon, located at point A (10°N, 120°E). The science team requires it to reach target point B (12°N, 122°E) to conduct spectral measurements before the end of the lunar day (8 hours remaining). It is known that: 1) The straight-line distance between the two points is 30km, but a detour around a 5km diameter crater is necessary; 2) The average driving speed of the lunar rover is 0.1km/h, and it slows to 0.06km/h when climbing; 3) 20% of the detour route is a 10° slope; 4) The remaining battery power supports continuous driving for 10 hours (on flat terrain).", + "question": "Please calculate whether Yutu-2 can safely reach the target point via the detour route within the energy and time constraints? Provide specific calculation steps.", + "answer": "1) Detour total distance = straight-line distance + half the circumference of the crater = 30 + (3.14*5/2) ≈ 37.85km; 2) Flat road distance = 37.85*80% ≈ 30.28km, time required = 30.28/0.1 ≈ 302.8 hours; 3) Slope road distance = 37.85*20% ≈ 7.57km, time required = 7.57/0.06 ≈ 126.2 hours; 4) Total time required = 302.8 + 126.2 = 429 hours >> 8 hours. Conclusion: It cannot arrive on time and the energy is insufficient (429h > 10h)." + }, + { + "id": 445, + "scenario_code": "2.6", + "instruction": " The Chang'e-4 lander is conducting long-term observations in the Von Kármán crater. The drift error model of its Inertial Navigation System (INS) is: position error = 0.1% * travel distance + 3m/hr, attitude error = 0.05°/hr. When the cumulative position error exceeds 50m or the attitude error exceeds 2°, the star sensor must be activated for correction. The lander has been operating continuously for 72 hours, during which the rover has traveled a cumulative distance of 800 meters.", + "question": "Is it currently necessary to activate the star sensor for correction? List the determination calculation process.", + "answer": "1) Position error = 0.1% * 800m + 3m/hr * 72hr = 0.8 + 216 = 216.8m > 50m; 2) Attitude error = 0.05°/hr * 72hr = 3.6° > 2°. Both indicators exceed the threshold, immediate correction is required." + }, + { + "id": 446, + "scenario_code": "3.3", + "instruction": " Yutu-2 needs to maintain the temperature of key equipment during the lunar night transition. The isotope heat source (RHU) has a rated heat output of 5W, and the electric heater has a maximum power of 20W. The current battery has a remaining capacity of 300Wh, the basic power consumption of the equipment is 2W, and the heating requirement is 15W. The lunar night lasts for 14 Earth days, with the first 7 days allowing the use of electric heating and the last 7 days only allowing the use of RHU.", + "question": "Calculate the minimum average daily heating time required during the first 7 days of electric heating (the electric heater must work intermittently) to ensure that the battery is not depleted when RHU works alone during the last 7 days.", + "answer": "Energy consumption for the last 7 days = (2W + 15W - 5W) * 24h * 7 = 2016Wh; the remaining battery capacity of 300Wh is insufficient to support this, indicating a contradiction in the problem setup (no feasible solution). It should be: the first 7 days need to make up for (2016Wh - 300Wh) / 20W = 85.8h / 7 ≈ 12.26h / day" + }, + { + "id": 447, + "scenario_code": "3.8", + "instruction": " Chang'e-7 lander mission cycle planning: ① Days 1-3 of the lunar day: drilling and sampling (peak power consumption 150W, average 6h per day); ② Days 4-5: data transmission (peak 80W, 2 times × 1h per day); ③ The rest of the time in standby (10W). The average daily power generation from solar panels is 1200Wh, the battery capacity is 5000Wh, and the initial SOC is 80%.", + "question": "Determine whether the energy budget will result in a power deficit (list the total energy consumption for drilling, transmission, and standby, and compare it with the power generation)?", + "answer": "Total energy consumption = drilling 150W * 6h * 3 = 2700Wh + transmission 80W * 1h * 4 = 320Wh + standby 10W * (14*24 - 6*3 - 1*4) = 2960Wh; total power generation = 1200Wh * 14 = 16800Wh; difference 16800 - (2700 + 320 + 2960) = 10820Wh > 0, no power deficit." + }, + { + "id": 448, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing exploration tasks within the Von Kármán crater, located at coordinate point A(10,20). It needs to travel to the scientific target point B(45,60) to collect samples. It is known that: 1) The lunar surface terrain is complex, and the driving path must avoid areas with a slope >15°; 2) The energy consumption model is E = 0.12*d + 2.5*h, where d is the horizontal distance (meters), and h is the cumulative ascent height (meters); 3) The current remaining battery energy is 1800Wh; 4) There are two candidate paths from A to B: Path 1 has a horizontal distance of 55 meters and a cumulative ascent of 8 meters; Path 2 has a horizontal distance of 50 meters and a cumulative ascent of 12 meters.", + "question": "To ensure that Yutu-2 can safely reach the target point B, which path should be chosen? Please explain the basis for your choice through calculations.", + "answer": "Path 1 should be chosen. Calculation process: Energy consumption for Path 1 E1 = 0.12*55 + 2.5*8 = 6.6 + 20 = 26.6Wh; Energy consumption for Path 2 E2 = 0.12*50 + 2.5*12 = 6 + 30 = 36Wh. 26.6Wh < 36Wh and both are much less than the remaining energy of 1800Wh, so the path with lower energy consumption, Path 1, should be chosen." + }, + { + "id": 449, + "scenario_code": "3.8", + "instruction": " The work cycle of the Chang'e-6 lander on the lunar surface is planned as follows: 14 Earth days during the lunar day, with the first 10 days conducting 3 scientific explorations daily (each instrument consuming 120W for 2 hours), and 2 data transmissions (each 80W for 1 hour); the last 4 days conducting continuous drilling operations (250W for 8 hours/day). The system's basic power consumption is 50W, the average daily power generation of the solar array is 5kWh, and the available capacity of the lithium-ion battery pack is 20kWh (SOC maintained between 20%-90%). The power consumption during the lunar night is 15W.", + "question": "Verify whether the mission plan meets the energy balance requirements? If not, propose how many days the drilling operation should be adjusted to meet the constraints (while maintaining the total drilling time of 32 hours unchanged)?", + "answer": "Verification steps: 1) Total energy consumption during the lunar day=[10*(3*120*2+2*80*1)+4*250*8]+14*24*50=34,400Wh; 2) Total power generation during the lunar day=14*5000=70,000Wh; 3) Energy consumption during the lunar night=14*24*15=5040Wh; 4) Battery needs to provide 5040-(70000-34400)=-30560Wh (surplus). Adjustment plan: the number of drilling days x satisfies 250*8*x + (14-x)*50*24 ≤70000-5040→x≤3.21 days. Choose 3 days to complete the drilling (10.67 hours per day), total consumption 34,133Wh< surplus 35,560Wh." + }, + { + "id": 450, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is executing a long-distance scientific exploration mission, needing to travel from its current location A (45.5°N, 177.8°E) to target point B (45.7°N, 178.1°E). According to orbiter terrain data, the straight-line distance between the two points is 1.2 kilometers, but there is a crater obstacle with a slope exceeding 15°. There are two alternative routes: Route 1 is 1.5 kilometers long with an average slope of 8°; Route 2 is 1.3 kilometers long with an average slope of 12°. The rover's mobility power consumption model is: flat ground power consumption P0=20W, power consumption increases by ΔP=1.5W for each additional 1° of slope. The battery currently has 500Wh of remaining energy, and the movement speed is constant at 0.05m/s.", + "question": "To ensure that Yutu-2 retains at least 100Wh of emergency power upon reaching the target point, which detour route should be chosen? Please calculate the total power consumption for both routes and explain the basis for your choice.", + "answer": "Total power consumption for Route 1 = (P0 + 8*ΔP) * (1500m / 0.05m/s) /3600 = (20+12)*30000/3600 = 266.67Wh; Total power consumption for Route 2 = (20+18)*26000/3600 = 274.44Wh. Route 1 should be chosen because its total power consumption of 266.67Wh < (500-100)=400Wh, meeting the margin requirement, and it is more energy-efficient than Route 2." + }, + { + "id": 451, + "scenario_code": "2.10", + "instruction": " The lunar research station rover needs to perform centimeter-level precise positioning sampling on a basalt outcrop with a diameter of 3 meters. Known: the visual navigation camera resolution is 0.1m/pixel at 10m distance; the laser rangefinder accuracy is ±2cm; the UWB beacon is deployed 5m north of the outcrop, with a ranging error of ±5cm; the current pose estimation error ellipse (1σ) of the rover is 20cm long axis, 10cm short axis, and an orientation angle of 30°. The control system requires that the final positioning error ellipse semi-axes be less than 5cm to start sampling.", + "question": "Determine whether the current precision requirements for sampling are met? If not, to what extent must the UWB ranging error be reduced to meet the standard? (Assuming other errors remain unchanged.)", + "answer": "Current total positioning error = sqrt(20^2*cos(30°)^2 + 10^2*sin(30°)^2 + 5^2 + 2^2) = 19.35cm > 5cm requirement. Let the new UWB error be x, it needs to satisfy sqrt(19.35^2 - 5^2 + x^2) ≤ 5 → x ≤ 3.27cm, i.e., the UWB error must be reduced to within ±3cm." + }, + { + "id": 452, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks in the Von Kármán crater, located at coordinate point A(10,20), and needs to reach scientific target point B(50,60). Terrain data indicates that there are three optional paths between the two points: Path 1 is a straight-line distance of 40 meters but with an 8° incline; Path 2 is a detour of 55 meters on a flat path (0° incline); Path 3 is a distance of 45 meters but includes a 5-meter area of loose lunar soil (the driving energy consumption coefficient for loose lunar soil is 3 times that of flat ground). It is known that the unit distance energy consumption of the lunar rover on flat ground E=0.1*d (d is the distance), and the additional energy consumption for uphill ΔE=0.05*incline*distance. The remaining battery energy is 6.5Wh, and at least 1Wh must be reserved for emergency power.", + "question": "Please calculate the total energy consumption of the three paths and determine which path is optimal under the energy constraint conditions.", + "answer": "Total energy consumption of Path 1 = 0.1*40 + 0.05*8*40 = 4 + 16 = 20Wh; Total energy consumption of Path 2 = 0.1*55 = 5.5Wh; Total energy consumption of Path 3 = 0.1*40 + 0.3*5 = 4 + 1.5 = 5.5Wh. The upper limit of available energy is 5.5Wh, so Path 2 or Path 3 can be chosen (equally optimal)." + }, + { + "id": 453, + "scenario_code": "2.7", + "instruction": " The lunar rover receives a solar proton event warning while patrolling near the terminator and needs to reach the nearest permanent shadow area within a 200-meter radius in 15 minutes. The current speed of the rover is 0.1m/s, and the inertial navigation system shows coordinates at (100,200). The known coordinates of the shadow areas are: (80,350), (300,150), (50,50). Communication delay prevents ground control from intervening in real time. The IMU drift error is 0.5°/h, and the current heading angle confidence interval is ±3°.", + "question": "Considering the navigation error, which shelter target should be chosen? Provide the key parameter calculation process for the decision.", + "answer": "The distance that can be traveled in 15 minutes = 0.1 * 900 = 90 meters. Distance to target 1 = sqrt((80-100)^2 + (350-200)^2) = 151m; Distance to target 2 = sqrt((300-100)^2 + (150-200)^2) = 206m; Distance to target 3 = sqrt((50-100)^2 + (50-200)^2) = 158m. Only targets 1 and 3 are within the theoretical reach range, choose the closer target 1 (in practice, the path extension due to heading error needs to be considered)." + }, + { + "id": 454, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover experienced a sudden communication interruption during the lunar day, with diagnostic information showing:\n1. The currently used relay link (Queqiao-3) is temporarily unavailable due to solar interference\n2. The backup relay satellite (Queqiao-R) is located at the Earth-Moon L4 point, increasing latency by 300ms\n3. Remaining cache data volume is 12GB, with a storage write speed of 50Mbps\n4. 4 hours of lunar day remain, with the rover's solar power supply reduced to 80W\n5. The DTN protocol retransmission mechanism requires a minimum transmission rate of 2Mbps", + "question": "Please evaluate whether to switch to the backup relay satellite to complete data transmission during the current lunar day window? Consider energy and latency constraints.", + "answer": "1. Transmission time requirement: 12GB/(2Mbps) ≈13.7h >4h → cannot complete\n2. Energy constraint: 80W*4h=320Wh > (12GB/50Mbps)*20W≈0.11Wh → energy is sufficient but time is not enough → should not switch" + }, + { + "id": 455, + "scenario_code": "5.7", + "instruction": " The SSD storage system of the Chang'e-7 orbiter is designed as follows:\n1. NAND flash block size is 128KB, with an erase life of 3000 cycles\n2. A dynamic wear leveling algorithm is used, with a standard deviation σ=120 cycles in historical write distribution\n3. The most worn block has been erased and written 1400 times\n4. The average daily write volume is 40GB, of which 70% is scientific data (lossless compression required)\n5. The total capacity of the SSD is 1TB, with 28% reserved for OP space", + "question": "Calculate the expected remaining mission life (years) under the current wear state, assuming a constant compression ratio of 1:0.6 for scientific data.", + "answer": "1. Actual daily write volume: 40GB*0.7*0.6 +40GB*0.3 =34.8GB\n2. Average daily erase cycles: 34800MB/128KB≈272k cycles/3000k blocks≈0.091 cycles/block·day\n3. Remaining life: (3000-1400-3σ)/(0.091*365)≈(3000-1400-360)/33≈37 years" + }, + { + "id": 456, + "scenario_code": "1.2", + "instruction": " Deploy a lunar-based telescope array unit at the edge of the Shackleton crater in the lunar south pole. The equipment consists of a main mirror module (120kg), a support structure (80kg), and an electronic control box (60kg), which must be installed in a specific order: the support structure must be secured first before installing the main mirror module, and the electronic control box must be connected after the main mirror module is calibrated. The lunar work robot has a maximum load capacity of 150kg and requires a 30-minute cooldown after each transport. The deployment site is 200 meters in a straight line from the lander, and the robot's movement speed is 0.1m/s (fully loaded) or 0.2m/s (unloaded). The current mission time window has 4 hours remaining.", + "question": "Can all components be transported and installed within this time window? If not, what is the minimum additional time required to complete the task? ", + "answer": "It can be completed. Total transportation time: (200/0.1)*3 + (200/0.2)*3 = 6000 seconds (100 minutes); cooling time: 30 minutes * 3 times = 90 minutes; installation time in sequence is approximately 60 minutes; total time required 100+90+60=250 minutes < 4 hours (240 minutes), actually need to extend 10 minutes." + }, + { + "id": 457, + "scenario_code": "1.4", + "instruction": " A lunar power grid simultaneously powers a drill (peak power 300W), a spectrometer (150W), and a robotic arm (200W). The solar array has a maximum output power of 500W, and the battery can provide an additional 100W of continuous power. The drill must stop for 5 minutes to cool down after every 10 minutes of operation, the spectrometer requires continuous power, and the robotic arm can operate for no more than 15 minutes per hour. The current battery charge is 200Wh (discharge efficiency 90%).", + "question": "In the next hour, how should the operation of the equipment be arranged to prevent the system from overloading? Provide the maximum allowable operating time for each device.", + "answer": "Plan: The drill operates for 20 minutes (in 2 sessions), the robotic arm for 15 minutes, and the spectrometer for 60 minutes. Peak power = 300 + 150 + 200 = 650W > 600W (500 + 100), peak shaving is required: the drill and robotic arm do not operate simultaneously, maximum total energy consumption = (300*20 + 150*60 + 200*15)/60 = 350Wh < 200Wh*90% + 500Wh = 680Wh." + }, + { + "id": 458, + "scenario_code": "1.8", + "instruction": " When deploying the seismometer, it was found that the local lunar soil bearing capacity is only 1.2kPa (design requirement ≥1.5kPa). The total weight of the instrument is 50kg, and the base area is 0.25m². There are three adjustment options: A) Expand the base to 0.4m²; B) Reduce the weight to 40kg; C) Move to a location 300 meters away where the measured bearing capacity is 1.8kPa. The movement speed is 0.05m/s, and redeployment requires an additional 30 minutes. The remaining task time is 45 minutes.", + "question": "From the perspective of engineering reliability, which option should be chosen? Please provide the specific calculation process.", + "answer": "Option A should be chosen. Calculation: A) Pressure = 50*9.8/0.4 = 1225Pa < 1.2kPa; B) Pressure = 40*9.8/0.25 = 1568Pa > 1.2kPa, still exceeds the limit; C) Movement time = 300/0.05 = 600 seconds = 10 minutes, total time required is 40 minutes < 45 minutes, but the reliability is lower than the direct modification of A." + }, + { + "id": 459, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. The characteristics of the lunar soil in this area are as follows: the surface layer 0-30cm is loose fine particles (viscosity coefficient k=0.8 Pa·s), and there are high-hardness basalt fragments (Mohs hardness 6.5) at 30-50cm. The probe is equipped with three sampling tools: a rotary impact drill (suitable for hardness >5, power consumption 120W), a spiral core sampler (suitable for viscosity <1Pa·s, power consumption 80W), and an electric shovel (universal type, power consumption 60W). The mission requires prioritizing the integrity of the sample, followed by energy consumption optimization.", + "question": "For sampling operations in the 30-50cm layer, which tool should be selected? Please explain the selection criteria based on the material properties and equipment parameters.", + "answer": "The rotary impact drill should be chosen. Because the Mohs hardness of the lunar rock in this layer is 6.5, which exceeds the applicable upper limit of the spiral core sampler and the electric shovel. The rotary impact drill is specifically designed for high-hardness materials, although it has higher power consumption, it can ensure the integrity of the sample." + }, + { + "id": 460, + "scenario_code": "4.4", + "instruction": " Yutu-2 is conducting exploration in the Von Kármán crater, obtaining the following remote sensing data: ① 100-meter resolution multispectral images show characteristic absorption peaks of KREEP in the northeast quadrant; ② LiDAR measurements indicate a slope <8° in the area; ③ Thermal infrared data show a surface temperature fluctuation <20K during the day. It is known that the rover's remaining power can support a travel of 300 meters or 2 hours of in-situ exploration. The scientific priority ranking is: mineral composition analysis > terrain safety > thermal environment stability.", + "question": "Based on the analysis of multi-source data, is this area suitable to be listed as a high-priority sampling point? List the key factors and their weights for the judgment.", + "answer": "It is suitable to be listed as a high-priority sampling point. Key factors and weights: ① KREEP mineral composition (50% weight); ② Terrain safety with a slope <8° (30% weight); ③ Thermal stability with temperature fluctuations <20K (20% weight). All three meet the scientific priority requirements and the exploration cost is within the budget." + }, + { + "id": 461, + "scenario_code": "4.9", + "instruction": " The design parameters of the lunar sample return capsule are as follows: ① The internal pressure of the sealed container is maintained at 1.3kPa ± 0.2kPa; ② The RFID tag must function normally in the temperature range of -180°C to +60°C; ③ The maximum allowable position deviation during docking with the ascent vehicle is ±5cm. Current telemetry data show that the temperature of a certain sample can is -150°C, the internal pressure is 1.4kPa, and the docking mechanism feedback indicates a lateral deviation of +3cm and an axial deviation of -2cm.", + "question": "Determine whether the sample container meets the handover conditions? Which key parameters need to be verified in sequence? ", + "answer": "The sample container meets the handover conditions. The following need to be verified: ① The internal pressure of 1.4kPa is within the allowable range of 1.1-1.5kPa; ② -150°C is within the RFID operating temperature range; ③ The lateral deviation of +3cm and the axial deviation of -2cm are both less than the tolerance of ±5cm." + }, + { + "id": 462, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 45°S, 176°E) and needs to communicate with the ground station via the Queqiao-2 relay satellite. Given:\n1. Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, approximately 65,000 km from the Moon's center\n2. At the current moment, the Moon's rotation has made the elevation angle between the lander and Queqiao 25°, and the maximum communication distance of the Earth-Moon relay link is 70,000 km\n3. The link budget requires the received signal strength to be ≥ -110 dBm, the current downlink frequency is 2.4 GHz, the transmission power is 20 W, and the antenna gain is 38 dBi\n4. The free space path loss formula: L = 92.45 + 20*lg(d) + 20*lg(f), where d is the distance (km) and f is the frequency (GHz).", + "question": "Calculate the free space path loss of the current relay link and determine whether it meets the communication requirements (specific values and comparison process must be provided).", + "answer": "Path loss L = 92.45 + 20*lg(65000) + 20*lg(2.4) ≈ 92.45 + 96.26 + 7.6 = 196.31 dB; Received signal strength = Transmission power (20W → 43 dBm) + Antenna gain (38 dBi) - L ≈ 43 + 38 - 196.31 = -115.31 dBm < -110 dBm, does not meet the requirement." + }, + { + "id": 463, + "scenario_code": "5.7", + "instruction": " The 128GB on-board SSD of the Chang'e-7 orbiter has encountered the following conditions:\n1. The NAND flash block size is 4KB, with a total write volume reaching 60TBW\n2. SMART monitoring shows that the bad block rate has risen to 0.8% (exceeding the 0.5% threshold)\n3. The file system uses FTL dynamic mapping, and the current wear leveling algorithm is static weighted round-robin\n4. The SSD controller supports bad block remapping and AES-256 encryption", + "question": "Propose three specific measures to extend the SSD's lifespan and ensure data security (technical basis must be explained in conjunction with the given parameters).", + "answer": "1. Switch to a dynamic wear leveling algorithm (such as hot zone migration based on erase counts) to reduce the burden on high-write blocks; 2. Enable the bad block remapping function to reserve 0.3% redundant blocks; 3. Enable compression before writing for non-real-time data to reduce actual write volume." + }, + { + "id": 464, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin. The characteristics of the soil in this area are: medium hardness (Mohs hardness 4-5), low viscosity, and volatile content of about 120 ppm. There are three sampling tools available: A-type rotary impact drill (suitable for hardness 5-7, power consumption 15W/min), B-type spiral grab (suitable for hardness 3-5, power consumption 8W/min), C-type vibration scraper (suitable for hardness 2-4, power consumption 5W/min). The mission requires a sampling depth of ≥10cm, a single operation time of ≤20 minutes, and prioritizes the preservation rate of volatiles.", + "question": "Based on the above conditions, which sampling tool should be chosen? Please explain the selection criteria by combining tool applicability, power consumption constraints, and scientific objectives.", + "answer": "The B-type spiral grab should be chosen. Reasons: 1) The hardness of the lunar soil (4-5) is completely within its applicable range; 2) The power consumption of 8W/min * 20min = 160W meets the time constraint; 3) Compared to the A-type drill, it is more energy-efficient and avoids excessive fragmentation of volatiles, and compared to the C-type scraper, it can better ensure a sampling depth of 10cm." + }, + { + "id": 465, + "scenario_code": "4.9", + "instruction": " The sample container transfer process between the ascender and the lander requires: 1) The container temperature must be stabilized at -50±5℃; 2) The relative velocity during transfer ≤0.05m/s; 3) The docking mechanism alignment error <3mm. Current monitoring data: Container temperature -48℃, ascender approach speed 0.03m/s (x-axis) + 0.04m/s (y-axis), docking ring center offset x=+2mm, y=-1mm. The temperature maintenance system power is 10W/℃, and the remaining power can support 30 minutes of full power operation.", + "question": "Determine if the current status meets the transfer conditions? If adjustments are needed, point out the most critical parameters and the correction plan (calculate the longest operating time of the temperature maintenance system).", + "answer": "The current status meets the transfer conditions. Reasons: 1) Temperature -48℃ is within the range of -55~-45℃; 2) Combined speed = sqrt(0.03^2 + 0.04^2) = 0.05m/s, reaching the upper limit but still qualified; 3) Total offset = sqrt(2^2 + 1^2) = 2.24mm < 3mm. The longest operating time of the temperature system = 30min * (10W/℃) / [10W/℃ * (|48-50|)] = 15min (if cooling to -50℃ is required)." + }, + { + "id": 466, + "scenario_code": "3.4", + "instruction": " Yutu-2 performs three tasks simultaneously during the 3rd hour of the lunar day: ① Continuous sampling by the X-ray spectrometer (power consumption 25W, high priority); ② Panoramic camera shooting (peak power consumption 45W, lasting 5 minutes, medium priority); ③ Mechanical arm drilling and sampling (instantaneous power consumption at startup 120W, stable at 60W, total duration 30 minutes, low priority). The power system has a maximum output power of 150W, and the battery can currently provide an additional 50W buffer power.", + "question": "Design a load scheduling plan to meet the needs of all equipment, ensuring that high-priority tasks run continuously, and provide the start and stop times for each device.", + "answer": "Scheduling plan: ① The X-ray spectrometer is on throughout (25W); ② The panoramic camera is on from 0-5 minutes (45W); ③ The mechanical arm operates in two segments: from 5-20 minutes (the first 15 minutes require 120W, using 50W buffer from the battery), and from 25-35 minutes (60W). The total power is always ≤150W." + }, + { + "id": 467, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, a shared energy grid needs to be established. The current system includes: 1 solar main power unit (peak output 1200W, working 14 hours during the day), 2 radioisotope thermoelectric generators (RTGs, each continuously outputting 200W), and 3 scientific payloads (A: Seismometer with a constant power consumption of 80W; B: Spectrometer with a working cycle of 10 minutes per hour and a peak power consumption of 300W; C: Drill working 3 times a day, each time for 15 minutes, with an instantaneous startup power of 2000W requiring support from a buffer capacitor). The energy bus adopts an intelligent priority allocation strategy: Life support > Data transmission > Scientific payloads.", + "question": "If on a certain day during the early part of the lunar day, the spectrometer and the drill start simultaneously (with no other loads), can the actual available power from the RTGs and the solar unit meet the demand? How should it be adjusted if not possible to meet the demand immediately? ", + "answer": "No. Total power demand = Spectrometer 300W + Drill 2000W = 2300W, available power = Solar 1200W + RTG 400W = 1600W, shortfall 700W. According to the priority, the drill startup should be delayed or the sampling frequency of the spectrometer should be reduced." + }, + { + "id": 468, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform sampling tasks in rugged areas, the one-way communication delay between Earth and the Moon is 1.3 seconds. The control system uses a predictive compensation algorithm: v_cmd = v_real + a_pred * t_delay, where a_pred is the predicted acceleration based on terrain data (range ±0.2m/s²). The current lunar rover is traveling at a speed of 0.15m/s, and there is a steep slope 3 meters ahead requiring emergency braking (maximum deceleration -0.25m/s²). The control command is sent from Earth when the latest sensor data from the vehicle is already 2 seconds old.", + "question": "Calculate the theoretical command speed v_cmd that should be sent to ensure the vehicle stops before the slope, given that the actual speed may have already changed.", + "answer": "v_cmd = v_real + a_pred * t_delay = 0.15 + (-0.25)*2 = -0.35m/s (but physically infeasible). In practice, the minimum v_cmd should be 0, because the stopping distance d under maximum deceleration = (v_real^2)/(2*|a|) = (0.15^2)/0.5 = 0.045m < 3m, so a direct stop command can be issued." + }, + { + "id": 469, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform rock sampling, the one-way communication delay between Earth and the Moon is 1.28 seconds. The lunar rover's motion control uses a predictive compensation algorithm, with its motion model being: actual displacement = commanded displacement * (1 - e^(-t/τ)), where τ = 0.8 seconds is the system time constant. The current movement command sent is to move forward in a straight line for 2 meters, and the command transmission time is included in the delay.", + "question": "If an obstacle is suddenly detected 3 seconds after sending the command and an emergency stop is required, what is the actual displacement of the lunar rover at this time? (e^-2.25≈0.105).", + "answer": "1.79 meters. Calculation process: Effective control time t = 3s - 1.28s = 1.72s; Displacement = 2 * (1 - e^(-1.72/0.8)) = 2 * (1 - 0.105) = 1.79m." + }, + { + "id": 470, + "scenario_code": "1.4", + "instruction": " The lunar surface energy grid needs to allocate peak power to 3 devices: a seismometer (continuous demand of 30W), a spectrometer (pulsed demand with a peak of 80W per 10-minute cycle), and a mobile rover (intermittent demand with a peak of 120W, randomly triggered). The system has a total power supply capacity of 200W, and it uses a priority strategy: rover > spectrometer > seismometer. Currently, the spectrometer is in the 3rd minute of its working cycle, and the rover suddenly initiates a 60-second emergency sampling task.", + "question": "Calculate whether the seismometer will be forced to reduce power to ensure system stability, and provide the actual power allocation values.", + "answer": "Total demand = 80W (spectrometer) + 120W (rover) = 200W ≤ 200W, the seismometer does not need to reduce power. The actual allocation is 30W (seismometer) + 80W (spectrometer) + 90W (rover), the rover does not reach its peak due to the total capacity limit." + }, + { + "id": 471, + "scenario_code": "2.7", + "instruction": " When the lunar rover is operating near the terminator, the ground station suddenly issues a solar proton event warning (lasting 4 hours). The current remaining power is 30%, and the minimum power required for safe mode is 10%. It is known that: the regular driving power consumption is 200W, and the power consumption for hazard avoidance hibernation is 50W; a 180° turn in place requires 5 minutes and consumes 18Wh; the nearest permanent shadow refuge is located 800 meters to the northwest (driving on flat terrain requires 20 minutes).", + "question": "To ensure safety redundancy, please calculate whether the lunar rover can complete the turn and reach the refuge while retaining 10% power? Assume the total battery capacity is 500Wh.", + "answer": "Available power = 30% - 10% = 20%, which is 100Wh. Turning power consumption 18Wh + driving power consumption = 200W*(20/60)h ≈ 66.67Wh, total power consumption 84.67Wh < 100Wh, it can complete the hazard avoidance." + }, + { + "id": 472, + "scenario_code": "2.10", + "instruction": " The detector needs to perform a millimeter-level spectral scan on a lunar surface rock with a diameter of 0.5 meters. Given: the visual navigation camera resolution is 2mm/pixel (working distance 2m), the end-effector positioning accuracy of the robotic arm is ±1cm, and the maximum deployable angle of the solar panels at the current position is ±30° (to avoid self-occlusion). The current distance between the detector and the rock is 1.8 meters, with a relative height difference of 15cm.", + "question": "Determine if the current distance meets the positioning accuracy requirement for spectral scanning. If not, calculate the optimal working distance to adjust to (while maintaining the same camera resolution).", + "answer": "At the current distance of 1.8m, the resolution = 2mm/pixel * (1.8/2) = 1.8mm/pixel > 1mm requirement, which does not meet the requirement. The distance d needs to be adjusted to satisfy 2*(d/2) ≤ 1 → d ≤ 1m, so the optimal working distance should be ≤1 meter and > the working radius of the robotic arm, 0.5m." + }, + { + "id": 473, + "scenario_code": "1.5", + "instruction": " Chang'e-7 lander is controlling the lunar rover to sample rocks through remote operation with a 1.3-second delay. The current speed of the lunar rover is 0.2m/s, and the positioning accuracy requirement for the end of the robotic arm is ±5cm. After the ground command is issued, the lunar rover needs to immediately execute a sampling sequence consisting of three consecutive actions: move forward 0.8m → extend the robotic arm → rotate 30 degrees to collect samples. It is known that the execution time for each action is 4 seconds, 2 seconds, and 3 seconds, respectively.", + "question": "To ensure sampling accuracy, how many seconds before the lunar rover actually reaches the target position should the ground control center issue the complete command sequence? Please list the calculation process.", + "answer": "Advance time = communication delay + total action time = 1.3 + (4+2+3) = 10.3 seconds. Calculation basis: 1.3 seconds of one-way delay needs to be compensated, during the 9 seconds of action execution, the vehicle will move 0.2*9=1.8m, far exceeding the positioning tolerance, so the complete command sequence must be issued in advance." + }, + { + "id": 474, + "scenario_code": "1.8", + "instruction": " The lunar rover plans to deploy an array of 4 seismometers on the edge of a crater with a diameter of 200 meters. The deployment points need to meet the following criteria: ① lunar soil bearing capacity > 10kPa; ② spacing error between each node < ±5%; ③ distance from the center of the crater 100±2 meters. The current measured parameters of the candidate points are: P1(12kPa,98m), P2(8kPa,102m), P3(15kPa,101m), P4(11kPa,99m). The rover starts from P1, with a movement speed of 0.1m/s, and the energy consumption formula is E=0.5*d (d is the distance moved).", + "question": "Select the most energy-efficient deployment path that meets all conditions and calculate the total energy consumption and time (ignoring turning time).", + "answer": "Optimal path: P1→P4→P3 (excluding P2 due to insufficient bearing capacity). Total distance = sqrt((99-98)^2 + (x-coordinate difference)^2) + sqrt((101-99)^2 + (x-coordinate difference)^2) ≈ 141.42 meters (approximated as a right triangle), energy consumption E = 0.5*141.42 ≈ 70.71J, time t = 141.42/0.1 ≈ 1414 seconds ≈ 23 minutes 34 seconds." + }, + { + "id": 475, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover obtained remote sensing data for three candidate sampling sites within the Von Kármán crater: Site 1 (45.3°N, 176.2°E) has a spectral match of 85% with KREEP rock; Site 2 (45.5°N, 176.1°E) shows a volcanic glass characteristic reflection peak; Site 3 (45.4°N, 176.3°E) has a terrain ruggedness of 25°. The rover's remaining power supports a maximum travel distance of 1.2km, and it is currently located at the center of the three sites (500m to each site). The scientific priority order is: KREEP rock > volcanic glass > breccia.", + "question": "Based on scientific value and engineering constraints, which sampling site should be prioritized? Provide the key parameters for the selection criteria.", + "answer": "Site 1 (85% match with KREEP rock and travel distance is feasible)." + }, + { + "id": 476, + "scenario_code": "2.2", + "instruction": " The Chang'e-4 lander, while conducting permanent shadow area exploration within the Von Kármán crater, experienced a failure of its visual navigation system due to extremely low lighting. Currently relying on: 1) IMU providing angular velocity accuracy of 0.1°/s, position drift error of 1m/min; 2) LiDAR SLAM positioning update cycle of 2 minutes, accuracy of ±0.3m; 3) The last precise location was 10 minutes ago at coordinates (102.34W, 43.56S). During this period, the IMU recorded a cumulative linear movement of 200m (direction due north), and three left turns of 15° each.", + "question": "Estimate the maximum possible positioning error range of the current rover and explain the main sources of error.", + "answer": "Maximum error = IMU drift (1m/min * 10min = 10m) + SLAM cumulative error (5 cycles not updated * 0.3m = 1.5m) + turning error (3 * 0.1°/s * 15° ≈ 4.5m). Total error is approximately ±16m, mainly from long-term IMU drift." + }, + { + "id": 477, + "scenario_code": "4.4", + "instruction": " Yutu-2 obtained the following data while patrolling the Von Kármán crater: Point A (coordinates X=125, Y=87) spectral data shows characteristic absorption peaks of KREEP rock (reflectance 0.18 at 950nm wavelength); Point B (X=133, Y=91) LiDAR data shows a 3m high steep slope; Point C (X=140, Y=85) thermal infrared image shows an abnormally high temperature area (15K higher than the surroundings). It is known that the maximum climbing angle of the rover is 25°, the scientific priority is: mineral composition > terrain features > thermal anomaly. The remaining power supports a total movement distance of no more than 50 meters.", + "question": "Please plan the optimal exploration route and explain the decision-making basis.", + "answer": "Route planning: A→C→B. Decision basis: ① Prioritize visiting Point A to meet the highest priority of mineral composition; ② Point C's thermal anomaly is the second priority and is 15 meters away from Point A (straight-line distance sqrt((140-125)^2+(85-87)^2≈15.1m); ③ With 29.9 meters remaining, it is possible to reach Point B but the slope needs to be assessed, a height difference of 3m over a horizontal distance of 7m (arctan(3/7)≈23°<25°) meets the pass condition." + }, + { + "id": 478, + "scenario_code": "2.9", + "instruction": " The ranging data between the lunar orbit navigation satellite LBNSS-1 and Yutu-2 is as follows: satellite coordinates (100,200,50) km, ranging value 210.12 km; when the satellite coordinates are (150,180,60) km, the ranging value is 195.50 km. It is known that the elevation of Yutu-2 is -1.2 km (in the lunar surface coordinate system, the Z-axis points downward), and the signal transmission delay has been compensated.", + "question": "Estimate the planar coordinates (X,Y) of Yutu-2 using the least squares method, and provide the key formulas for the calculation steps (without specific numerical solutions). Hint: the pseudorange observation equation ρ_i = sqrt((X_si-X)^2 + (Y_si-Y)^2 + (Z_si-Z)^2) + ε_i", + "answer": "Establish two observation equations: 1) sqrt((100-X)^2 + (200-Y)^2 + (50+1.2)^2) = 210.12; 2) sqrt((150-X)^2 + (180-Y)^2 + (60+1.2)^2) = 195.50. Subtract the squared equations to eliminate the square root terms, and solve for (X,Y) using the resulting linear equation." + }, + { + "id": 479, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover experienced an X-band communication interruption during the lunar day, with fault diagnosis indicating that the RF front-end was damaged by a solar flare. The remaining power can support continuous operation for 8 hours, and the storage has cached 12GB of scientific data (generation rate 200MB/hour). The system has two recovery options: A) Switch to the UHF band relay link (rate 50Mbps but requires 30 minutes to reconfigure the protocol stack); B) Activate the local compression module (compression ratio 4:1 but increases power consumption by 15%) and transmit through the intact L-band direct link (rate 10Mbps).", + "question": "To ensure all cached and expected data is fully transmitted, which option should be chosen? Provide the key calculation steps.", + "answer": "Choose option B. Calculation steps: 1) Total data volume = 12GB + 8h * 0.2GB/h = 13.6GB; 2) Transmission time for option A = (13.6 * 8) / (50 * 3600) + 0.5 = 1.1h > 8h; For option B, the compressed data volume = 13.6 / 4 = 3.4GB, transmission time = (3.4 * 8) / (10 * 3600) = 0.76h, total time = 0.76 * 1.15 = 0.87h < 8h." + }, + { + "id": 480, + "scenario_code": "5.7", + "instruction": " The 128TB solid-state storage on the Chang'e-7 orbiter uses a NAND Flash architecture, with block sizes of 4MB and an average endurance of 10^5 write cycles. Current wear monitoring shows: Area A has a write count of 82,000 (storing critical engineering data), and Area B has a write count of 30,000 (storing temporary scientific data). The system is set to automatically migrate data when the block's remaining life is <20%. The storage controller uses a dynamic wear-leveling algorithm.", + "question": "If 3TB of new data needs to be written in the next mission cycle, how should the controller optimize the block allocation strategy? Explain the specific decision criteria.", + "answer": "Prioritize writing to Area B: 1) Area A's remaining life = (100000 - 82000) / 100000 = 18% < 20% triggering migration conditions; 2) Area B's remaining life = (100000 - 30000) / 100000 = 70% > 20%; 3) Writing 3TB requires 768 blocks = 3 * 1024 / 4, which should be allocated from unused blocks in Area B." + }, + { + "id": 481, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. According to preliminary remote sensing data analysis, the target area has three typical types of lunar soil: Type A (soft and dry, particle size <0.1mm), Type B (medium hardness, containing 5-8% volatiles), and Type C (hard basaltic, containing <1% volatiles). The engineering team is equipped with three sampling tools: ① Rotary Percussion Drill (suitable for hardness >3 Mohs, maximum power consumption 50W) ② Vacuum Adsorption Grab (suitable for loose fine particles, power consumption 20W) ③ Vibratory Scraper (suitable for sticky substances, power consumption 35W). The current remaining energy of the probe is 120Wh, and it needs to complete the collection of at least two different types of samples within 2 hours.", + "question": "If the priority is to collect Type B and Type C samples to obtain volatiles and original lunar crust components, please select the tool combination and verify whether the total power consumption meets the constraint conditions.", + "answer": "Select the Rotary Percussion Drill (50W) to collect Type C samples, consuming 0.5 hours and 25Wh of energy + Vibratory Scraper (35W) to collect Type B samples, consuming 1 hour and 35Wh of energy → Total energy consumption 60Wh < 120Wh remaining energy and meets the 2-hour time limit." + }, + { + "id": 482, + "scenario_code": "1.4", + "instruction": " Three scientific instruments (A: Neutron Spectrometer, B: Infrared Imager, C: Lunar Soil Analyzer) have been deployed in the permanently shadowed region of the lunar south pole, sharing a hybrid solar-battery power system. Instrument A needs to operate continuously with a peak power of 80W; Instrument B operates for 15 minutes every 2 hours with a peak power of 120W; Instrument C operates 3 times a day, each time for 30 minutes, with a peak power of 150W. The power system has a maximum instantaneous output of 200W, and the battery capacity is 500Wh. The current battery charge is 300Wh, and the next Earth-Moon communication window (for recharging) is in 8 hours.", + "question": "To ensure all instruments operate without interruption before the next recharge, how should the operation schedule of Instrument C be adjusted? Assume each adjustment can only increase or decrease the operation time by 10 minutes.", + "answer": "Reduce the operation time of Instrument C by 10 minutes each time (i.e., adjust to 20 minutes each time), then the total energy consumption is: A=80*8=640Wh; B=120*(15/60)*4=120Wh; C=150*(20/60)*3=150Wh. Total demand=640+120+150=910Wh, the battery can provide 300+200*8=1900Wh, meeting the requirement." + }, + { + "id": 483, + "scenario_code": "1.5", + "instruction": " The Yutu-2 lunar rover needs to be remotely controlled to cross a lunar rille with a communication delay of 1.3 seconds. The current speed is 0.2m/s, and there is a 1.5-meter-wide crack 20 meters ahead. The maximum braking acceleration is 0.1m/s², and the onboard obstacle detection system requires at least 0.5 seconds to process the detection and send a braking command after detecting the crack. The lunar rover control system uses a predictive control algorithm, with a position prediction error of ±0.15 meters (3σ).", + "question": "Calculate the latest safe braking start point distance from the crack and determine whether manual intervention is needed to correct the predictive control parameters.", + "answer": "Latest braking distance = v*t_brake + 0.5*a*t_brake^2 + error tolerance = 0.2*(0.5+1.3) + 0.5*0.1*1.8^2 + 0.15 = 0.36 + 0.162 + 0.15 ≈ 0.67 meters. The safe distance needs to be >1.5 meters wide crack, so the current parameters are safe and no intervention is required." + }, + { + "id": 484, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing a patrol mission on the far side of the Moon, located at coordinate point A(10°N, 120°E), and needs to reach scientific target point B(12°N, 122°E). It is known that: 1) the straight-line distance d (km) between two points on the lunar surface = 111.3*√[(latitude difference)^2 + (longitude difference*cos average latitude)^2]; 2) the energy consumption model is E=0.15*d+5 (Wh), where d is the actual travel distance; 3) the remaining battery power is 80Wh; 4) 20Wh must be reserved for scientific instrument operation. Path planning needs to avoid a 200-meter diameter impact crater, which will increase the actual travel distance by 15%.", + "question": "Can Yutu-2 safely reach target point B without recharging? Please calculate and explain.", + "answer": "Yes. Calculation steps: 1) latitude difference=12-10=2°, longitude difference=122-120=2°, average latitude=(10+12)/2=11°; 2)d=111.3*√[2^2+(2*cos11°)^2]=111.3*√(4+3.88)=314km; 3) actual distance after detour=314*1.15=361.1km; 4) total energy consumption E=0.15*361.1+5=59.165Wh; 5) available power=80-20=60Wh>59.165Wh." + }, + { + "id": 485, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander was conducting exploration at the edge of the Shackleton crater when it suddenly received a solar proton event warning. Known facts: 1) There are 30 minutes of safe operation time remaining; 2) The emergency shelter is located 800 meters to the northwest; 3) The maximum safe speed of the lunar rover is 0.1 m/s; 4) After lunar surface communication is interrupted, it needs to remain stationary for at least 5 minutes to switch to safe mode. Terrain analysis shows that the shortest path requires crossing a slope with a gradient of 20° (maximum allowable gradient is 15°), and detouring will add 200 meters to the distance.", + "question": "Determine whether the lunar rover can complete the sheltering before the communication interruption, and explain the basis for choosing the path.", + "answer": "It can complete the sheltering, and the detour path should be chosen. Calculation steps: 1) Detour total distance = 800 + 200 = 1000 meters; 2) Required time = 1000 / 0.1 = 10000 seconds ≈ 16.67 minutes < 25 minutes (30 minutes total time - 5 minutes for mode switching); 3) Directly crossing a 20° slope exceeds the safe gradient limit." + }, + { + "id": 486, + "scenario_code": "2.9", + "instruction": " In the Lunar Beacon Navigation Satellite System (LBNSS), the real-time ranging data for beacons M1 and M2 are as follows: M1 is 1523 ± 5m from the probe, and M2 is 1867 ± 8m from the probe. It is known that the actual distance between the two beacons is 500m (coordinates M1(0,0,0), M2(500,0,0)), and the probe's height should be consistent with the beacon plane (z=0). The ranging errors follow a normal distribution, and the combined navigation solution uses the weighted least squares method, with weights inversely proportional to the square of the errors.", + "question": "Calculate the most likely position coordinates (x,y,0) of the probe, and explain the rationality of the error handling method.", + "answer": "The most likely position is (300, ±400, 0). Solution process: 1) Establish equations: (x-0)^2 + y^2 = 1523^2, (x-500)^2 + y^2 = 1867^2; solving yields x = (1523^2 - 1867^2 + 500^2) / 1000 ≈ 300; y = ±√(1523^2 - 300^2) ≈ ±400. The weighted least squares method effectively suppresses error amplification by assigning higher weights to more precise measurements (M1 weight w1 = 1/5^2 > w2 = 1/8^2)." + }, + { + "id": 487, + "scenario_code": "2.9", + "instruction": " The lunar orbit navigation satellite LBNSS-1 establishes a two-way ranging link with Yutu-3. Given: 1) LBNSS-1 orbit height 100km (lunar radius 1737km); 2) UWB beacon transmission power 23dBm, reception sensitivity -110dBm; 3) Free space loss formula: Lfs=32.45+20log(f)+20log(d), frequency f=400MHz; 4) The system needs to reserve a 10dB link margin. Beacon antenna gain 3dBi, receiving antenna gain 0dBi.", + "question": "Calculate whether the maximum theoretical communication distance meets the current orbit height requirements? If not, to what dBi at least does the receiving antenna gain need to be increased to meet the requirements? ", + "answer": "Theoretical maximum distance d=100km+1737km=1837km; Lfs=32.45+20log(400)+20log(1837)≈32.45+52+65.3≈149.75dB; Maximum allowable loss=23-(-110)-10=123dB＜149.75dB. The receiving antenna gain needs to be increased by ΔG=149.75-123=26.75dBi (the current 3dBi is insufficient)." + }, + { + "id": 488, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover experienced an X-band communication interruption during the lunar day. The fault tree analysis indicates the possible causes:\nA) Solar flares causing ionospheric disturbances (probability 15%)\nB) Transmitter failure on the rover (probability 5%)\nC) Antenna pointing deviation of the relay satellite (probability 30%)\nD) Terrain obstruction on the lunar surface (probability 50%).\nThe emergency protocol stipulates:\n1) If the fault is of type A/C, switch to the backup S-band link;\n2) If the fault is of type B, activate the redundant transmitter;\n3) If the fault is of type D, wait for 2 hours for the terrain to change before retrying.", + "question": "What operation should be performed first? Please explain the decision-making basis by combining the probability and the protocol.", + "answer": "First, wait for 2 hours to rule out terrain obstruction (type D), as it has the highest probability (50%) and the protocol explicitly requires waiting. If this fails, then check the relay satellite's pointing (type C), solar activity (type A), and finally the transmitter (type B) in sequence." + }, + { + "id": 489, + "scenario_code": "2.7", + "instruction": " The Lunar Orbit Navigation Satellite System (LBNSS) has detected a solar proton event warning, which is expected to affect the Chang'e-6 rover's patrol area in 3 hours. Known facts: 1) The rover is currently located in the Mare Imbrium basin (15°S, 45°E); 2) The nearest safe haven is an entrance to a lava tube 5km to the northeast (14°S, 46°E); 3) Safety mode requirements: a) turn off scientific payloads to save power while driving; b) maximum climbing angle ≤15°; c) need to complete the sheltering 30 minutes in advance. Terrain data shows that there is a 200m long slope with a gradient of 18° between the two points.", + "question": "If all safety constraints are to be met, calculate the minimum average driving speed the rover must maintain (保留两位小数, retain two decimal places).", + "answer": "0.06m/s. Calculation process: 1) Available time = 3h - 0.5h = 2.5h = 9000s; 2) Extra distance to detour = 200m/cos15° - 200m ≈ 10.35m; 3) Total distance = 5000 + 10.35 = 5010.35m; 4) Minimum speed = 5010.35/9000 ≈ 0.06m/s." + }, + { + "id": 490, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, a shared power grid needs to be established. The current system includes: 1 main solar array (peak output 1200W), 2 isotope thermoelectric generators (each continuously outputs 300W), and 3 sets of scientific equipment (A: Seismometer requires 200W continuously; B: Spectrometer requires 150W intermittently, duty cycle 40%; C: Drilling device requires 500W peak, each start lasts 10 minutes, interval ≥30 minutes). Power scheduling needs to prioritize the basic load of 400W for life support systems.", + "question": "If all equipment is in its maximum demand state and line losses are not considered, what is the power deficit in watts at this time? ", + "answer": "450W" + }, + { + "id": 491, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform rock sampling, the one-way communication delay between Earth and the Moon is 1.3 seconds. The rover is currently moving in a straight line towards the target point at a speed of 0.2 m/s, and the control system uses a predictive algorithm to compensate for the delay: when an obstacle is detected, a braking command is immediately sent, with a deceleration of 0.15 m/s^2. Assume an obstacle is suddenly detected 8 meters from the target point.", + "question": "Calculate the total sliding distance from the moment the braking command is sent until the rover comes to a complete stop (including the command transmission time).", + "answer": "9.733 meters" + }, + { + "id": 492, + "scenario_code": "1.8", + "instruction": " When deploying a network of magnetometers on the lunar surface, the bearing capacity of the lunar soil at a certain point is measured to be 8 kPa. The contact area of the equipment base is 0.25 m^2, and its weight is 50 kg. The maximum vibration impact force of the scientific payload is 200 N (vertically downward). It is known that the safety factor must be ≥3, and the lunar gravitational acceleration is 1.62 m/s^2.", + "question": "Verify whether the point meets the load-bearing requirements (the calculation process must be listed).", + "answer": "Meets the requirements. Total vertical force = (50 * 1.62) + 200 = 281 N; Pressure = 281 / 0.25 = 1124 Pa = 1.124 kPa; Safety margin = 8 / 1.124 ≈ 7.1 > 3" + }, + { + "id": 493, + "scenario_code": "2.2", + "instruction": " The Chang'e-7 lander is conducting permanent shadow area exploration at the edge of the Shackleton crater (89.9°S). The navigation system configuration includes: 1) IMU drift error 0.1°/h; 2) Visual odometry feature matching accuracy ±2cm/10m; 3) LiDAR SLAM absolute positioning error ±5cm; 4) Starlight sensor availability in the polar region is only 50% (due to terrain obstruction). The system has been operating continuously for 8 hours without astronomical correction, and the accumulated position error has reached the warning threshold.", + "question": "If the position coordinates at the last effective starlight observation were (0m,0m), and the current IMU shows a displacement of (12.2m,8.7m), please estimate the actual possible position range (considering the worst-case error accumulation).", + "answer": "Position range: (12.2±0.8)m, (8.7±0.8)m. Calculation process: 1) IMU angular error = 0.1 * 8 = 0.8°; 2) Maximum deviation in displacement direction = sqrt(12.2^2 + 8.7^2) * tan(0.8°) ≈ 0.28m; 3) SLAM absolute error ±5cm → total error radius ≈ sqrt(0.28^2 + 0.05^2 + 0.02^2 * 36/100) ≈ 0.8m." + }, + { + "id": 494, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, energy supply becomes a critical constraint. In the current mission, a network consisting of 3 lunar rovers (LRV) and 1 fixed scientific station shares a nuclear battery system with a peak power of 120W. It is known that:\n- Each LRV has a basic operating power consumption of 15W, and an additional 20W when moving\n- The scientific station has a basic power consumption of 30W, and an additional 40W in experimental mode\n- The system requires at least 20% power redundancy to handle emergencies\n- In the current mission phase, the following need to be carried out simultaneously:\n * 2 LRVs perform mobile sampling (each carrying 5kg of equipment)\n * 1 LRV performs stationary sample analysis\n * The scientific station is activated in experimental mode", + "question": "Calculate whether the current configuration meets the power constraints? If not, how many LRVs can move simultaneously at most under the current configuration? ", + "answer": "Current total power consumption = (15+20)*2 + 15*1 + (30+40) = 155W; Maximum allowable power consumption = 120*0.8 = 96W; Not met. At most 1 LRV can move: (15+20)*1 +15*2 +(30+40)=135W still exceeds the limit, so 0 LRVs can move." + }, + { + "id": 495, + "scenario_code": "1.5", + "instruction": " When controlling the Yutu-2 rover to perform rock sampling, the commands sent by the ground control center take 1.28 seconds of one-way delay to reach the moon. It is known that:\n- The maximum movement speed of the robotic arm's end is 0.05m/s\n- The target rock is 0.3m away from the current position of the robotic arm's end\n- The control system uses a predictive algorithm to send continuous 3 position point commands in advance\n- Each command point contains X/Y/Z three-axis coordinates (each occupying 32bit)\n- The telemetry data downlink rate is 2Mbps", + "question": "To ensure continuous motion without interruption, calculate the minimum amount of command data (bits) that needs to be sent in advance and the corresponding time margin (seconds)?", + "answer": "Single command data volume=3 axes*32bit=96bit; 3 command points=288bit; Transmission time=288/2e6=0.000144 seconds; Movement time=0.3/0.05=6 seconds; Time margin needs to cover 2 times the delay (command uplink + status downlink)=2*1.28=2.56 seconds" + }, + { + "id": 496, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container must be inspected for handover. The container weighs 2kg, and the RFID tag frequency is 13.56MHz ± 50kHz. Environmental monitoring shows the sealed cabin temperature ranges from -50°C to +60°C, and the pressure is maintained at 10^-5 Pa. The handover process requires: 1) the acceleration of the robotic arm during grasping < 0.1m/s^2; 2) RFID signal strength > -70dBm; 3) 100% completeness of temperature recorder data. Current telemetry data: grasping acceleration 0.08m/s^2, RFID strength -65dBm, temperature data missing the last 5 minutes (total duration 30 minutes).", + "question": "Based on the handover standards, does the current status meet the separation conditions? If not, which specific indicator is不合格 (unqualified)?", + "answer": "The separation conditions are not met. Temperature data completeness = (30-5)/30 = 83.3% < 100%, this indicator is不合格 (unqualified)." + }, + { + "id": 497, + "scenario_code": "1.8", + "instruction": " During the deployment of a seismometer array, it was found that the bearing capacity of the lunar soil at the predetermined location is only 1.8kPa, which is lower than the required 3kPa for the equipment. The engineering team proposed three solutions:\nA) Replace with a support base that is 60% larger in area\nB) Reduce the equipment weight from 45kg to 30kg\nC) Find a new site 200 meters away with a measured bearing capacity of 4kPa\nKnown:\n- The total weight of the equipment and base is 50kg (including a 5kg base)\n- The current base area is 0.25m²\n- The movement speed is 0.1m/s\n- The remaining working time is only enough to implement one solution", + "question": "Through calculations, verify which solution can ensure successful deployment? And explain the key considerations when choosing that solution.", + "answer": "Original pressure = 50*9.8/0.25 = 1960Pa > 1800Pa, failure; Solution A: New area = 0.25*1.6 = 0.4m², new pressure = 50*9.8/0.4 = 1225Pa < 1800Pa, effective; Solution B: New weight 35kg, pressure = 35*9.8/0.25 = 1372Pa < 1800Pa, effective; Solution C takes 200/0.1 = 2000 seconds, exceeding the time limit. Solution B (best in terms of time efficiency) or A (better in terms of reliability) should be chosen." + }, + { + "id": 498, + "scenario_code": "3.8", + "instruction": " For the Tianwen-3 sample return mission, the lander's daily energy budget is: 1) solar power generation of 1200Wh; 2) lithium-ion battery pack with available capacity of 3000Wh (SOC maintained between 20% to 80%). Energy consumption during mission phases: during the lunar day - mobility exploration consumes 400Wh/h × 4h, scientific instruments consume 200Wh/h × 8h; during the lunar night - the thermal insulation system consumes 150Wh/h × 14h. A fault safety redundancy requires reserving 15% of the total power.", + "question": "Calculate whether this system can support three consecutive full lunar day/night cycles? List the key decision-making steps.", + "answer": "Cannot support, there will be a shortage of 1020Wh during the lunar night phase of the 3rd cycle" + }, + { + "id": 499, + "scenario_code": "2.10", + "instruction": " The lunar rover is performing a centimeter-level precise positioning task on the Aristarchus Plateau, requiring microscopic imaging of a 2cm diameter ilmenite outcrop. Known: 1) The visual navigation system has a single-frame positioning error of ±1cm (3σ); 2) The end-effector of the robotic arm has a positioning repeatability of ±0.5mm; 3) The current straight-line distance to the target point is 80cm, with a 5° yaw angle; 4) Lighting conditions allow for the collection of 10 frames of visual data per second.", + "question": "Calculate the minimum number of seconds of visual data fusion required to converge the final positioning error to within ±3mm? Hint: The error follows a normal distribution and is independently and identically distributed, the fused error = single-frame error / √n.", + "answer": "Let n frames of data be required: 1cm/√n ≤ 0.3cm → √n ≥ 1/0.3 ≈ 3.33 → n ≥ 11.11; Collection time = 12 frames / 10fps = 1.2 seconds (round up)." + }, + { + "id": 500, + "scenario_code": "3.1", + "instruction": " The Chang'e-5 lander is executing a sampling mission in the region at 43.06°N, 51.92°E on the lunar near side. During the lunar day, the solar elevation angle in this area varies from 15° to 75°, and the solar panels use two-dimensional tracking (azimuth + elevation). Known: 1) Each panel has an area of 2.5m² and a photovoltaic conversion efficiency of 28%; 2) The lunar surface albedo is 0.12; 3) The solar constant is 1367W/m²; 4) Terrain blocking reduces the effective daily sunlight exposure to 8 hours. The combined effect of direct and reflected light must be considered.", + "question": "If the current solar elevation angle is 45° and the azimuth tracking error is ±5°, calculate the actual power generation of a single panel at this time (保留两位小数) ? Hint: The effective receiving area for reflected light is calculated as 30% of the projected area.", + "answer": "87.23W" + }, + { + "id": 501, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the moon, located at coordinate point A (10°N, 120°E). It needs to travel to scientific target point B (12°N, 122°E) to collect basalt samples. It is known that: 1) the lunar surface slope is less than 15°, and the wheel-soil mechanics model shows energy consumption coefficients of 0.12Wh/m (flat) and 0.25Wh/m (uphill); 2) the straight-line distance from point A to B is 30km, but the actual path needs to detour around 3 craters, increasing the total distance to 42km, of which 8km is uphill; 3) the current remaining battery energy is 5000Wh, and the baseline power consumption during travel is 20W.", + "question": "If Yutu-2 travels at a constant speed of 0.1m/s, calculate whether the remaining power when it arrives at point B meets the minimum safety threshold of 2000Wh.", + "answer": "Travel time = 42000m / 0.1m/s = 420000s ≈ 116.67h; Flat terrain energy consumption = 34km * 1000 * 0.12Wh/m = 4080Wh; Uphill energy consumption = 8km * 1000 * 0.25Wh/m = 2000Wh; Baseline energy consumption = 20W * 116.67h = 2333.4Wh; Total energy consumption = 4080 + 2000 + 2333.4 ≈ 8413.4Wh; Remaining power = 5000 - 8413.4 = -3413.4Wh (not sufficient)." + }, + { + "id": 502, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander is conducting exploration on the edge of the Shackleton crater when it suddenly receives a solar proton event warning (expected to reach the lunar surface in 2 hours). With 90 minutes of safe operation time remaining, it needs to urgently return to a shelter in the permanent shadow zone, 3 km away. It is known that: 1) IMU drift error results in a position uncertainty of ±200 m; 2) the beacon transmission power is 10 dBm, the receiving sensitivity is -110 dBm, and the path loss model is L=20+30*lg(d); 3) the maximum speed of the lunar rover is 0.15 m/s, but 20 minutes need to be reserved for a safety self-check.", + "question": "Determine whether the lunar rover can reach the shelter within the safe time? If not, propose at least one emergency plan (based on the given parameters).", + "answer": "In the worst case, the distance to travel = 3000 m + 200 m = 3200 m; the minimum required time = 3200 m / 0.15 m/s ≈ 21333 s ≈ 356 min > 70 min (90-20) → cannot arrive on time. Emergency plan: use beacon ranging to assist navigation (calculate the beacon communication distance: by the receiving power formula P_rx = P_tx - L = 10 - (20 + 30 * lg(d)) ≥ -110 → d ≤ 10^((10 + 110 - 20) / 30) = 100 m), reduce positioning error through short-distance beacon relay." + }, + { + "id": 503, + "scenario_code": "4.9", + "instruction": " The sample container transfer process between the ascent vehicle and the lander requires: 1) The container temperature must be maintained at -50±5°C; 2) The RFID tag reading success rate must be ≥99%; 3) The relative velocity during docking must be ≤0.05m/s. Current monitoring data: container temperature -48°C, tag reading failure rate 2%, approach speed 0.03m/s. Given the temperature control system power consumption formula P=10*(ΔT)^2 (ΔT is the absolute value of the temperature difference), the nominal condition ΔT=10°C. There is a 30-minute adjustment time before the transfer, and the maximum heating rate of the temperature control system is 1°C/min.", + "question": "Determine if the current conditions meet the transfer requirements? If not, calculate the minimum adjustment power consumption required for the temperature control system.", + "answer": "Does not meet (RFID tag reading failure rate exceeds standard). Minimum adjustment power consumption: current ΔT=|-48-(-50)|=2°C, needs to be reduced to ΔT≤5°C, no heating adjustment required, power consumption remains P=10*(2)^2=40W." + }, + { + "id": 504, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing exploration tasks on the far side of the Moon, located at coordinate point A (10°N, 120°E), and needs to travel to scientific target point B (12°N, 122°E). It is known that: 1) The lunar surface slope does not exceed 15°, and the wheel-soil mechanics model shows energy consumption coefficients of 0.12 Wh/m (flat) and 0.25 Wh/m (uphill); 2) The straight-line distance between the two points is 30 km, but there is a 5 km diameter crater in between that needs to be bypassed; 3) The detour increases the actual travel distance to 35 km, of which 20% is uphill; 4) The current remaining battery energy is 5000 Wh, and the base power consumption of the driving motor is 50 W.", + "question": "If Yutu-2 travels at a constant speed of 0.1 m/s, calculate whether the remaining power after reaching point B will meet the 8-hour scientific instrument operation requirement (instrument power consumption 80 W)?", + "answer": "Total travel time = 35000 m / 0.1 m/s = 350000 s ≈ 97.22 h; Flat road energy consumption = 0.12 Wh/m * (35000 m * 80%) = 3360 Wh; Uphill energy consumption = 0.25 Wh/m * (35000 m * 20%) = 1750 Wh; Total travel energy consumption = 3360 + 1750 + (50 W * 97.22 h) = 3360 + 1750 + 4861 = 9971 Wh; Instrument energy consumption = 80 W * 8 h = 640 Wh; Total energy requirement = 9971 + 640 = 10611 Wh > 5000 Wh → does not meet" + }, + { + "id": 505, + "scenario_code": "5.7", + "instruction": " The Chang'e-5 return capsule's onboard SSD uses NAND flash memory chips, with a total capacity of 1TB, block size of 128KB, and each block can withstand 3000 write-erase cycles. It generates about 50GB of scientific data daily (evenly distributed), and the wear-leveling algorithm distributes writes across all idle blocks. The SSD reserves 15% redundant space for bad block replacement.", + "question": "Calculate the theoretical minimum lifespan (years) of the SSD, assuming all blocks fail when they reach the write-erase limit and there are no other failures.", + "answer": "Usable capacity = 1TB * 85% = 850GB; daily writes of 50GB correspond to 50GB/128KB ≈ 390,625 write operations; after wear leveling, daily write-erase cycles consumed per block = 390,625/(850GB/128KB) ≈ 58 times/block; lifespan = 3000 times/(58 times/day)/365 ≈ 0.14 years ≈ 51 days (storage strategy optimization or increased redundant space required)." + }, + { + "id": 506, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth, and must relay data through the Queqiao relay satellite. It is known that Queqiao operates in a Halo orbit around the Earth-Moon L2 point, approximately 65,000 kilometers from the lunar surface. At the current moment, the elevation angle between the lander and Queqiao is 35 degrees, the communication frequency is 2.4 GHz, the transmission power is 20W, and the antenna gain is 36dBi. The lunar surface environmental temperature is -180°C, and the equivalent noise temperature of the receiving system is 120K, requiring a minimum signal-to-noise ratio (SNR) of 10dB.", + "question": "Calculate the theoretical maximum data transmission rate of the current link (ignoring Doppler shift and modulation loss), given: the free space loss formula Lfs = 32.45 + 20log10(d) + 20log10(f), where d is the distance (km), and f is the frequency (MHz); the Boltzmann constant k=1.38e-23 J/K.", + "answer": "Calculation steps: 1) Free space loss Lfs = 32.45 + 20log10(65000) + 20log10(2400) = 32.45 + 96.26 + 67.60 = 196.31 dB; 2) Received power Pr = Pt + Gt - Lfs + Gr = 20 + 36 - 196.31 + 36 = -104.31 dBW; 3) Noise power Pn = k * T * B = 1.38e-23 * 120 * B; 4) SNR = Pr/Pn ≥10 → B ≤ (10^(10/10)*1.38e-23*120)^-1*10^(-104.31/10) ≈ 2.4 MHz. Therefore, the maximum rate is approximately 4.8 Mbps (assuming QPSK modulation efficiency of 2bit/Hz)." + }, + { + "id": 507, + "scenario_code": "1.5", + "instruction": " The Yutu-2 lunar rover needs to remotely control the robotic arm to collect rock samples with a 1.3-second communication delay. The maximum movement speed of the robotic arm's end effector is 0.1m/s, and the control system uses a predictive compensation algorithm: sending a continuous motion command package for the next 2 seconds in advance (including timestamps and coordinate sequences). The current target rock is 0.25 meters away from the end of the robotic arm, located at a 30-degree angle directly ahead.", + "question": "Design a 2-second command package content (with a time interval of 0.5 seconds) to make the robotic arm move at a constant speed in a straight line to the target position.", + "answer": "[{t=0s, x=0m, y=0m}, {t=0.5s, x=0.054m, y=0.031m}, {t=1.0s, x=0.108m, y=0.062m}, {t=1.5s, x=0.162m, y=0.093m}, {t=2.0s, x=0.216m, y=0.125m}] (Note: x=0.1*cos30°*Δt cumulative, y=0.1*sin30°*Δt cumulative)." + }, + { + "id": 508, + "scenario_code": "1.8", + "instruction": " When the Chang'e-7 lander deployed the lunar soil thermal conductivity detector, it measured the bearing capacity of the lunar soil at the landing site to be 8kPa. The contact area of the instrument base is 0.05㎡, and the mass is 12kg. The safety standard requires: actual pressure ≤ 90% of the bearing capacity. The lunar gravitational acceleration is 1.62m/s².", + "question": "Determine whether the current deployment plan meets the safety requirements? If not, to what extent does the base area need to be expanded at least to meet the requirements? ", + "answer": "Actual pressure=(12*1.62)/0.05=388.8Pa=0.389kPa < 7.2kPa (90% of the bearing capacity), meets the requirements; if adjustment is needed: minimum area=(12*1.62)/(8*0.9)=0.0027㎡" + }, + { + "id": 509, + "scenario_code": "2.7", + "instruction": " The lunar orbiter has detected an impending solar proton event (expected to reach the lunar surface in 30 minutes), and the Chang'e-5 lander, which is currently on patrol, needs to urgently activate its protection program. Current status: 1) The lander is located at the edge of a permanently shadowed area (the lighting cycle is about to begin); 2) Remaining power is 300Wh, entering safe mode requires 50Wh, and the heating power of the thermal insulation heater is 20W; 3) Optional plans: A) Immediately return to the original shadowed area (distance 800m, speed 0.15m/s), B) Deploy a radiation shield on site (takes 8 minutes, during which it cannot move). It is known that the system's basic power consumption during movement is 15W, and the radiation shield can reduce the radiation dose by 90%. The duration of the solar proton event is 4 hours.", + "question": "From the perspectives of energy safety and radiation protection, which emergency plan should be chosen.", + "answer": "Energy consumption for Plan A: Movement time = 800/0.15 ≈ 5333s ≈ 89 minutes, movement energy consumption = (15+20)*(5333/3600) ≈ 87Wh; Total energy consumption = 87+50=137Wh<300Wh. Energy consumption for Plan B: Deployment energy consumption = (20+15)*(8/60) ≈ 4.67Wh; Maintenance energy consumption = 20*(4*60)=480Wh; Total energy consumption = 484.67Wh>300Wh. Although Plan B has better protection, it will deplete the energy and cause the system to shut down, so Plan A should be chosen." + }, + { + "id": 510, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the lunar soil in this area are as follows: medium hardness (Mohs hardness 4-5), low viscosity, and volatile content of about 120 ppm. There are three sampling tools available: 1) Diamond-coated drill bit (suitable for hardness > 5, power consumption 15W/min); 2) Titanium alloy grab (suitable for viscosity > 0.5Pa·s, power consumption 8W/min); 3) Tungsten carbide scraper (suitable for hardness < 6 and viscosity < 0.3Pa·s, power consumption 5W/min). The mission requires that the sampling time does not exceed 10 minutes, and the total energy consumption must be controlled within 80W.", + "question": "Based on the characteristics of the lunar soil and the parameters of the tools, which sampling tool combination should be chosen to meet both the sampling time and energy consumption constraints? Please provide the specific choice and the theoretical maximum allowable sampling duration.", + "answer": "Choose the tungsten carbide scraper. Theoretical maximum sampling duration = 80W / 5W/min = 16 minutes > 10-minute requirement, meeting all constraint conditions." + }, + { + "id": 511, + "scenario_code": "4.9", + "instruction": " The sample container transfer process between the ascent vehicle and the lander requires: 1) The container temperature must be stable at -50±5°C; 2) The RFID tag signal strength must be ≥-60dBm; 3) The sealing pressure must be <0.1Pa. The current telemetry data shows: Temperature -48°C, RFID -58dBm, Pressure 0.08Pa. The maximum allowable deviation for the container and ascent vehicle docking mechanism is: Axial ±2mm / Radial ±1mm / Angular ±0.5°. The actual measured deviation values are: Axial +1.8mm / Radial -0.9mm / Angular +0.3°.", + "question": "Determine whether the current environmental parameters and mechanical docking status meet the sample transfer conditions? If not, specify the specific items that exceed the limits.", + "answer": "All conditions are met: Temperature (-48°C ∈ [-55,-45]), RFID (-58 > -60), Pressure (0.08 < 0.1); Mechanical deviations (Axial 1.8 < 2, Radial 0.9 < 1, Angular 0.3 < 0.5) are all within the tolerance range." + }, + { + "id": 512, + "scenario_code": "3.1", + "instruction": " Chang'e-7 lander is located at the edge of the Shackleton crater in the lunar south pole (latitude 85°S), and its solar panels use a two-dimensional tracking algorithm. According to the lunar almanac, it is currently lunar noon, with a solar elevation angle of 10° and an azimuth angle of 180° (due south). Topographic mapping shows that there is a 3-meter-high permanently shadowed cliff 50 meters due south. The theoretical maximum output power of the solar panels is 120W/m², the area of a single panel is 2.5m², and the projection area factor of the part shaded by the cliff is 0.4.", + "question": "Calculate the actual total output power of the solar panels under the current conditions (considering the efficiency loss due to terrain shading).", + "answer": "Actual total output power = (1 - projection area factor) * theoretical maximum output power * single panel area * 2 = (1 - 0.4) * 120 * 2.5 * 2 = 360W" + }, + { + "id": 513, + "scenario_code": "3.6", + "instruction": " The Yutu-2 rover is about to enter the lunar night hibernation mode. Its lithium-ion battery pack has a capacity of 150Wh, and the state of health (SOH) is 90%. The scientific instruments require continuous power consumption of 8W for thermal insulation, and the electric heater's power is adjustable (range 5-20W). According to the thermal model calculations: when the ambient temperature is -180°C, if the heating power is less than 15W, the battery temperature will decrease by 0.5°C per minute (safe lower limit -40°C); the current battery temperature is -20°C and the remaining power is 120Wh.", + "question": "To ensure that the battery does not fall below the safe temperature and does not run out of power during the lunar night (14 Earth days), calculate the constant power setting for the electric heater.", + "answer": "Minimum heating power = max(15W required to maintain temperature, (total energy consumption requirement)/(lunar night duration)) = max(15, (8*336 + 15*336)/150*0.9) → 15W satisfies both constraints" + }, + { + "id": 514, + "scenario_code": "3.8", + "instruction": " In the Chang'e-6 sample return mission, the lander needs to complete three energy-consuming tasks during the lunar day: ① Core drilling (peak power consumption 300W, lasting 2 hours) ② Spectral analysis (steady power consumption 80W, lasting 4 hours) ③ Data transmission (instantaneous power consumption 450W, 4 times each for 15 minutes). The system's daily power supply limit is 2000Wh, and the battery pack can provide an additional 500Wh buffer power.", + "question": "Design a task scheduling plan that meets the energy constraints, prioritizing the complete execution of core drilling, and provide the start times of each task (assuming the start of the lunar day is T0).", + "answer": "[T0+0h] Core drilling (300W×2h) → [T0+2h] Spectral analysis (80W×4h) → [T0+6h] First data transmission (450W×0.25h) → [After each 1h of spectral analysis, insert 1 transmission], total energy consumption = 300*2 + 80*6 + 450*1 = 2000Wh" + }, + { + "id": 515, + "scenario_code": "5.1", + "instruction": " The Chang'e-6 lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S), and plans to communicate with the ground station via the Queqiao-2 relay satellite. It is known that:\n1. Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, about 65,000km from the Moon's center\n2. Ground station (Beijing station) geographic coordinates: 116.4°E, 39.9°N\n3. The current UTC time is 2024-06-15T12:00:00, and the lunar rotation phase makes the angle between the line connecting the lander and Queqiao-2 and the lunar surface normal 35°\n4. The X-band antenna gain of the relay satellite is 38dBi, and the lander's antenna gain is 12dBi\n5. The free space path loss formula: L = 20log10(4πd/λ), where λ=0.075m", + "question": "Calculate the total free space loss (dB) of the Earth-Moon relay link at the current moment, considering the distances of the two sub-links from Queqiao-2 to the lander and from Queqiao-2 to the ground station are 66,200km and 406,000km, respectively.", + "answer": "Total loss = 20log10(4π*66200000/0.075) + 20log10(4π*406000000/0.075) ≈ 197.8 + 214.6 = 412.4dB" + }, + { + "id": 516, + "scenario_code": "5.4", + "instruction": " While the Yutu-2 rover is performing scientific exploration tasks, it encounters a sudden solar proton event, causing the UHF link with the Queqiao relay satellite to be interrupted. The emergency communication system built into the rover can switch to: ① Direct Earth communication in the S band (requires 15 W of power, success rate 40%); ② Establish a mesh network through nearby relay nodes (requires 8 W of power, success rate 70%). The remaining energy can only support 20 W of power output for 30 minutes. The scientific data buffer is 85% full, and if it cannot be transmitted within 60 minutes, the data discard mechanism will be triggered.", + "question": "From the perspective of energy consumption and data rescue success rate, calculate the expected amount of data that can be transmitted within 30 minutes for both options (assuming the transmission rate is 1 Mbps for both), and provide a recommended option.", + "answer": "Option ① expected transmission volume = 0.4*(30*60)*1e6 ≈ 720 Mb; Option ② expected transmission volume = 0.7*(30*60)*1e6 ≈ 1260 Mb. Since option ② has a higher expected transmission volume and lower energy consumption, it is recommended to use the mesh network option." + }, + { + "id": 517, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform rock sampling, the one-way communication delay between Earth and the Moon is 1.3 seconds. The rover's motion control uses a predictive compensation algorithm, with its motion model being: actual displacement = command speed * (command duration - delay compensation time). It is known that the maximum safe speed for the current terrain is 0.15m/s, and the control system sets the delay compensation time to 2 seconds.", + "question": "If the ground sends a command to 'move forward at 0.12m/s for 4 seconds', but the actual network delay suddenly increases to 1.5 seconds and the compensation time is not automatically adjusted, calculate the actual displacement of this movement and whether it exceeds the safety threshold (safe movement tolerance ±5%)？", + "answer": "Actual displacement = 0.12 * (4 - 2) = 0.24m; the ideal displacement should be 0.12 * (4 - 1.5) = 0.3m; error rate = (0.3 - 0.24) / 0.3 = 20% > 5% safety threshold. Exceeds the tolerance range." + }, + { + "id": 518, + "scenario_code": "1.8", + "instruction": " Before deploying a drilling device, the bearing capacity of the lunar soil must be assessed. Given that the drill bit weighs 8kg and has a contact area of 50cm²; the lunar soil's compressive strength model is: bearing stress (Pa) = 12000 + 300 * compaction (%). The measured compaction of the current area is 65±5%, and the drilling operation requires a safety factor ≥2.", + "question": "Calculate the maximum allowable drilling pressure (unit: N) of the drill bit within the current compaction fluctuation range, and determine whether the standard operating pressure of 400N is safe？", + "answer": "Minimum bearing stress = 12000 + 300 * 60 = 30000Pa; maximum allowable pressure = 30000 * 50 * 10^-4 / 2 = 75N; 400N > 75N, unsafe." + }, + { + "id": 519, + "scenario_code": "5.7", + "instruction": " The Chang'e-5 return vehicle's onboard SSD uses NAND flash memory chips to store sample data, with a total capacity of 512 GB, and employs a dynamic wear-leveling algorithm. It is known that the chip's programming/erase cycle limit is 3000 times, and the current average wear level is 1200 times. The data write rate is 50 MB/s, with an effective write time of 4 hours per day. The file system uses Reed-Solomon(32,28) encoding for error tolerance, with a bad block rate monitoring threshold of 5%.", + "question": "Calculate the expected remaining life (in days) of the SSD under the current wear condition, and determine whether the bad block detection program needs to be initiated (assuming the current bad block rate is 3.8%).", + "answer": "Remaining wear cycles = 3000-1200 = 1800 times; daily wear cycles = (50*3600*4)/512e3 ≈ 1.406 times; remaining life ≈ 1800/1.406 ≈ 1280 days. Since 3.8% < 5%, there is no need to initiate bad block detection for now." + }, + { + "id": 520, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the Moon's south pole, it is necessary to allocate shared power for 3 devices (seismometer, magnetometer, infrared spectrometer). The power system provides a peak power of 200W and a continuous power supply of 150W. The power consumption of the devices is as follows: seismometer standby 5W/operation 30W, magnetometer standby 8W/operation 40W, infrared spectrometer standby 10W/operation 60W. The mission requires that at least 2 devices be in operation simultaneously, and the seismometer must remain operational to monitor seismic activity.", + "question": "If the magnetometer needs to enter a 30-minute high-precision measurement mode (operating power +20%), can the infrared spectrometer simultaneously start a 10-minute sample analysis? Provide the specific power consumption calculation process.", + "answer": "No. Calculation process: Magnetometer high-precision mode power consumption = 40*1.2 = 48W, seismometer operation 30W, at this point the base load = 48+30 = 78W; after the infrared spectrometer starts, the total load = 78+60 = 138W, although it is below the 150W continuous power supply capability, the remaining power 150-138 = 12W is insufficient to maintain the minimum standby requirement of the third device (magnetometer/spectrometer) (8W or 10W), violating the 'at least 2 devices in operation' constraint." + }, + { + "id": 521, + "scenario_code": "2.10", + "instruction": " The Chang'e-6 sampling robotic arm needs to perform millimeter-level precise positioning on a 3 cm diameter ilmenite outcrop. The end-effector positioning error of the robotic arm follows a normal distribution σ=±5mm (3σ). The visual system uses a binocular camera: baseline distance 200mm, focal length 20mm, pixel size 5μm. The distance measurement formula is Z = (f*b)/d, where b is the baseline distance, f is the focal length, and d is the disparity (pixels). The lunar surface lighting results in a signal-to-noise ratio (SNR) of 40dB, with a ranging error of ±0.3 pixels. The control response delay of the robotic arm is 100ms.", + "question": "Can the positioning accuracy requirements be met under the current conditions? If not, to what dB must the SNR be increased at least? (It is known that the ranging error is proportional to 10^(-SNR/20))", + "answer": "The current disparity error of ±0.3 pixels corresponds to a ranging error of ±9mm, the total error sqrt(5^2+9^2)=10.3mm>3mm; SNR must be ≥10*log10(9/0.5)=52dB" + }, + { + "id": 522, + "scenario_code": "3.1", + "instruction": " The Chang'e-5 lander is executing a sampling mission in the region at 43.06°N, 51.92°W on the near side of the Moon. The solar elevation angle during the lunar day in this area varies from 5° to 35°, and the solar panels use a two-dimensional tracking mode (azimuth + elevation). It is known that: 1) each solar panel has an area of 2 square meters, with a photoelectric conversion efficiency of 28%; 2) the solar radiation intensity on the lunar surface is 1360 W/m^2; 3) terrain obstruction reduces the effective power generation time by 30% each day; 4) the current solar elevation angle is 25° with an azimuth tracking error of ±3°.", + "question": "Calculate the actual output power of the solar panels under the current operating conditions (considering the cosine effect of the elevation angle, efficiency loss due to tracking error, and terrain obstruction factors).", + "answer": "Actual output power = 1360 * 2 * 0.28 * cos(25°) * (1 - 0.03) * (1 - 0.3) ≈ 456.7 W" + }, + { + "id": 523, + "scenario_code": "3.6", + "instruction": " The Yutu-2 rover needs to maintain a cabin temperature above -40°C during the lunar night. Given: 1) The cabin surface area is 5 m², and the equivalent thermal resistance of the multi-layer insulation material is 8 K·m²/W; 2) The isotope heat source has a rated heat output of 15 W; 3) The maximum power of the electric heater is 20 W; 4) The lunar night environmental temperature is -180°C, and the heat generated by the equipment inside the cabin is 5 W.", + "question": "Calculate the minimum electric heating power required to maintain the target temperature (consider the heat conduction formula Q = ΔT / R).", + "answer": "The required total heat Q = (40 - (-180)) / 8 = 27.5 W; Electric heating power = 27.5 - 15 - 5 = 7.5 W" + }, + { + "id": 524, + "scenario_code": "3.8", + "instruction": " The mission cycle of the Chang'e-4 relay satellite is 12 hours, with energy consumption including: 1) The X-band communication machine consumes 80 W when working (4 times a day, each time 30 minutes); 2) The average power consumption of the attitude control system is 15 W; 3) The energy consumption of the scientific payload in working mode A is 50 Wh (triggered twice a day); 4) The battery pack capacity is 1200 Wh, with a charge and discharge efficiency of 92%.", + "question": "Verify whether the energy budget meets the needs of 3 consecutive mission cycles (total energy consumption and available energy need to be calculated).", + "answer": "Total energy consumption = (80*0.5*4 + 15*12 + 50*2)*3 = 1740 Wh; Available energy = 1200*0.92*3 = 3312 Wh; Meets the requirement" + }, + { + "id": 525, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the moon, located at coordinate point A(10°N, 120°E). The mission center has planned three scientific target points: B(11°N, 121°E), C(9.5°N, 122°E), D(10.5°N, 119.5°E). It is known that the energy consumption model of the lunar rover is E = 0.15*d + 2.5, where d is the driving distance (unit: km), and E is the energy consumption (unit: Wh). The lunar rover currently has 50Wh of remaining power and needs to reserve at least 10Wh for emergency operations. The distance calculation formula between two points on the lunar surface is d = R * arccos(sinφ1*sinφ2 + cosφ1*cosφ2*cosΔλ), where R=1737km is the lunar radius, φ is the latitude, and λ is the longitude (all converted to radians for calculation).", + "question": "If Yutu-2 needs to visit as many target points as possible before the power is depleted, please calculate its optimal visiting sequence and actual total energy consumption.", + "answer": "The optimal sequence is A→D→B→C, total energy consumption=0.15*(26.3+38.9+53.2)+3*2.5=37.86Wh" + }, + { + "id": 526, + "scenario_code": "3.10", + "instruction": " After 26 months of operation, the solar panels of the Chang'e-4 relay satellite accumulated lunar dust, with monitoring showing: 1) the light transmittance of the panels decreased from an initial 92% to 68%; 2) the increase in series resistance due to lunar dust reduced the fill factor FF from 0.72 to 0.65. Original parameters: open-circuit voltage Voc=42V, short-circuit current Isc=5A, maximum power point voltage Vmpp=36V. Assuming other parameters remain unchanged and the operating temperature is constant.", + "question": "Calculate the percentage decrease in the maximum output power Pmpp of the solar panels in the current state compared to the initial value (保留两位小数). Hint: Pmpp=Voc*Isc*FF.", + "answer": "Calculation steps: 1) Initial Pmpp=42*5*0.72=151.2W; 2) Current Pmpp=42*5*(0.65*(68/92))=42*5*0.48=100.8W; 3) Decrease ratio=(151.2-100.8)/151.2≈33.33%." + }, + { + "id": 527, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration in the Von Kármán crater, obtaining the following remote sensing data: ① 3 outcrops of KREEP rock (spectral characteristics: Th content > 5 ppm, K/U ratio > 2500); ② 2 breccia zones (multicolored breccia proportion > 40%); ③ 1 suspected volcanic glass belt (reflectance < 10%, particle size distribution peak 0.1 mm). The scientific priority weights are: KREEP rock = 3, breccia = 2, volcanic glass = 1. The remaining power of the rover supports visiting no more than 4 sites, with the movement energy consumption formula being: E = 0.8 * d (d is in kilometers). The distance matrix between each site is as follows (unit km): \nA(KREEP)→B(KREEP):0.5 | A→C(KREEP):1.2 | A→D(breccia):0.8 | A→E(breccia):1.0 | A→F(glass):1.5", + "question": "Please plan the energy-optimal 4-point exploration path, requiring coverage of at least 2 types of rocks and maximizing the total scientific weight. Provide the path sequence and total energy consumption.", + "answer": "Optimal path: A→B→D→E. Path logic: ① Prioritize visiting KREEP rock B (weight 3) and breccia D/E (weight 2*2); ② Total travel distance = 0.5(A→B) + 0.8(B→D) + 0.2(D→E) = 1.5 km; ③ Total energy consumption = 0.8 * 1.5 = 1.2 kWh; ④ Total scientific weight = 3 + 2 + 2 = 7." + }, + { + "id": 528, + "scenario_code": "1.2", + "instruction": " In the Chang'e-7 mission, a drilling and sampling integrated device needs to be deployed at the lunar south pole. The device consists of a drilling module, a sample storage cabin, and a sealed transfer pipeline. The installation sequence must meet the following requirements: 1) The drilling module must be fixed to the lunar surface first (30 minutes); 2) The sample storage cabin can only dock after the drilling module has been calibrated (15 minutes); 3) The sealed transfer pipeline installation must connect the already fixed drilling module and the storage cabin (20 minutes). The current lander's solar panels will enter a shadow area in 2 hours, and all operations must be completed before this time.", + "question": "If deployment starts from the current moment, by what time point at the latest should the installation of the sealed transfer pipeline be initiated before the deadline is reached to ensure all operations are completed on time and within the 2-hour window before the solar panels enter the shadow area, considering the installation sequence and time requirements mentioned above.", + "answer": "The latest time to start the installation of the sealed transfer pipeline is 1 hour and 15 minutes after the start. Calculation: Drilling module fixation (30 minutes) + Calibration (15 minutes) + Transfer pipeline installation (20 minutes) = 65 minutes; Remaining buffer time 2 hours - 65 minutes = 55 minutes." + }, + { + "id": 529, + "scenario_code": "1.5", + "instruction": " In the Chang'e-7 mission, the ground control center needs to control the lunar rover to avoid obstacles through remote operation commands with a delay of 1.3 seconds. The current speed of the lunar rover is 0.2m/s, and there is an obstacle 30 meters ahead. The control system uses a predictive compensation algorithm: it sends continuous control commands for the next 2.6 seconds (2 * delay) in advance and verifies the sensor data in real time. The maximum braking acceleration is 0.1m/s^2.", + "question": "Calculate the shortest distance required for the lunar rover to come to a complete stop from the moment the braking command is issued, and determine if the current distance is safe.", + "answer": "Braking time t=v/a=0.2/0.1=2s; Braking distance d=v*t-0.5*a*t^2=0.2*2-0.5*0.1*4=0.4-0.2=0.2m. Considering the command delay: the distance moved during the prediction period=0.2*2.6=0.52m; Total distance=0.52+0.2=0.72m<30m, safe." + }, + { + "id": 530, + "scenario_code": "1.8", + "instruction": " When Yutu-2 traveled to the latitude 82° area, the onboard lunar soil bearing capacity sensor showed a local pressure threshold of 8kPa. It is known that the rover's self-weight is 140kg (including payload), the contact area of each of the 6 wheels with the lunar surface is 0.02m², and the lunar surface gravitational acceleration is 1.62m/s². The engineering standard requires a safety factor of no less than 2.", + "question": "Based on the real-time monitoring data, determine whether the current area is suitable for continued travel? Provide a specific calculation process.", + "answer": "Not suitable. Calculation: Total force F=140kg*1.62m/s²=226.8N; Pressure per wheel P=(226.8N/6)/0.02m²=1890Pa=1.89kPa; Safety threshold 8kPa/2=4kPa; Since 1.89kPa<4kPa theoretically it can pass, but the characteristics of lunar soil in the polar region are unstable, in practice, travel should be stopped and reassessed." + }, + { + "id": 531, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed areas of the lunar south pole, a temporary energy sharing network needs to be established. There are currently 3 devices: A (seismometer, peak power demand 120W), B (magnetometer, peak power 80W), C (heat flow probe, peak power 60W). The power module has a maximum output power of 200W and uses a dynamic priority allocation strategy: Device A has the highest priority (weight 3), B is second (weight 2), and C is the lowest (weight 1). When the total demand exceeds 200W, the power is reduced according to the weight ratio.", + "question": "If all three devices enter peak operating mode simultaneously, calculate the actual power allocated to each device.", + "answer": "Total demand=120+80+60=260W>200W; Overload 60W. Allocate the reduction according to the weight ratio 3:2:1: A reduction=60*(3/6)=30W→actual 120-30=90W; B reduction=60*(2/6)=20W→actual 80-20=60W; C reduction=60*(1/6)=10W→actual 60-10=50W. Final allocation: A=90W, B=60W, C=50W." + }, + { + "id": 532, + "scenario_code": "5.7", + "instruction": " The 'Chang'e-5' orbiter SSD storage chip uses a NAND Flash architecture, with a total capacity of 1 TB, block size of 128 KB, and each block can withstand 100,000 write-erase cycles. The average daily data write volume is 80 GB (evenly distributed), and the wear leveling algorithm uses dynamic address mapping. The chip's design life requirement is ≥3 years.", + "question": "Verify whether the SSD meets the life requirement and calculate its actual maximum theoretical lifespan (assuming constant daily write volume).", + "answer": "Calculation steps: 1) Total write-erase cycles = (1 TB/128 KB) * 100,000 = (1,048,576 KB/128 KB) * 100,000 = 819,200 million times; 2) Average daily write-erase cycles = 80 GB/128 KB = (80*1024)/128 = 640 times; 3) Theoretical lifespan = Total cycles / Average daily cycles / 365 ≈ 819,200 million / (640*365) ≈ 350 years >> 3 years. Conclusion: Far exceeds the design requirement." + }, + { + "id": 533, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the far side of the Moon. Analysis of the soil characteristics in this area shows: the top layer 0-30cm consists of loose fine particles (shear strength <5kPa), 30-50cm contains a cemented layer (shear strength 15-20kPa), and below 50cm is basaltic debris (Mohs hardness 5.5). The probe carries three sampling tools: ① Rotary impact drill (suitable for hardness >4, maximum power consumption 300W); ② Electric grab (suitable for strength <10kPa, power consumption 150W); ③ Helical sampler (suitable for strength 5-15kPa, power consumption 200W). The total power limit for the sampling system is 400W, and a single point sampling must be completed within 10 minutes.", + "question": "If undisturbed samples are to be obtained at a depth of 50cm, which tool combination should be chosen? Please calculate the maximum allowable working time for the combined tools.", + "answer": "Choose the rotary impact drill + helical sampler combination. Maximum allowable working time calculation: 300W + 200W = 500W > 400W limit, so it is not feasible; rotary impact drill working alone: 300W < 400W, available time = 10 minutes; helical sampler working alone: 200W < 400W, but cannot handle basalt with a hardness of 5.5. Final solution: use only the rotary impact drill, maximum allowable working time 10 minutes." + }, + { + "id": 534, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth. The 'Queqiao' relay satellite is deployed in a Halo orbit at the Earth-Moon L2 point, about 65,000 kilometers from the Moon. The X-band antenna gain of the relay satellite is 42 dBi, the ground station antenna gain is 54 dBi, and the system noise temperature is 150 K. During the current communication window, the distance between the relay satellite and the ground station is 400,000 km, and the free space path loss formula is: L = 20 * log10(4 * π * d / λ), where λ=0.0375 meters (8 GHz band). The transmission power is 20 W, and the transponder loss is 3 dB.", + "question": "Calculate the received signal power (dBm) of the current Earth-relay satellite link. Given that the system margin needs to be ≥6 dB for stable communication, determine if the current link meets the requirements.", + "answer": "Calculation steps: 1) Free space loss L = 20 * log10(4 * π * 400,000,000 / 0.0375) ≈ 214.5 dB; 2) EIRP = 10 * log10(20) + 42 - 3 = 43 + 42 - 3 = 82 dBm; 3) Received power Pr = EIRP - L + Gr = 82 - 214.5 + 54 = -78.5 dBm; 4) System margin = Pr - (-150 + 10 * log10(150) + 6) ≈ -78.5 - (-150 + 21.8 + 6) = -78.5 + 122.2 = 43.7 dB >6 dB. Conclusion: Meets the requirements." + }, + { + "id": 535, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover needs to transmit 500 MB of scientific data daily through the 'Queqiao' relay satellite during the lunar day. During a communication session, a solar conjunction interruption (the Sun is on the Earth-Moon line) is encountered, expected to last for 2 hours. The remaining storage capacity of the rover is 600 MB, and the data generation rate is 2 MB/min. During the interruption, data is continuously collected using a lossy compression algorithm (compression ratio 4:1), and after the connection is restored, priority should be given to transmitting critical data (30% of the total).", + "question": "Calculate the storage occupancy rate of the rover after the interruption ends, and determine the amount of original data (decompressed) that should be transmitted in the first 30 minutes after the connection is restored.", + "answer": "Calculation steps: 1) Original data volume during the interruption = 2 MB/min * 120 min = 240 MB; 2) Compressed data = 240 / 4 = 60 MB; 3) Total occupancy = 500 + 60 = 560 MB < 600 MB; 4) Transmission volume in the first 30 minutes after restoration = 30% * 560 = 168 MB original data (needs to be decompressed to 672 MB for transmission). Storage occupancy rate = 560 / 600 ≈ 93.3%." + }, + { + "id": 536, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration within the Von Kármán crater, obtaining the following regional data: Area A (coordinates 12.3°N,123.5°E) shows characteristic absorption peaks of KREEP rock in the hyperspectral data; Area B (12.1°N,123.6°E) shows a 3-meter high steep slope in the LiDAR data; Area C (12.2°N,123.4°E) shows thermal infrared anomalies and XRF detection of sulfur enrichment. The rover's remaining power supports a total travel distance of 800 meters (linear distance conversion factor 1.2), and it is currently located at the central point (12.2°N,123.5°E). The distance conversion formula between points is: d(km)=111*√[(Δlat)^2+(Δlon*cos(lat))^2].", + "question": "Sort the sampling routes according to scientific value priority and verify whether the total travel distance meets the constraint (take cos(12.2°)=0.978).", + "answer": "Priority order: Area A (KREEP rock) > Area C (sulfur anomaly) > Area B (steep slope danger). Path calculation: Central → A → C → Central. Central-A distance = 111*√[(0.1)^2+(0*0.978)^2] = 11.1km → actual travel distance = 11.1*1000*1.2/1000 = 13.32 meters; A-C distance = 111*√[(0.1)^2+(-0.1*0.978)^2] = 15.3km → 18.36 meters; C-Central distance is the same as A-C. Total travel distance = 13.32 + 18.36 + 18.36 = 50.04 meters < 800 meters, meeting the constraint." + }, + { + "id": 537, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the transfer of the sample container must be verified. The container weighs 1.8kg, and the RFID tag reading success rate is related to the distance as P=1-0.2*d (d is the distance in meters). The mechanical arm has a docking accuracy of ±3cm, and the transfer channel length is 20cm. The requirements are: ① The detected weight of the container must be ≥1.75kg; ② The RFID reading success rate must be >90% at least from 3 different angles; ③ The temperature must be maintained at -10℃±5℃ throughout the docking process. The current telemetry shows the cabin temperature is -8℃, and the positioning error of the mechanical arm's end is 2cm.", + "question": "Determine whether the current conditions meet the transfer requirements? If the RFID reader is installed 15cm from the channel entrance, calculate the actual expected reading success rate.", + "answer": "Transfer requirements are met: ① Weight 1.8kg > 1.75kg; ② Positioning error 2cm < ±3cm; ③ -8℃ is within the range of -15℃ to -5℃. RFID reading success rate calculation: Maximum reading distance = channel length 20cm + positioning error 2cm = 22cm = 0.22m; P=1-0.2*0.22=95.6% > 90%, meeting the requirement." + }, + { + "id": 538, + "scenario_code": "3.4", + "instruction": " The Yutu-2 rover plans to perform three tasks simultaneously during the 8th hour of the lunar day: ① The X-band communication machine continuously transmits data at 8W power (priority 3); ② The infrared imaging spectrometer operates at 12W power for 20 minutes (priority 1); ③ The probe-type lunar soil temperature sensor runs at 5W power for 30 minutes (priority 2). The energy management system stipulates that the instantaneous total power consumption must not exceed 18W, and it must ensure that at least one priority 1 task is fully executed.", + "question": "Design a reasonable task scheduling plan, requiring the start and stop times of each device (in minutes) to be specified and verify that the total power consumption never exceeds the limit.", + "answer": "0-20 minutes: Spectrometer (12W) + Thermometer (5W) = 17W; 20-30 minutes: Thermometer (5W) + Communicator (8W) = 13W; 30-60 minutes: Communicator (8W)." + }, + { + "id": 539, + "scenario_code": "3.6", + "instruction": " Before entering the lunar night, the lunar rover needs to activate the heating system, which requires the core components to be maintained above -40℃. It is known that: ① The initial temperature inside the cabin is -50℃; ② The electric heater has a power of 10W, with a heat capacity C=200J/℃; ③ The multi-layer thermal insulation material results in a heat loss rate Q_loss=0.5*(T_out-T_in) W (T_out is the external environment at -180℃). The isotope heat source can provide a constant 5W heating power.", + "question": "Calculate the shortest time (in seconds) required to raise the cabin temperature to -40℃ using only the electric heater? If the combined heating mode (electric heating + isotope) is used, by what percentage can this time be reduced? ", + "answer": "4000 seconds; reduced by 33.33%." + }, + { + "id": 540, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the Moon's south pole, a temporary energy-sharing network needs to be established. Currently, there are 3 devices: A (seismometer, continuous power 20W), B (spectrometer, peak power 150W/operating cycle 30%), C (drilling device, instantaneous start-up power 300W/each operation lasts 10 minutes). The total output capacity of the power station is 200W, equipped with a supercapacitor that can provide an additional 100W/10 minutes of instantaneous compensation. The priority order of the devices is: C > B > A. Currently, B is operating (current consumption 45W), A is running continuously, and now C requests to start.", + "question": "Calculate the current load of the power station and the power distribution plan when C starts, and explain whether the supercapacitor compensation needs to be activated.", + "answer": "Current load = A(20W) + B(45W) = 65W; C requires 300W to start, remaining available power = 200W - 65W = 135W < 300W. The supercapacitor compensation of 100W needs to be activated, final allocation: A remains at 20W, B is downgraded to 0W (lowest priority), C receives 200W - 20W + 100W = 280W (still lacks 20W, which is compensated by the task system automatically reducing the drilling speed)." + }, + { + "id": 541, + "scenario_code": "1.5", + "instruction": " The Yutu-2 lunar rover needs to be remotely controlled to navigate around a 2-meter diameter lunar crater with a 1.3-second communication delay. The vehicle is 1.5 meters long, with a maximum speed of 0.2m/s, and a braking distance of 0.1*v^2 (v is the current speed). Control commands must include three parts: speed setting, steering angle, and execution duration. Currently, the vehicle's heading direction forms a 30-degree angle with the line connecting to the center of the crater, and it is 3 meters away from the edge of the crater.", + "question": "Design a set of safe obstacle-avoidance command parameters (v, angle, duration), requiring that the minimum distance between any part of the vehicle and the edge of the crater throughout the process is ≥0.5 meters.", + "answer": "Command parameters: v=0.1m/s (ensuring braking distance=0.1*0.1^2=0.001m Point B > Point C. Basis: 1) Point A has the highest match with KREEP rock (85%); 2) Point B contains breccia but has slope risks; 3) Point C has unclear scientific value and is the farthest. Time verification: To reach Point A, the rover needs to travel √[(12.3-11)^2+(45.6-45)^2]≈1.3m grid distance, time required = 1.3/0.05 = 26 seconds << 2-hour constraint." + }, + { + "id": 543, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the final status of the sealed sample canister must be confirmed. The inspection checklist requires: 1) Pressure inside the canister < 0.1Pa; 2) Temperature recorder showing between -50°C to +20°C; 3) RFID tag signal strength ≥ -60dBm. The actual measurement data is: pressure 0.08Pa, temperature -30°C, RFID signal -55dBm, no visible damage to the canister. The launch window for the ascent vehicle is 5 minutes away.", + "question": "Based on the inspection data, determine whether the sample canister meets the handover standards? If the RFID signal suddenly drops to -65dBm, how should it be handled? ", + "answer": "Meets handover standards: 1) 0.08Pa < 0.1Pa; 2) -30°C within the permitted range; 3) -55dBm > -60dBm threshold. If the RFID signal drops to -65dBm: Immediately terminate the automatic process and initiate emergency manual verification (as a signal below the threshold may affect ground tracking), prioritize checking the physical connection of the tag or replacing the backup canister (if time permits)." + }, + { + "id": 544, + "scenario_code": "1.4", + "instruction": " When deploying scientific payloads in the permanently shadowed regions of the Moon's south pole, a temporary energy-sharing network needs to be established. Currently, there are three devices: a drill (peak power 120W), a spectrometer (80W), and a robotic arm (60W), powered by a rechargeable battery pack with a total output of 200W. The priority order of the devices is: drill > spectrometer > robotic arm. When the total demand exceeds 200W, the system dynamically allocates power according to the priority.", + "question": "If all three devices start at the same time, what is the actual power allocated to the robotic arm in watts (W)?", + "answer": "0W" + }, + { + "id": 545, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 rover is performing exploration tasks at the lunar south pole, and its solar wings use a two-dimensional tracking algorithm. At the current moment, the solar elevation angle is 15 degrees, and the azimuth angle is 30 degrees (0 degrees is due north). The initial angle between the normal direction of the solar wings and the sunlight is 45 degrees. The maximum output power of the solar wings P_max = 200W (when the normal is directly facing the sun), and the actual output power P_actual = P_max * cos(θ), where θ is the angle. The lunar terrain causes a permanent shadow in the direction of 10 degrees azimuth angle to the left, and if the solar wings are turned in that direction, they will not be able to generate any power at all.", + "question": "To increase the current power generation to more than 90% of the theoretical maximum while avoiding turning into the shadow area, calculate the minimum azimuth angle change required for the normal of the solar wings (considering only rotation in the horizontal plane).", + "answer": "The solar wings need to rotate 20 degrees clockwise (new azimuth angle 50 degrees), at which point the angle θ = arccos(0.9) = 25.84 degrees, the original azimuth angle 30 degrees needs to increase Δφ = arcsin(sinθ/sinα) = arcsin(sin25.84/sin15) = 20 degrees" + }, + { + "id": 546, + "scenario_code": "3.6", + "instruction": " Chang'e-7 lander needs to maintain the equipment cabin temperature above -40°C during the lunar night. It is known that: ① The cabin surface area is 2m², and the equivalent thermal resistance of the multi-layer insulation material R=2 m²·K/W; ② The rated heat output of the isotope heat source Q_rhp=8W; ③ The standby power of the electric heater Q_elec=0~20W adjustable; ④ The lunar night environmental temperature T_env=-180°C, and the heat output of the equipment in the cabin Q_dev=2W. The steady-state temperature calculation formula: T_in = T_env + (Q_rhp + Q_elec + Q_dev) * R / A", + "question": "Calculate whether the equipment cabin can meet the thermal insulation requirements without starting the electric heater? If not, find the minimum electric heating power that needs to be set.", + "answer": "Without starting, T_in=-180+(8+2)*2/2=-170°C <-40°C does not meet the requirement; Q_elec≥(40+180)*2/2-(8+2)=210W exceeds the standby power upper limit, so it cannot be met alone" + }, + { + "id": 547, + "scenario_code": "3.3", + "instruction": " The Yutu-2 rover is about to enter the lunar night hibernation mode. The current state of charge (SOC) of the lithium-ion battery pack is 65%, and the state of health (SOH) is 90%. The lunar night lasts 14 Earth days, and maintaining the minimum power consumption of electronic devices requires 2W, while the average power consumption of the thermal insulation system is 8W. The battery pack has a nominal capacity of 120Wh, and the depth of discharge limit is 30%. The isotope heat source can provide a total heat of 500kJ, equivalent to saving about 40Wh of battery power.", + "question": "If the isotope heat source is not activated, can the battery pack alone safely survive the lunar night? If so, what is the remaining SOC at the end of the lunar night? (Consider the impact of SOH in the calculation.)", + "answer": "No" + }, + { + "id": 548, + "scenario_code": "3.8", + "instruction": " The daily power generation budget for a certain lunar base energy system is: 4.5kWh from solar arrays, and 1.2kWh from fuel cell backup. The power consumption allocation for the day's tasks is: 2.8kWh for drilling operations (priority 1), 1.5kWh for the spectrometer (priority 2), and 0.8kWh for data transmission (priority 3). An unexpected meteorite impact caused the actual power generation from the solar array to decrease by 30%.", + "question": "After ensuring power supply according to the task priority, what is the remaining available energy for the day in kilowatt-hours (kWh)?", + "answer": "0.26kWh" + }, + { + "id": 549, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 lander is located on the edge of an impact crater at 45° south latitude on the near side of the Moon. Its solar wings use a two-dimensional tracking algorithm. According to the lunar calendar, the current solar elevation angle is 15°, and the azimuth angle is 30° (0° is due north, increasing clockwise). The western side of the impact crater forms a continuous terrain obstruction in the range of 60° to 120° of the solar wing's azimuth. It is known that the maximum output power of the solar wing P_max=200W (when unobstructed), and the output linearly attenuates to 50% (when fully obstructed) due to obstruction.", + "question": "If the current solar wing tracks to the optimal tilt angle (perpendicular to sunlight), calculate the actual power generation at this time.", + "answer": "150W" + }, + { + "id": 550, + "scenario_code": "3.3", + "instruction": " The Yutu-2 rover is about to enter the lunar night, with its lithium-ion battery pack having a remaining state of charge (SOC) of 40% (total capacity 10kWh). The lunar night lasts for 14 Earth days, and the base power consumption to maintain the electronic equipment at a constant temperature of -20°C is 5W, with an isotope heat source providing 2W of continuous heating. The remaining heat must be supplemented by electric heating (efficiency η=85%). It is known that: 1. The equipment compartment heat loss coefficient K=0.8W/°C; 2. The average environmental temperature during the lunar night T_env=-180°C; 3. The battery discharge cut-off SOC=15%.", + "question": "Calculate the maximum additional lunar night energy consumption that can be allocated to scientific instruments (unit: Wh).", + "answer": "2040Wh" + }, + { + "id": 551, + "scenario_code": "3.8", + "instruction": " The scientific exploration mission profile of the Chang'e-7 lander includes: 1. Continuous operation of the laser rangefinder for 2 hours (power consumption 80W); 2. Intermittent operation of the spectrometer 3 times (each time 20 minutes, power consumption 50W); 3. Data transmission by the telemetry system for 30 minutes after the ranging is completed (power consumption 120W). The system's baseline power consumption is 20W, the solar power supply is stable at 150W, and the current SOC of the battery is 60% (capacity 15kWh).", + "question": "Verify whether the mission can be completed without triggering the low battery voltage protection (SOC≥30%)？", + "answer": "Yes" + }, + { + "id": 552, + "scenario_code": "3.1", + "instruction": " The Chang'e-7 lander is located at the edge of the Shackleton crater in the lunar south pole (latitude 85°S), and its solar panels use a two-dimensional tracking algorithm. According to the lunar calendar, the current solar elevation angle during the lunar day is 5°, and the azimuth angle changes linearly over time (0°→180°). The crater's western ring mountain causes a 2-hour shadow in the morning, with the shadow area covering ±30° of the normal direction of the solar panels. It is known that the nominal power of a single wing is 200W (when the light is perpendicular), and the actual output power P_actual = P_nominal * cos(θ), where θ is the angle of incidence of sunlight.", + "question": "If the current solar azimuth angle is 90°, the solar panel tracking algorithm selects the direction directly facing the sun (θ=0°), but due to terrain obstruction, the actual effective illumination direction is an azimuth of 60° and an elevation angle of 5°, what is the actual output power of a single wing and the percentage of power loss at this time? ", + "answer": "The actual angle of incidence θ = arccos(cos(5°) * cos(30°)) ≈ 30.2°, P_actual = 200 * cos(30.2°) ≈ 172.6W, the percentage of power loss = (200 - 172.6)/200 *100% = 13.7% " + }, + { + "id": 553, + "scenario_code": "3.4", + "instruction": " The Yutu-2 rover performs three tasks simultaneously during the 8th hour of the lunar day: ① Heating of the X-ray spectrometer (peak power consumption 25W/10 minutes), ② Sampling by the robotic arm (peak power consumption 40W/5 minutes), ③ Data transmission (peak power consumption 15W for 20 minutes). The energy management system uses a dynamic load scheduling strategy: when the instantaneous total power consumption exceeds 50W, the lowest priority task is automatically delayed. The task priority order is ②>③>①. The current maximum discharge capacity of the battery is 60W.", + "question": "If the three tasks are executed completely overlapping according to the initial time plan, what is the final actual execution order and the actual start time offset for each task (assuming that once a task starts, it cannot be interrupted)?", + "answer": "Execution order: ② starts immediately (0 offset), ③ is delayed until after ② ends (+5 minute offset), ① is delayed until after ③ ends (+25 minute offset)." + }, + { + "id": 554, + "scenario_code": "3.6", + "instruction": " The lander is about to enter the lunar night phase, and its thermal insulation system operates with an electric heater (efficiency 95%) and an isotope heat source (constant output 20W). The critical equipment compartment must maintain a temperature above -20℃. It is known that: 1) The heat loss coefficient of the compartment K=1.5 W/℃; 2) The lunar night environment temperature is stable at -180℃; 3) The current remaining energy in the battery is 800Wh, and the lunar night will last 336 hours.", + "question": "Calculate the minimum electric heating power required to maintain the equipment compartment temperature at -20℃ and determine whether the battery can support the entire lunar night.", + "answer": "Minimum electric heating power calculation: 1) Temperature difference ΔT=-20-(-180)=160℃; 2) Total heat loss P_loss=K*ΔT=1.5*160=240W; 3) Electric heating power required P_heater=(240-20)/0.95≈231.6W. Battery verification: Total demand = 231.6 * 336 ≈ 77,818Wh >> 800Wh, so it cannot support. The insulation temperature needs to be lowered or the heating time reduced." + }, + { + "id": 555, + "scenario_code": "1.4", + "instruction": " The lunar surface energy grid needs to power three devices simultaneously: an X-ray spectrometer (peak power 120W, priority 1), a laser rangefinder (intermittent 80W, priority 3), and a robotic arm temperature control system (continuous 60W, priority 2). The current output limit of the solar array is 200W, and the energy storage battery can provide an additional 100W of continuous power but will accelerate aging. The system uses a dynamic priority scheduling algorithm: when total demand exceeds supply, it allocates according to descending priority, and devices of the same priority are proportionally reduced.", + "question": "If the spectrometer suddenly has a peak demand of 150W and the rangefinder is operating, what is the actual power received by each device at this time? ", + "answer": "Spectrometer 150W (full demand, priority 1), temperature control system 60W (priority 2), rangefinder 200+100-150-60=90W remaining, allocated 80*(80/(80+60))=45.7W (proportional allocation with temperature control system of the same priority)." + }, + { + "id": 556, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover for rock sampling, the ground command transmission delay is 1.28 seconds. The current speed of the lunar rover is 0.25m/s, and the emergency braking distance is 0.4m. The predictive control algorithm requires: when the warning time (T_warning) for detecting obstacles is less than the delay time (T_delay) + braking time (T_brake=v/a, a=0.3m/s^2), autonomous obstacle avoidance should be initiated. The maximum detection range of the on-board LiDAR is 10 meters.", + "question": "Calculate the minimum safe distance for the system to reliably identify obstacles ahead? (Consider delay, braking, and detection coverage.)", + "answer": "T_brake=0.25/0.3≈0.83s; Minimum safe distance=v*(T_delay+T_brake)=0.25*(1.28+0.83)=0.53m < 10m, take MAX(0.53,0.4)=0.53m" + }, + { + "id": 557, + "scenario_code": "1.2", + "instruction": " In the Chang'e-7 mission, a drilling and sampling integrated device needs to be deployed at the lunar south pole. The device consists of a drilling module, a sample storage cabin, and a sealed transfer channel, and the installation sequence must meet: 1) The drilling module must be fixed to the lunar surface base first; 2) The sample storage cabin must be connected to the drilling module through the sealed transfer channel; 3) The deployment of the sealed transfer channel must be carried out within ±5cm accuracy after both are positioned. The base positioning error is ±3cm, the autonomous movement accuracy of the storage cabin is ±4cm, and the channel cannot be readjusted after deployment.", + "question": "If the standard process of 'base positioning → storage cabin movement → channel deployment' is adopted, can the system ensure the successful deployment of the sealed transfer channel? If not, how should the installation sequence be adjusted to ensure success? ", + "answer": "No. Under the standard process, the maximum cumulative error is ±7cm (base ±3cm + storage cabin ±4cm), exceeding the ±5cm requirement for channel deployment. It should be changed to: 1) Base positioning; 2) Pre-deployment of the channel to a semi-locked state; 3) Movement of the storage cabin and active docking with the channel; 4) Final locking of the channel." + }, + { + "id": 558, + "scenario_code": "1.4", + "instruction": " The lunar base energy grid needs to power three devices simultaneously: an X-ray spectrometer (peak power 120W, priority 1), a lunar soil analyzer (80W, priority 2), and an environmental monitoring station (60W, priority 3). The grid has a maximum output of 200W, and when overloaded, devices are shut down in descending order of priority. Currently, the spectrometer is in the preheating phase consuming 40W, the analyzer is running at full power, and the monitoring station is operating intermittently with an average of 30W. Suddenly, the monitoring station enters a lunar dust storm monitoring mode requiring an additional 50W (total 80W).", + "question": "What power distribution plan will the system adopt? Please list the final operating power of each device.", + "answer": "Shut down the environmental monitoring station (lowest priority), keep the X-ray spectrometer at 40W and the lunar soil analyzer at 80W. Final allocation: spectrometer 40W, analyzer 80W, monitoring station 0W, total power consumption 120W." + }, + { + "id": 559, + "scenario_code": "1.5", + "instruction": " The Yutu-2 rover needs to operate its robotic arm to collect rock samples with a communication delay of 1.28 seconds. The end-effector positioning error model is: base error ±2mm + 0.5mm/second * delay time. The target area size is 3cm×3cm, and the robotic arm's motion control must ensure the end-effector remains within the target area. The current plan is for a single continuous action lasting 4 seconds (including command transmission time).", + "question": "Calculate whether the maximum allowable trajectory deviation for a single action meets the requirements? If not, how should the operation strategy be adjusted to meet the requirements? ", + "answer": "Not met. Maximum error = 2mm + 0.5mm/second * (4 + 1.28) seconds = 4.64mm > half the width of the target area 15mm/2 = 7.5mm, although not exceeding the limit, it is close to the boundary. It should be changed to segmented operations: each segment ≤ 2 seconds, then the error ≤ 2mm + 0.5 * (2 + 1.28) = 3.64mm, leaving a safety margin." + }, + { + "id": 560, + "scenario_code": "2.7", + "instruction": " The lunar orbiter has detected an impending solar proton event, expected to last 4 hours. The lunar rover is currently at coordinates (10,20) and needs to return to the lander base at (30,40) within 3 hours to seek shelter. The maximum speed of the lunar rover is 0.2m/s, and the terrain is flat with no obstacles. The communication system provides a 10-minute Earth-to-space communication window every 30 minutes.", + "question": "Determine if the lunar rover can return to the base in time? If it can return, calculate the shortest required time (in minutes).", + "answer": "It can return. Distance=sqrt((30-10)^2+(40-20)^2)=28.28m; Time=28.28/0.2=141.42 seconds=2.36 minutes<180 minutes" + }, + { + "id": 561, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover encountered a sudden communication interruption during scientific exploration in the lunar day. Given:\n1. The interruption was caused by a solar proton event damaging the RF front end.\n2. The remaining power can support continuous operation for 8 hours.\n3. The backup UHF band communication module consumes only 30% of the main system's power, but its maximum rate is only 2kbps.\n4. There are 3MB of critical scientific data to be transmitted in the cache.\n5. The next available relay window opens in 6 hours and lasts for 45 minutes.", + "question": "To ensure the rescue transmission of data, how should the transmission parameters of the backup module be configured? Provide the specific basis for the choice of operating mode.", + "answer": "Activate the UHF module in the lowest power consumption mode for continuous transmission, which must satisfy: 2kbps * (45*60)s ≥ 3MB → actually transmissible 5.4MB > 3MB" + }, + { + "id": 562, + "scenario_code": "5.7", + "instruction": " The 128GB NAND flash memory carried by the 'Chang'e-5' orbiter must meet a 15-year lifespan requirement. It is known that:\n1. The SSD write amplification factor WA=1.5, with an average daily write volume of 20GB\n2. The NAND chip is rated for 3000 write/erase cycles, using a dynamic wear leveling algorithm\n3. The storage system reserves 28% redundant space for bad block replacement", + "question": "Verify whether this design meets the lifespan requirement (considering the impact of redundant space}", + "answer": "Actual usable capacity: 128GB * (1-0.28) = 92.16GB\nDaily equivalent write volume: 20GB * WA =30GB\nTotal writable data volume: 92.16GB *3000=276480 GB\nTheoretical lifespan in days: 276480/30=9216 days≈25 years>15 years\nConclusion: Meets requirements" + }, + { + "id": 563, + "scenario_code": "5.7", + "instruction": " The 128GB radiation-resistant SSD carried by the Chang'e-7 orbiter has the following conditions:\n1. The bad block rate has reached 0.15% (exceeding the warning threshold of 0.1%)\n2. The file system uses a dynamic wear leveling algorithm\n3. The current write amplification factor is 1.8\n4. SSD life model: PE cycles = 10000*(1-badblock_rate/0.002)^2", + "question": "Calculate the actual remaining programmable erase cycles (PE cycles) and determine whether to activate read-only protection mode (threshold: remaining PE<500).", + "answer": "Remaining PE cycles = 10000*(1-0.0015/0.002)^2 = 625 >500, no need to activate read-only mode yet" + }, + { + "id": 564, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located in the South Pole-Aitken Basin on the far side of the Moon, unable to communicate directly with Earth. The 'Queqiao' relay satellite is deployed in a Halo orbit at the Earth-Moon L2 point, about 65,000 kilometers from the lunar surface. Known:\n1. The relay satellite's X-band antenna gain is 38dBi, the lander's transmission power is 10W, and the antenna gain is 15dBi\n2. Free space loss formula: L = 92.45 + 20*lg(f) + 20*lg(d), where f is in GHz and d is in km\n3. The current communication frequency is 7.2GHz, and the receiver sensitivity is -110dBm\n4. The lunar surface equipment has two 4-hour relay communication windows each day", + "question": "Calculate the total uplink loss (including free space loss and antenna gain) from the lander to the relay satellite when the Earth-Moon distance is 400,000 kilometers, and determine whether the signal can be normally received.", + "answer": "Total uplink loss = free space loss - transmit antenna gain - receive antenna gain = (92.45 + 20*lg(7.2) + 20*lg(65000)) - 15 - 38 ≈ 210.3dB; Received signal strength = 10W→40dBm - 210.3dB = -170.3dBm < -110dBm, cannot be normally received" + }, + { + "id": 565, + "scenario_code": "2.10", + "instruction": " The lunar rover needs to perform millimeter-level spectral detection on an olivine outcrop with a diameter of 30cm. Known: 1) The visual navigation system has a positioning accuracy of ±5cm; 2) The UWB beacon ranging error is ±2mm (effective range 10m); 3) The end-effector positioning of the robotic arm must meet |Δx|<1cm, |Δy|<1cm; 4) The current straight-line distance to the target is 8m, azimuth angle 45°.", + "question": "To achieve precise docking of the spectrometer, how should visual navigation and UWB beacons be combined? Provide the final theoretical positioning accuracy range.", + "answer": "At 8m, the visual navigation error of 5cm exceeds the requirement, so the UWB beacon must be activated within 10m; the theoretical positioning accuracy after combination = max(visual angular error, UWB error) = max(5cm*sin45°, ±2mm) = ±3.5cm > 1cm requirement, multiple iterations are needed to approach the target" + }, + { + "id": 566, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration near the Von Kármán crater, obtaining the following remote sensing data: 1) KREEP rock distribution probability map (resolution 10m, areas with confidence >80% at 3 locations); 2) Breccia thermal infrared feature zone (diameter about 15m); 3) Polarization reflection anomaly points suspected to be volcanic glass (1.2km from the current position). The remaining power of the rover supports a maximum movement distance of 4km, and the scientific priority weights are: KREEP rock (0.6) > breccia (0.3) > volcanic glass (0.1).", + "question": "Please plan the optimal exploration route, requiring: 1) Total movement distance ≤3.5km; 2) Visit at least 2 types of targets; 3) Maximize the total scientific weight. Provide the visiting order and the total path length.", + "answer": "Route: KREEP rock A → KREEP rock B → Breccia area. Scientific weight = 0.6 + 0.6 + 0.3 = 1.5. Assuming the three points are in a straight line and 1km apart, total length = 1 + 1 + 1 = 3km < 3.5km." + }, + { + "id": 567, + "scenario_code": "4.9", + "instruction": " The sample container transfer between the ascent vehicle and the lander must meet the following criteria: 1) The internal temperature of the container must always be <-60°C; 2) The RFID tag reading success rate must be ≥99%; 3) The transfer time must be <15 minutes. Current monitoring data: Container A has a temperature of -65°C but an RFID read rate of 98%, Container B has a temperature of -55°C but an RFID read rate of 99.5%, Container C meets both criteria but has a 0.5mm deviation in the mechanical arm docking mechanism.", + "question": "Based on the transfer standards, which container can be safely transferred? If a choice must be made, which parameter (temperature/RFID/mechanical) should be prioritized for correction first？", + "answer": "No container fully meets the criteria. Prioritize correcting the temperature parameter (Container B), because: 1) The RFID error is at the acceptable margin; 2) Exceeding the temperature limit may lead to loss of volatile components in the samples." + }, + { + "id": 568, + "scenario_code": "3.4", + "instruction": " The Yutu-2 rover executes three tasks simultaneously during the 8th hour of the lunar day: ① Continuous X-ray spectrometer detection (steady power consumption 25W); ② Mechanical arm sampling (instantaneous peak power consumption 120W, lasting 3 minutes); ③ Transmitting data to the relay satellite (transmitter power consumption 75W). The power system uses a lithium-ion battery pack (rated capacity 3000Wh), with the current SOC at 65%. The power management strategy stipulates: The total load at any time must not exceed 200W, otherwise, the load will be cut off according to priority (1 is the highest: data transmission > sampling > detection).", + "question": "When the mechanical arm starts sampling, how should the power management system adjust the load distribution? Please explain the specific operations and the remaining battery capacity (assuming the solar input power remains constant at 80W before and after adjustment).", + "answer": "Cut off the X-ray spectrometer with the lowest priority (25W), maintaining data transmission (75W) + mechanical arm (120W) = 195W < 200W. Remaining capacity = 3000Wh * 65% - (195W - 80W) * 3/60h = 1950Wh - 5.75Wh = 1944.25Wh" + }, + { + "id": 569, + "scenario_code": "3.6", + "instruction": " The Chang'e-4 lander is about to enter the lunar night phase. The critical electronic equipment compartment requires a working temperature of -20°C to +40°C, while the lunar night environmental temperature will drop to -180°C. The thermal control system is configured as follows: ① 8 layers of MLI thermal insulation material (overall thermal resistance R=2m^2K/W); ② Two 100W isotope heat sources; ③ Electric heaters as backup (maximum power 50W). It is calculated that the heat flow loss Q of the equipment compartment to the environment is Q=(T_in-T_out)/R, where T_in is the internal compartment temperature, and T_out is the environmental temperature.", + "question": "If only relying on isotope heat sources to maintain the internal temperature no lower than -20°C, please verify whether this system meets the requirements? If not, how much electric heating power still needs to be activated? ", + "answer": "The minimum required heat power Q=(-20-(-180))/2=80W. The total power of the two isotope heat sources 200W > 80W, meeting the requirements and no need to activate the electric heater" + }, + { + "id": 570, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. The characteristics of the lunar soil in this area are: average hardness 3.5 on the Mohs scale (similar to feldspar), medium viscosity, and volatile content of about 120ppm. There are three sampling tools available: A-type rotary impact drill (suitable for hardness > 4, power consumption 300W), B-type spiral core drill (suitable for hardness 2-4, power consumption 200W), and C-type vibrating grab (suitable for loose lunar soil, power consumption 150W). The current output power of the probe's solar panel is stable at 350W, and it needs to power the sampling tool and other scientific instruments simultaneously (base load 100W).", + "question": "According to the given conditions, which sampling tool should be chosen? Please explain the selection criteria and verify whether the power consumption meets the constraints.", + "answer": "Choose the B-type spiral core drill. Justification: 1) The lunar soil hardness of 3.5 falls within its applicable range (2-4); 2) Power consumption of 200W + base load of 100W = 300W < 350W power limit. The A-type drill does not meet the hardness requirement and the total power consumption of 400W exceeds the limit, while the C-type grab is not suitable for medium viscosity lunar soil." + }, + { + "id": 571, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is conducting a scientific exploration mission across complex terrain. Currently located at coordinate point A (10,20), it needs to reach target point B (50,60). Terrain data indicates: Area 1 (coordinate range x=10-30, y=20-40) is a flat basaltic plain with a unit distance energy consumption coefficient of 0.8; Area 2 (x=30-50, y=40-60) is a loose lunar soil slope with a unit distance energy consumption coefficient of 1.5. The remaining battery capacity is 100Wh, the base power consumption of the driving mechanism is 3W, and the maximum speed is 0.1m/s. The straight-line distance between the two points is 56.57 meters, but the actual path must consider terrain constraints.", + "question": "If the straight line AB is chosen, calculate whether the total energy consumption for the entire journey exceeds the battery capacity? If a safety margin of 15% is required, which path strategy should be chosen to ensure safety and efficiency of the mission? ", + "answer": "Total energy consumption on the straight path = (28.28m * 0.8 + 28.28m * 1.5) / 0.1m/s * 3W + (28.28m * 0.8 + 28.28m * 1.5) = 65.05Wh + 65.05Wh = 130.1Wh > 85Wh (100Wh*85%), the path should prioritize passing through Area 1 to extend the flat section." + }, + { + "id": 572, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration near the Von Kármán crater. According to the high-value area heat map generated from the orbiter's multispectral data: the probability of KREEP rock enrichment at coordinates (12.3N, 45.6E) is 82%, 1.2km away from the current position; the probability of volcanic glass at coordinates (12.1N, 45.8E) is 67%, 0.8km away. The rover's moving speed is 0.05km/h, and the remaining battery power supports a maximum of 4 hours of movement (including energy consumption for scientific payloads). The priority coefficient for sampling KREEP rocks is 1.5 (volcanic glass is 1.0).", + "question": "Calculate the comprehensive priority index (priority coefficient / travel time) for the two candidate points, and determine the optimal sampling point and the required round-trip time.", + "answer": "KREEP rock point: travel time = 1.2km / 0.05km/h = 24h (exceeds limit); volcanic glass point: travel time = 0.8km / 0.05km/h = 16h round trip 32h (still exceeds limit). Due to energy limitations, it is impossible to reach either target point, and a new path must be planned or the rover must wait for recharging. Note: KREEP rock priority index = 1.5 / 24 = 0.0625; volcanic glass = 1.0 / 16 = 0.0625 (theoretical value but not feasible in practice)." + }, + { + "id": 573, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. Container specifications: 20cm diameter cylinder, RFID tag located 2cm above the center point of the bottom surface. The robotic arm positioning accuracy is ±1mm, and the RFID reading distance needs to be maintained at 3±0.5cm. The tilt angle of the lander platform, as measured, is 2 degrees (along the x-axis), and there is an 8mm offset in the y-axis direction from the nominal position where the container is placed.", + "question": "Calculate the y-axis compensation amount that the robotic arm's end-effector should adjust to bring the RFID reading distance into the effective range (considering the tilt and existing offset). Given that tan(2°) = 0.0349.", + "answer": "Total y-axis deviation = initial offset 8mm + deviation caused by tilt 20cm * tan(2°) = 6.98mm ≈ 14.98mm. Adjustment is needed to compensate to the center position of the RFID tag: the reading distance of 3cm corresponds to an allowable y-axis deviation range of ±sqrt(30^2 - 20^2) = ±22.36mm. The current 14.98mm is already within the effective range, so no additional compensation is required." + }, + { + "id": 574, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth. The 'Queqiao' relay satellite is deployed in the Earth-Moon L2 Halo orbit, about 65,000 kilometers from the Moon. Known: the X-band antenna gain of the relay satellite is 42 dBi, the lander's transmission power is 20 W, the antenna gain is 38 dBi, and the free space path loss formula is: L = 92.45 + 20 * log10(f) + 20 * log10(d), where f is the frequency (GHz), and d is the distance (km). The current communication frequency is 8 GHz, and the system requires a minimum received power of -110 dBm.", + "question": "Calculate the free space path loss at the current Earth-Moon distance, and determine if the communication link meets the minimum received power requirement (ignoring other loss factors)?", + "answer": "Free space path loss L = 92.45 + 20 * log10(8) + 20 * log10(65000) ≈ 92.45 + 18.06 + 96.26 ≈ 206.77 dB; Received power P = transmission power (20W→43 dBm) + transmission antenna gain (38 dBi) - L (206.77 dB) + receiving antenna gain (42 dBi) = 43 + 38 - 206.77 + 42 ≈ -83.77 dBm > -110 dBm, meeting the requirement." + }, + { + "id": 575, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. According to preliminary remote sensing data analysis, the hardness of the soil in the target area is unevenly distributed, with some areas containing high-hardness basalt fragments (Mohs hardness 6-7), while the rest is loose lunar soil (Mohs hardness 2-3). The probe carries three sampling tools: a rotary impact drill (suitable for hardness ≥5), a vibratory sampling tube (suitable for hardness 2-5), and a mechanical shovel (suitable for hardness ≤3). It is known that the surface hardness of the current sampling point, as measured by a pre-test, is 4.5, but there is a hardness change layer (measured 7.2) 10 cm below the surface. The maximum axial pressure of the probe's robotic arm is 200N, and the rotary impact drill requires at least 150N contact pressure to start effective drilling.", + "question": "To ensure successful acquisition of samples below 10 cm depth, which sampling tool should be chosen? Please explain the selection criteria based on the characteristics of the tools, hardness data, and mechanical constraints.", + "answer": "The rotary impact drill should be chosen. Reasons: 1) The target layer hardness of 7.2 exceeds the upper limit of the vibratory sampling tube; 2) The mechanical shovel cannot handle high-hardness layers; 3) The maximum pressure of 200N meets the 150N start-up requirement of the rotary impact drill; 4) The surface hardness of 4.5 can be pre-processed by the vibratory sampling tube before switching tools." + }, + { + "id": 576, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration in the Von Kármán crater, obtaining the following prior data: Point A (coordinates X12,Y34) shows strong KREEP rock characteristics (enriched in rare earth elements) in the hyperspectral data; Point B (X15,Y37) shows the presence of a 1.2m diameter fresh impact crater in the LiDAR data; Point C (X18,Y32) indicates the possible presence of water ice in the thermal infrared inversion. The rover's remaining power supports up to 3 hours of operation, with a movement speed of 0.05m/s, and scientific investigations require a 40-minute stay at each point. The straight-line distances between points are: A-B=210m, B-C=320m, A-C=280m. Sampling KREEP rocks has the highest priority, followed by water ice detection, and the observation of a fresh impact crater has the lowest priority.", + "question": "Please plan the optimal exploration route to ensure the completion of the highest priority task before the power runs out, and calculate the total time spent and the remaining power percentage (assuming a base power consumption of 20W, +15W during movement, +30W during investigation, and a battery capacity of 180Wh).", + "answer": "Optimal route: Directly to Point A → Point C. Total time spent = (280m/0.05m/s)/3600 + 2*40min = 1.56h + 1.33h = 2.89h; Remaining power = [180-(20+15)*1.56-(20+30)*1.33]/180*100% = 9.17%." + }, + { + "id": 577, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover needs to transmit 1.2 GB of scientific data through the 'Queqiao' relay satellite during the lunar day. A sudden solar flare causes the X-band link to be interrupted for 3 hours, and the remaining storage capacity of the rover is only 800 MB. It is known that the next visible window for the relay satellite is 4 hours later, and the data transmission rate can be dynamically adjusted to 2 Mbps or 4 Mbps (with a corresponding compression rate of 50% but a loss of 10% data accuracy). The power consumption of the equipment in sleep mode is 5 W, and the communication module consumes 15 W when working. The current remaining battery energy is 180 Wh.", + "question": "To ensure the complete transmission of data without depleting the power, which transmission rate mode should be chosen? Provide key calculation steps.", + "answer": "Original data 1.2 GB = 9600 Mb; Choosing 2 Mbps mode: transmission time = 9600/2 = 4800 seconds ≈ 1.33 hours, total energy consumption = (1.33*15) + (4-1.33)*5 ≈ 20 + 13.35 = 33.35 Wh < 180 Wh; Choosing 4 Mbps mode: effective data = 9600*0.9 = 8640 Mb, transmission time = 8640/4 = 2160 seconds = 0.6 hours, total energy consumption = (0.6*15) + (4-0.6)*5 ≈ 9 + 17 = 26 Wh < 180 Wh; but the 4 Mbps mode will lose 10% data accuracy, so the 2 Mbps mode should be chosen to ensure data integrity and meet the power consumption constraints." + }, + { + "id": 578, + "scenario_code": "5.7", + "instruction": " The 'Chang'e-5' orbiter's solid-state storage uses a NAND Flash array with a total capacity of 1 TB, including 4 parallel operation channels. Each channel contains 2 Dies, and each Die block size is 128 KB, with a programming/erasing cycle limit of 3000 times. The current wear leveling algorithm uses dynamic address mapping and cold/hot data separation strategies. A sample shows that: Die1 of Channel 0 has been erased and written on average 1200 times, while Die0 of Channel 3 has only been erased and written 400 times.", + "question": "If 500 MB of new data (evenly distributed) is to be written next, estimate how the wear leveling algorithm should allocate the write operations to make the wear of each Die tend to be consistent.", + "answer": "Total number of blocks to be written = 500 MB / 128 KB ≈ 4000 blocks; current average wear of each Die: (1200*7 + 400) / 8 = 850 times; to make the wear of the Dies even, priority should be given to Die0 of Channel 3 (the least 400 times): the amount that can be allocated = (850-400) * 128 KB ≈ 57 MB (about 456 blocks), the remaining 443 MB (about 3544 blocks) should be allocated proportionally to the other 7 Dies (about 506 blocks per Die). The final additional erase/write times for each Die: Die0 of Channel 3 increases by 456 blocks ≈ 456 times; the rest of each Die increases by 506 blocks ≈ 506 times." + }, + { + "id": 579, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. Container specifications: internal volume 500cm³, current internal temperature -60℃±5℃, pressure 10^-3Pa. Handover process requirements: 1) RFID tag read success rate ≥99%; 2) Seal leakage rate <1×10^-6Pa·m³/s; 3) Temperature recorder data integrity 100%. Actual measurement data: three RFID read success rates 98.7%/99.2%/99.5%, helium mass spectrometer leak detector shows leakage rate 8×10^-7Pa·m³/s, temperature record missing data for the last 12 minutes (total recording duration 6 hours).", + "question": "According to the handover standards, determine whether the current sample container is allowed to separate from the ascent vehicle? If not, point out all non-conformities and specific values.", + "answer": "Separation is not allowed. Non-conformities: 1) RFID read success rate did not reach 99% on the first attempt (minimum 98.7%); 2) Temperature record integrity = (360-12)/360*100% = 96.67% < 100%. Note: Leakage rate is qualified (8×10^-7 < 1×10^-6)." + }, + { + "id": 580, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover plans to transmit exploration data to Earth via the 'Queqiao' relay satellite during the lunar day. Suddenly, a solar conjunction causes a communication interruption (lasting 15 minutes), during which the rover's solid-state storage has already cached 350 MB of untransmitted data, with 200 MB of remaining storage space. The scientific payload continuously generates data at a rate of 50 kbps, and the engineering data is generated at a rate of 20 kbps. The device uses a dynamic caching strategy: when the remaining space is below 100 MB, lossy compression (compression ratio 3:1) is automatically enabled, and when it is below 50 MB, secondary scientific payloads are paused.", + "question": "If the communication link rate recovers to 512 kbps after the solar conjunction, calculate the shortest time from the recovery of communication to the next storage warning trigger (consider all possible data flow changes)?", + "answer": "Initial state: 350 MB of untransmitted data + (50+20)*15*60/8 ≈ 406 MB of data to be transmitted; 200 MB of remaining space. After recovery, the transmission rate is 512 kbps → net transmission rate is 512 - (50+20) = 442 kbps (deducting newly generated data). First, transmitting 406 MB takes 406*8/442 ≈7.35 minutes; at this time, the newly generated data=(50+20)*7.35*60/8≈385 MB is still less than the remaining space 200 MB + (406-385)=221 MB. Thereafter, 70 kbps of data is continuously generated while transmitting at 512 kbps: net release rate=512-70=442 kbps=55.25 MB/min. When the remaining space drops to 100 MB, 221-100=121 MB of space needs to be consumed → t=121/55.25≈2.19 minutes. Therefore, the shortest warning trigger time=7.35+2.19≈9.54 minutes" + }, + { + "id": 581, + "scenario_code": "5.7", + "instruction": " The onboard SSD of the Chang'e-5 return capsule uses NAND flash chips, with a total capacity of 1 TB, organized in 4 KB/page, 128 page/block. The wear-leveling algorithm requires that the difference in the number of erase/write cycles between each block does not exceed ±5%. The current oldest block has been erased/written 3521 times, and the newest block 3698 times. The controller uses a dynamic hot spot recognition strategy: when a block is continuously written more than 20% above the average, it is automatically marked as a hot spot and data migration is initiated. It is known that the current average erase/write cycle is 3600 times, and the SSD has a daily write volume of about 40 GB (evenly distributed).", + "question": "Calculate whether the current wear-leveling state is compliant? If a block stores key telemetry data leading to an additional 12 GB of writes in a single day, determine whether a hot spot migration needs to be triggered.", + "answer": "(1) The current maximum difference=(3698-3521)/3600≈4.92% <5%, which meets the wear-leveling requirements. (2) The write volume of this block in a single day=40GB/(1TB/4KB/128)≈163 basic writes + (12GB/4KB)=307200 additional writes; the total number of erase/write cycles=163+307200 far exceeds the average value of 3600+(40GB equivalent to 163 times)=3763 times by 120% (4516 times), so a hot spot migration needs to be triggered." + }, + { + "id": 582, + "scenario_code": "4.9", + "instruction": " The lunar sample return capsule is designed with a double-layer sealed structure: the inner chamber is filled with 0.8atm of high-purity nitrogen and equipped with an RFID tag, while the outer chamber serves as a vacuum insulation layer. During the ascent phase, the following parameters need to be monitored: ① the pressure change rate dp/dt ≤ 5%/h; ② the temperature gradient ΔT ≤ 15°C; ③ the RFID signal strength maintained ≥ -60dBm. If the telemetry data before a certain handover shows: the pressure decreased from 0.82atm to 0.78atm (over 2 hours), the temperature difference is 12°C, and the RFID signal is -58dBm.", + "question": "Determine if the container meets the safety handover standards? List the specific parameter verification process.", + "answer": "Meets the standards. Verification process: ① Pressure change rate = (0.82-0.78)/0.82/2 = 2.44%/h < 5%/h; ② ΔT = 12°C < 15°C; ③ RFID = -58dBm > -60dBm. All parameters are within the threshold range." + }, + { + "id": 583, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently conducting patrol exploration on the far side of the moon, located at coordinate point A (10°N, 120°E), and needs to travel to scientific target point B (12°N, 122°E) for sampling. It is known that: 1) the lunar surface terrain is complex, with multiple small impact craters on the path, which will increase the distance if detoured; 2) the average driving speed of the lunar rover is 0.05 m/s; 3) the energy consumption model is E = 0.15 * d + 5 (d is the driving distance in meters, E is the energy consumption in Wh); 4) the current remaining power is 80 Wh; 5) the direct straight-line distance AB is 3000 meters, but the total distance needs to be increased to 3500 meters due to detours. The mission requires that the rover must reach point B before the power is exhausted and retain at least 10 Wh of emergency power.", + "question": "Please calculate whether the rover choosing the detour path meets the energy constraints? If not, what is the maximum allowable detour distance (rounded to the nearest integer)?", + "answer": "Detour energy consumption E = 0.15 * 3500 + 5 = 530 Wh; available power = 80 - 10 = 70 Wh. 530 Wh > 70 Wh, does not meet the requirement. The maximum allowable detour distance d_max must satisfy 0.15 * d_max + 5 ≤ 70 → d_max ≤ 433 meters." + }, + { + "id": 584, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. The characteristics of the soil in this area are: medium hardness (Mohs hardness 4-5), high viscosity (cohesion about 2kPa), and volatile content of about 120ppm. There are three sampling tools available: A-type rotary impact drill (suitable for hardness 5-7, power consumption 300W), B-type spiral grab (suitable for viscosity <1.5kPa, power consumption 200W), and C-type vibrating scraper (suitable for volatile content >150ppm, power consumption 150W). The maximum allowable power consumption of the sampling system is 250W, and the sampling success rate must be guaranteed to be >90%.", + "question": "According to the given constraints, which sampling tool should be chosen? Please list the key selection criteria.", + "answer": "The B-type spiral grab should be chosen. Reasons: 1) The lunar soil viscosity of 2kPa is within the applicable range of the B-type tool (<1.5kPa deviation is acceptable); 2) The power consumption of 200W is below the 250W limit; 3) The A-type tool is too hard and exceeds the power limit, while the C-type tool does not meet the volatile content threshold." + }, + { + "id": 585, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is conducting exploration tasks within the Von Kármán crater, currently located at coordinate point A(10,20). It needs to travel to the scientific target point B(85,60) to collect basalt samples. Known: 1) The lunar surface terrain energy consumption model is E = 0.12*d + 2.5*|Δh| (d is horizontal distance/km, Δh is elevation difference/m); 2) Elevation at point A is -5930m, at point B is -5925m; 3) Current remaining energy is 180Wh; 4) There is a 15m diameter fresh impact crater on the straight path AB that cannot be directly crossed.", + "question": "If choosing to detour around the impact crater increases the horizontal distance by 8m, calculate whether the total energy consumption after detouring is within the safety margin (≥20Wh)?", + "answer": "Original straight-line distance d = sqrt((85-10)^2+(60-20)^2) = 85km; elevation difference Δh = |-5925-(-5930)| = 5m; after detouring d' = 85 + 0.008 = 85.008km; total energy consumption E = 0.12*85.008 + 2.5*5 = 10.20096 + 12.5 = 22.70096Wh; remaining energy 180 - 22.70096 = 157.29904Wh >20Wh, meets the safety margin." + }, + { + "id": 586, + "scenario_code": "3.4", + "instruction": " During the lunar day, the lunar rover needs to perform three tasks simultaneously: ① Drilling and sampling (peak power consumption 300W/lasting 20 minutes) ② Data transmission (peak power consumption 200W/lasting 15 minutes) ③ Spectral analysis (steady-state power consumption 80W). The power system has a maximum output power of 400W, and the current available capacity of the lithium-ion battery is 1200Wh. Task scheduling requirements: Drilling must be completed continuously, and data transmission must start within 10 minutes after drilling begins.", + "question": "Design a task sequence plan that meets the power constraints and calculate the battery's remaining capacity after completing all tasks (assuming an initial SOC of 100%, and a system base power consumption of 50W).", + "answer": "Sequence plan: Start drilling first (0-20 minutes), start data transmission at the 10th minute (10-25 minutes), and start spectral analysis at the 20th minute (20-end). Total energy consumption = (300*20 + 200*15 + 80*5 + 50*25)/60 = 266.67 Wh, remaining capacity = 1200 - 266.67 = 933.33 Wh" + }, + { + "id": 587, + "scenario_code": "2.5", + "instruction": " The Chang'e-7 rover, while traversing the Artemis crater, detected an unmarked impact crater 15 meters ahead using its forward-looking stereo camera. The obstacle avoidance system parameters are as follows: braking distance d_brake = v^2 / (2 * μ * g_moon), where v=0.05m/s is the current speed, μ=0.3 is the wheel-soil friction coefficient, and g_moon=1.62m/s². Maneuvering to turn requires an additional 1.2 meters of safety distance.", + "question": "Determine if the rover needs to brake immediately to avoid falling into the crater? If so, calculate the minimum safe braking distance.", + "answer": "Braking distance = (0.05)^2 / (2 * 0.3 * 1.62) ≈ 0.0026m; total avoidance distance = 0.0026 + 1.2 ≈ 1.2026m <15m. No immediate braking is required, but there is ample time to plan a turn." + }, + { + "id": 588, + "scenario_code": "3.6", + "instruction": " The lander will enter hibernation mode during the lunar night, and its electronic equipment compartment needs to maintain a working temperature of -20°C to +40°C. The compartment has a surface area of 2.4㎡, a thermal conductivity of 0.05 W/(m·K), and a designed temperature difference of 200K between inside and outside (internal +10°C, external -190°C). The isotope heat source provides a nominal 30W thermal power, and the electric heater has a backup power of 50W. The lunar night lasts 14 Earth days, with available battery energy of 5000Wh.", + "question": "Verify if the isotope heat source alone can meet the thermal insulation requirements? If not, calculate the minimum time ratio that the electric heater needs to be activated (assuming 100% thermal efficiency).", + "answer": "Required thermal power = 2.4 * 0.05 * 200 / 0.01 = 240 W > 30W. The insufficient part of 210W needs to be supplemented by electric heating, the total energy consumption during the lunar night = 210 * 14 * 24 = 70560 Wh > 5000 Wh, the minimum time ratio = 5000 / (210 * 336) * 100% ≈ 7.1%." + }, + { + "id": 589, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is conducting exploration tasks on the edge of the Von Kármán crater, with its power system using a combination of solar cells and lithium batteries. The current remaining power in the lithium battery is 800 Wh, and the solar charging power is 100 W (effective only during the lunar day). According to the mission plan, Yutu-2 needs to reach a scientific target point 1.2 km away within 8 hours. The known mobility energy consumption model is: E = 0.15 * d + 5 * t (d is the driving distance/km, t is the driving time/h), and the basic power consumption in a stationary state is 2 W. The remaining lunar day time is 6 hours.", + "question": "If the shortest path is chosen for straight-line driving (taking 2 hours), please calculate the remaining power in the lithium battery when reaching the target point (considering the energy consumption of driving and idling, and the charging gain).", + "answer": "Driving energy consumption E_move = 0.15 * 1.2 + 5 * 2 = 10.18 Wh; Idle energy consumption E_idle = 2 * (8-2) = 12 Wh; Charging gain E_charge = min(6,8)*100 = 600 Wh; Remaining power = 800 - (10.18+12) + 600 = 1377.82 Wh" + }, + { + "id": 590, + "scenario_code": "2.5", + "instruction": " The Chang'e-7 rover, while exploring a permanently shadowed area, detected a new impact crater about 1.5 meters in diameter 30 meters ahead (not marked in the pre-stored digital elevation model). The obstacle avoidance system parameters are as follows: maximum lateral maneuvering angle of 30 degrees, minimum turning radius of 2 meters, and current speed of 0.1 m/s. The lunar surface friction coefficient μ=0.6, and the safe braking distance formula is s = v^2 / (2*μ*g_moon), g_moon=1.62 m/s^2.", + "question": "Determine whether the rover needs to brake immediately to avoid falling into the crater? If so, calculate the minimum braking distance and the feasible obstacle avoidance direction (left/right/bidirectional).", + "answer": "Safe braking distance s = (0.1)^2 / (2*0.6*1.62) ≈ 0.005 m <30 m, no emergency braking is required; left or right turning (bidirectional feasible) can be chosen, as the turning radius of 2m < the lateral offset requirement of 1.5m/2=0.75m for the crater." + }, + { + "id": 591, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration on the north side of the Von Kármán crater. Orbiter multispectral data shows: there is a KREEP rock characteristic absorption peak at coordinates (12.3°S, 125.8°E) (iron content 8-12%, thorium concentration 15ppm); the laser altimeter measures a height difference of +3.2m and a horizontal distance of 82m from the current position; the rover's maximum climbing angle is 15°, travel speed is 0.05m/s, and the scientific payload can operate continuously for 30 minutes per session.", + "question": "Can the rover reach the target point and complete at least 10 minutes of in-situ detection within one scientific operation cycle? Key path planning parameters need to be verified.", + "answer": "The horizontal distance of 82m corresponds to a slope length = sqrt(82^2 + 3.2^2) = 82.06m, slope angle = arctan(3.2/82) = 2.24° < 15°, which is feasible. Travel time = 82.06 / 0.05 = 1641 seconds ≈ 27.4 minutes, leaving 2.6 minutes < 10 minutes required. Conclusion: unable to complete the detection." + }, + { + "id": 592, + "scenario_code": "4.9", + "instruction": " The lunar sample return capsule is designed with a double-layer sealed structure: the inner chamber is filled with 0.8atm high-purity nitrogen and equipped with an RFID tag (operating temperature -40~85℃), while the outer chamber is a vacuum insulation layer. During the ascent phase, it will experience: ① 120 seconds of vibration during the launch segment (frequency 20-200Hz, acceleration 5g) ② external temperature fluctuations during the Earth-Moon transfer (-180~+100℃). It is known that the sealing ring material's elastic modulus decreases by 30% at temperatures >80℃, and the RFID chip may cold weld at temperatures <-50℃.", + "question": "Analyze which phase of the ascent poses the highest risk? Specific failure modes and corresponding environmental parameter thresholds need to be explained.", + "answer": "The highest risk occurs during the high-temperature phase of the Earth-Moon transfer: when the external temperature >100℃, the vacuum insulation layer may fail, causing the inner chamber temperature to exceed 80℃, leading to a decrease in the sealing ring's elastic modulus and causing a leak; direct sunlight may also raise the temperature of the RFID tag above its 85℃ operating limit." + }, + { + "id": 593, + "scenario_code": "2.9", + "instruction": " The ranging accuracy between the Lunar Navigation Satellite System (LBNSS-1) and the lander is ±3 meters (1σ), with a beacon signal update frequency of 1 Hz. The Ultra-Wideband (UWB) beacon carried by the lander has a ranging accuracy of ±0.1 meters (1σ) with the lunar rover, but its maximum effective range is 200 meters. Given the current position of the lunar rover: the ranging value from the orbiting satellite is 5427m±3m, the UWB ranging value is 185m±0.1m, and the geometric angle between the two beacons and the lunar rover is 120 degrees. The formula for calculating the weight in the integrated navigation is: w=1/σ^2", + "question": "Calculate the weight ratio of the orbiting satellite and UWB ranging data in the current optimal position estimate (保留��位小数, keep two decimal places).", + "answer": "Orbiting satellite weight w_orbit = 1/(3^2) ≈0.111; UWB weight w_uwb =1/(0.1^2)=100; Weight ratio w_orbit:w_uwb ≈0.11:100 → 1:909.09" + }, + { + "id": 594, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. Analysis of the characteristics of the lunar soil in this area shows: the top layer 0-30cm consists of loose fine particles (shear strength <5kPa), 30-50cm contains a cemented and hardened layer (shear strength 15-20kPa), and below 50cm there is a layer of high-titanium basalt debris (Mohs hardness 6-7). There are three sampling tools available: Type A rotary impact drill (suitable for hardness >5, maximum power consumption 300W), Type B helical core sampler (suitable for strength <10kPa, power consumption 150W), and Type C vibratory grab (suitable for loose particles, power consumption 80W). The total power limit of the sampling system is 400W, and it needs to complete sampling at a single point within 10 minutes.", + "question": "If it is necessary to obtain both loose lunar soil from the surface and deep basalt samples in a single operation, please design a tool combination plan and calculate the remaining power margin.", + "answer": "Select Type B helical core sampler (150W) to collect loose lunar soil from the top 30cm + Type A rotary impact drill (300W) to collect deep basalt. Total power consumption is 450W, exceeding the limit, not feasible. Adjusted plan: Type C vibratory grab (80W) to collect surface layer + Type A drill (300W) to collect deep layer, total power consumption 380W, remaining margin 20W." + }, + { + "id": 595, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander, while performing exploration tasks at the edge of the Shackleton crater, suddenly receives a solar proton event warning, predicting that high-energy particle flow will reach the lunar surface in 30 minutes. The lander needs to immediately evacuate to the nearest permanent shadow area for shelter (coordinate point C, 1.2km away). It is known that the emergency maneuver mode speed is 0.05m/s, and the regular movement mode is 0.1m/s but requires a 5-minute switching preparation time. The safety radius of the shadow area is 200m, and after entering, a stationary posture must be maintained to avoid lunar dust interference. The current remaining power supports the longest full system operation of 40 minutes.", + "question": "Determine which movement mode the lander should adopt to ensure safe arrival at the shelter area? Calculate the actual remaining safe time after arrival.", + "answer": "Emergency mode takes 1.2/0.05=24 minutes < 30-minute warning window; Regular mode preparation 5 minutes + movement 12 minutes = 17 minutes < 30 minutes. Both modes meet the time constraint, preferring the more reliable regular mode. After arrival, the remaining safe time = 40-(5+12)=23 minutes > 200m safety radius required stationary time (default 10 minutes according to regulations), meeting the requirements." + }, + { + "id": 596, + "scenario_code": "5.4", + "instruction": " Yutu-2 rover plans to transmit 3 sets of scientific data to Earth via a relay satellite during the lunar day (priority: mineral spectra > panoramic camera data > radar data). A sudden solar proton event caused the X-band link signal-to-noise ratio to drop by 8dB, leaving only 4 hours of the lunar day. The characteristics of each data packet are as follows:\n- Mineral spectra: 12GB, lossless compressed to 8GB, minimum transmission rate 2Mbps\n- Panoramic images: 20GB, lossy compressed to 6GB, minimum rate 1.5Mbps\n- Radar data: 15GB, lossy compressed to 5GB, minimum rate 1Mbps\nCurrent available bandwidth allocation options:\nOption A: Ensure 2Mbps + 1.5Mbps dual channels\nOption B: Open 1Mbps + 1.5Mbps + 2Mbps triple channels but reduce each by 30%.", + "question": "Which bandwidth allocation option should be chosen? List the highest priority data transmission combination that meets all constraints.", + "answer": "Choose Option A. Transmission combination: Mineral spectra data (8GB/2Mbps=1.23h) + Panoramic image data (6GB/1.5Mbps=1.14h), total time approximately 2.37 hours < 4 hours" + }, + { + "id": 597, + "scenario_code": "2.9", + "instruction": " The ranging accuracy between the lunar orbit navigation satellite LBNSS-1 and the rover is ±3m (1σ), and the UWB beacon ranging accuracy is ±0.1m but is limited to a range of 5km. Currently, the rover is simultaneously receiving signals from LBNSS-1 (82km away) and two UWB beacons (4.2km and 4.8km away), with three sets of independent ranging data being 82107m, 4199m, and 4803m, respectively. It is known that the geometric distance from the true position to the beacon should satisfy: sqrt((x-x1)^2+(y-y1)^2)=d1. Assuming the beacon positions have no error, and the position error of LBNSS-1 can be ignored.", + "question": "When using the weighted least squares method for integrated navigation calculations, how should the weight coefficients of each observation be set? (Hint: The weight is inversely proportional to the measurement variance.)", + "answer": "The weight of LBNSS-1 w1=1/(3^2)=0.111; the weight of UWB beacon 1 w2=1/(0.1^2)=100; the weight of UWB beacon 2 w3=100. After normalization, w1'=0.111/(0.111+100+100)=0.00055, w2'=w3'=100/200.111≈0.4997" + }, + { + "id": 598, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S). The current geometric relationship between the ground station (Beijing Station) and the Moon is: Earth-Moon distance 384,402 km, Beijing Station elevation angle 12°, and the inclination of the Moon's rotational axis causes the lander to be continuously invisible to the ground station for 14 hours. The Queqiao-2 relay satellite operates in the Earth-Moon L2 halo orbit, with a coverage angle of 60° to the Moon and 15° to the Earth. It is known that the maximum allowable elevation angle for direct communication links is 5°, and the relay link transmission delay is 2.7 seconds.", + "question": "If the scientific payload needs to transmit a set of 256GB exploration data 3 hours after the start of the invisible period, what communication strategy should be adopted? Calculate the maximum available duration of the relay link at this time (ignoring equipment switching time).", + "answer": "Adopt the Queqiao-2 relay communication strategy. Maximum available duration = (14-hour invisible period - 3 hours elapsed) - (2.7 seconds * 2 round-trip delay) ≈ 11 hours" + }, + { + "id": 599, + "scenario_code": "3.1", + "instruction": " The Chang'e-7 lander is located near the lunar south pole (latitude 85°S), and its solar panels use a two-dimensional tracking algorithm (azimuth + elevation). It is currently lunar noon, with a solar elevation angle of 1.5° and an azimuth of 180° (due south). The maximum power point tracking (MPPT) efficiency of the solar panels is 98%, each panel has an area of 2.5m², and the conversion efficiency under standard test conditions (STC) is 30%. The albedo of the lunar surface is 0.12, and terrain obstruction results in the actual received sunlight time being 82% of the theoretical value.", + "question": "Calculate the actual power generation of a single panel (unit: watts), given that the solar radiation intensity under STC is 1367W/m², and direct radiation, scattered radiation, and MPPT efficiency must be considered.", + "answer": "The actual power generation of a single panel = 1367 * (sin(1.5°) + 0.12 * (1 - sin(1.5°))) * 2.5 * 0.3 * 0.98 * 0.82 ≈ 34.6W" + }, + { + "id": 600, + "scenario_code": "3.4", + "instruction": " The Yutu-2 rover performs three tasks simultaneously during the lunar day: ① X-ray spectrometer (peak power consumption 120W, lasting 15 minutes) ② Panoramic camera shooting (80W, lasting 8 minutes) ③ Mechanical arm sampling (250W, lasting 5 minutes). The current state of charge (SOC) of the lithium-ion battery pack is 65%, with a maximum discharge depth limit of 20%. The energy management system uses a priority strategy: scientific instruments > mobility system > communication.", + "question": "Determine if the current battery capacity (assuming a full capacity of 2000Wh) can support the complete execution of all tasks in the order of priority? If not, how should the task order be adjusted? ", + "answer": "Total energy consumption = (120*0.25) + (80*8/60) + (250*5/60) ≈ 30 + 10.67 + 20.83 = 61.5Wh; Available power = 2000*(0.65-0.2) = 900Wh > 61.5Wh, which can support the original sequence of execution. No adjustment is needed." + }, + { + "id": 601, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin. Analysis of the characteristics of the lunar soil in this area shows: the top layer 0-30cm is loose fine particles (shear strength <5kPa), 30-50cm has a cemented layer (shear strength 15kPa), and below 50cm is basaltic debris (Mohs hardness 6). The probe is equipped with three sampling tools: No.1 rotary impact drill (maximum output torque 8Nm, suitable for hardness ≥5), No.2 helical core sampler (suitable for shear strength 5-20kPa), and No.3 electric shovel (suitable for loose materials). The sampling system needs to complete the operation within 20 minutes, and each tool switch takes 90 seconds.", + "question": "If it is necessary to obtain basalt samples below 50cm within the specified time, which tool combination should be chosen? Does the total time required meet the constraints? (Assuming the time required for each 10cm of drilling: drill bit 2 minutes/helical 1.5 minutes/shovel 0.5 minutes).", + "answer": "Combination plan: first use No.3 electric shovel to collect 0-30cm (time 3*0.5=1.5 minutes), switch to No.2 helical core sampler to collect 30-50cm (time 2*1.5=3 minutes), and finally switch to No.1 rotary impact drill to collect below 50cm (at least 10cm, time 2 minutes). Total time = 1.5+3+2+2*90 seconds = 11.5 minutes < 20 minutes. Meets the constraints." + }, + { + "id": 602, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (180°E longitude, 45°S latitude), and plans to communicate with Earth through the Queqiao-2 relay satellite. It is known that Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, at an average altitude of 8000km above the lunar surface; the ground station is located in Beijing (116.4°E, 39.9°N). At the current moment, the lunar rotation phase makes the line-of-sight elevation angle between the lander and Queqiao-2 25°, the antenna gain of the relay satellite is 42dB, the transmission power of the lander is 10W, and the frequency is 2.4GHz.", + "question": "Calculate the free space loss (FSL) of the Earth-Moon communication link under the current conditions, and determine whether it meets the minimum received power requirement (known ground station receiver sensitivity -120dBm)?\n(Tip: FSL=20lg(4πd/λ), speed of light c=3×10^8m/s).", + "answer": "Wavelength λ=c/f=3×10^8/2.4×10^9=0.125m; distance d=8000km; FSL=20lg(4π*8×10^6/0.125)≈201.6dB. Total received power=10W→40dBm+42dB-201.6dB=-119.6dBm＞-120dBm, meets the requirement." + }, + { + "id": 603, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover experienced an X-band communication interruption during the lunar day, diagnosed as being caused by a solar conjunction leading to signal attenuation exceeding the threshold. The rover is equipped with a dual-mode communication system (X-band direct-to-Earth link + UHF relay link), and the remaining power supports continuous operation for 48 hours. At the time of interruption, the size of the untransmitted data packet was 500MB, the solid-state memory had 2GB of remaining capacity, and the UHF link rate was 50kbps. The next visible window for the ground station is in 36 hours.", + "question": "Please design the optimal data rescue plan, which must include: 1) whether to switch communication modes 2) estimation of data transmission time 3) whether the memory capacity meets the caching requirements", + "answer": "1) Immediately switch to the UHF relay link; 2) Transmission time=500*8*1024/50≈81920 seconds≈22.76 hours＜36 hours; 3) 2GB＞500MB×2(original+compressed data), capacity is sufficient. The plan is feasible." + }, + { + "id": 604, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the moon, located at coordinate point A(10,20), and needs to reach the scientific target point B(50,60). Terrain data indicates that there are two optional paths between the two points: Path 1 is a straight-line distance of 40 meters but requires crossing a 15° slope, Path 2 is a zigzag distance of 60 meters but with a slope of less than 5° throughout. It is known that the motor efficiency curve of the lunar rover shows: the energy consumption model for driving per unit distance on a slope of θ is E = 0.1 + 0.05*θ (unit: Wh/m, θ in degrees), and the current remaining battery energy is 5Wh.", + "question": "If only considering the energy consumption constraint, which path should Yutu-2 choose to ensure it can reach the target point? Please calculate the total energy consumption of the two paths and provide the basis for your choice.", + "answer": "Total energy consumption for Path 1 = (0.1 + 0.05*15)*40 = 3.5*40 = 140Wh; Total energy consumption for Path 2 = (0.1 + 0.05*5)*60 = 0.35*60 = 21Wh. Since the remaining energy is only 5Wh, neither path can be completed, and recharging or re-planning is required." + }, + { + "id": 605, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform rock sampling, the ground command transmission delay is 1.28 seconds. The lunar rover's motion control uses a predictive compensation algorithm: actual displacement = commanded displacement * (1 - 0.05 * delay in seconds). A command to move forward 3 meters is currently being sent, and the onboard obstacle detection system has detected an obstacle 0.8 meters ahead. The braking distance formula is known: d = 0.6 * v^2 (v is the current speed, in m/s).", + "question": "If the initial speed is 0.4m/s, determine whether the compensated actual displacement will trigger an emergency stop.", + "answer": "It will trigger (compensated displacement 2.81 meters > remaining safe distance 2.2 meters)." + }, + { + "id": 606, + "scenario_code": "1.5", + "instruction": " When controlling the lunar rover to perform rock sampling, the commands sent from the ground control center take a one-way delay of 1.3 seconds to reach the rover. The current speed of the lunar rover is 0.2m/s, and a target rock is detected 2 meters ahead. The control system uses a predictive algorithm to compensate for the delay: when an obstacle is detected, it immediately brakes at a deceleration of a=0.1m/s^2, while the vehicle continues to move at the original speed during the transmission of the ground command. The braking distance formula is d=v^2/(2*a).", + "question": "If no emergency braking command is sent, and only the onboard autonomous obstacle avoidance system is relied upon, will the lunar rover collide with the rock？", + "answer": "It will collide. The autonomous braking distance d=0.2^2/(2*0.1)=0.2m, but the distance the vehicle moves during the delay=1.3*0.2=0.26m, the remaining distance=2-0.26=1.74m > 0.2m, unable to stop in time." + }, + { + "id": 607, + "scenario_code": "1.8", + "instruction": " When deploying the seismometer array, it was found that the local lunar soil bearing capacity is only 60% of the expected value. The original plan to use a tripod structure with 4 support points (each leg bearing 25kg) needs to be adjusted. The new plan requires: the load on a single leg does not exceed the actual bearing capacity of 18kg, and the projection of the center of gravity must always be within the support triangle. The total mass of the instrument is 70kg, the size is 0.8×0.8×1m (height), and the center of gravity is 0.6m above the geometric center.", + "question": "If a 6-leg symmetric layout with uniform load is used instead, will it meet the bearing capacity requirements? Calculate the actual load on a single leg and determine the stability.", + "answer": "It meets the requirements. The load on a single leg=70/6≈11.67kg ≤18kg; a 6-leg symmetric layout will inevitably keep the projection of the center of gravity within the support polygon, meeting the stability requirements." + }, + { + "id": 608, + "scenario_code": "2.7", + "instruction": " The lunar rover receives a solar proton event warning while driving near the terminator and needs to reach a safe haven within a 200-meter radius within 30 minutes. The current speed of the rover is 0.1m/s, and the communication window will be interrupted after 25 minutes. The safe haven is located 150 meters directly north of the current position, but there is a 3-meter deep fissure on the direct path. The detour plan requires moving 100 meters east, then 200 meters north, and finally 100 meters west.", + "question": "Can the lunar rover reach the safe haven before the communication is interrupted? Does the detour plan meet the time constraint? (Assume the time for turning operations is negligible.)", + "answer": "Direct path time = 150m / 0.1m/s / 60 = 25 minutes, but it is not feasible; the total detour distance = 100 + 200 + 100 = 400m, time required = 400 / 0.1 / 60 ≈ 66.7 minutes > 30-minute constraint. Conclusion: It cannot arrive within the time limit." + }, + { + "id": 609, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander is performing exploration tasks at the edge of the Shackleton crater when it suddenly receives a solar proton event warning (expected to arrive in 30 minutes). The lander is currently in safe mode, with solar panels folded and relying on built-in battery power (remaining capacity 200 Wh). The emergency shelter plan requires:\n1. Must reach the permanent shadow area shelter 500 meters away within 20 minutes;\n2. The energy consumption model for movement is E=0.15*d +5 (d is the distance moved, unit: meters);\n3. The basic power consumption after entering safe mode is 10 W.", + "question": "Determine whether the lander can complete the sheltering before the power is exhausted? Key calculation steps need to be explained.", + "answer": "It can complete the sheltering. Calculation steps:\n1. Movement energy consumption = 0.15*500 +5 =80 Wh;\n2. Power consumption for 20 minutes of movement =10W*(20/60)h≈3.33 Wh;\n3. Total energy consumption=80+3.33=83.33 Wh <200 Wh (remaining power is sufficient)." + }, + { + "id": 610, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the soil in this area are as follows: medium hardness (Mohs hardness 4-5), low viscosity, and a higher content of volatiles (about 3%). There are three sampling tools available: 1) A diamond-coated rotary drill (suitable for rocks with hardness >6); 2) A titanium alloy scoop (suitable for loose lunar soil); 3) A scraper with heating function (suitable for samples containing volatiles). The power consumption of each tool is: drill 50W/h, scoop 20W/h, scraper 30W/h. The mission requires that the sampling time does not exceed 30 minutes, and the total power consumption must be controlled within 25W.", + "question": "Based on the above characteristics of the lunar soil and the mission constraints, which sampling tool should be chosen? Please explain the basis for your choice and verify whether it meets the power consumption requirements.", + "answer": "The scraper with heating function should be chosen. Basis: 1) The lunar soil hardness is moderate (4-5) and does not require a diamond drill; 2) It contains volatiles which require a heating function; 3) Scraper 30W/h * 0.5h = 15W < 25W, meeting the power consumption constraint." + }, + { + "id": 611, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration in the Von Kármán crater, obtaining the following remote sensing data: 1) Probability map of KREEP rock distribution (probability reaches 78% at coordinates X12Y34); 2) Laser radar shows a slope of 8° at X12Y34; 3) Infrared spectroscopy indicates abnormal thermal radiation in the area. The rover is currently located at X10Y30, moving at a speed of 0.05m/s, with a maximum climbing ability of 15°, and 2 hours remaining for scientific investigation. It is known that the path planning principle is: prioritize areas where the probability of KREEP rock is >70% and the slope is <10°.", + "question": "Determine whether X12Y34 should be prioritized as a sampling point? If it goes to this point and samples (expected to take 40 minutes), can it be completed within the remaining time?)", + "answer": "X12Y34 should be prioritized. Basis: 1) KREEP rock probability 78% > 70%; 2) Slope 8° < 10°. Distance to move = sqrt((12-10)^2 + (34-30)^2) = 4.47m, time required = 4.47 / 0.05 = 89.4 seconds ≈ 1.5 minutes, total time required 41.5 minutes < 120 minutes, it can be completed." + }, + { + "id": 612, + "scenario_code": "4.9", + "instruction": " The sample container transfer between the ascent vehicle and the lander must meet the following conditions: 1) The internal temperature of the container is maintained at -50±5℃; 2) The success rate of RFID tag reading is ≥99%; 3) The sealing pressure is <0.01Pa. The current telemetry data shows: temperature -48℃, RFID read failure rate 2%, sealing pressure 0.008Pa. The transfer procedure allows up to 3 retries, with parameters automatically corrected every 5 minutes. Temperature control can be adjusted by ±2℃ each time, RFID can improve the success rate by 5% by adjusting the antenna power, and the sealing system is not adjustable.", + "question": "Can the transfer be conducted directly under the current status? If not, what corrective measures need to be taken? What is the maximum number of minutes required to complete the corrections if needed? ", + "answer": "Direct transfer cannot be conducted (RFID failure rate 2% > 1%). Measures needed: 1) Adjust the RFID antenna power (one adjustment to increase the success rate by 5% to meet the requirement); 2) No temperature adjustment needed (-48℃ is within the range). Maximum time required = 1 adjustment * 5 minutes = 5 minutes." + }, + { + "id": 613, + "scenario_code": "1.8", + "instruction": " When deploying a lunar-based telescope, it is observed that the local lunar soil bearing capacity is 8kPa (minimum requirement is 10kPa). The adjustment plan is: ① Expand the base area to 1.5 times the original plan; or ② Distribute the load through 3 support points (each bearing 40% of the total load). The total mass of the equipment is 120kg, the original base area is 0.12m², and the lunar gravitational acceleration is 1.62m/s².", + "question": "Calculate which adjustment plan meets the bearing capacity requirement? Provide key calculation steps.", + "answer": "Plan ① meets the requirement. Calculation: original pressure = (120kg * 1.62m/s²) / 0.12m² = 1620Pa; new pressure = 1620Pa / 1.5 = 1080Pa <10kPa. For plan ②, the pressure on a single support point = (120kg * 1.62 * 0.4) / (0.12 / 3) = 1944Pa > 10kPa, which does not meet the requirement." + }, + { + "id": 614, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the soil in this area are: medium hardness (Mohs hardness 4-5), low viscosity, and high volatile content (about 0.5%). There are three sampling tools available: 1) Diamond drill bit (suitable for rocks with hardness >6, power consumption 120W); 2) Titanium alloy grab (suitable for loose lunar soil, power consumption 80W); 3) Tungsten carbide scraper (suitable for medium-hardness lunar soil, power consumption 60W). The mission requires prioritizing sample integrity and low power consumption.", + "question": "Based on the given lunar soil characteristics and mission requirements, which sampling tool should be chosen? Please explain the basis for your choice.", + "answer": "The tungsten carbide scraper should be chosen. Justification: 1) The lunar soil has medium hardness (4-5), and the tungsten carbide scraper is specifically designed for medium-hardness soil; 2) The scraper has the lowest power consumption (60W), meeting the low power consumption requirement; 3) Although the volatile content is high, the mechanical action of the scraper causes less damage to volatiles compared to the high-temperature effect of the drill bit." + }, + { + "id": 615, + "scenario_code": "2.2", + "instruction": " The Chang'e-4 lander is conducting visual navigation tests within the Von Kármán crater. Known: the displacement measurement error of the Visual Odometry (VO) is ±3%/km, the IMU accelerometer zero bias stability is 0.1mg/√Hz (equivalent position error growth 1m/√hour), and the star tracker attitude angle measurement accuracy is 0.01°. After the current integrated navigation system has been running for 1 hour, the VO cumulatively reports a movement distance of 800m, the IMU calculates a displacement of 850m, and the star tracker measures a heading angle deviation of 0.5°.", + "question": "According to the multi-sensor fusion weight distribution principle (inverse of the square of the error), calculate the current optimal estimated displacement value (保留2位小数)？", + "answer": "VO error variance=(800m*0.03)^2=576m²; IMU error variance=(1m*√1)^2=1m²; star displacement equivalent variance=(800m*sin(0.5°))^2≈48.7m². Optimal estimate=(800/576 +850/1 +800*cos(0.5°)/48.7)/(1/576+1/1+1/48.7)≈849.62m" + }, + { + "id": 616, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. Known: 1) The container seal pressure should be maintained at 1.01±0.02bar; 2) The temperature recorder must show the entire process within -50℃~+20℃; 3) The RFID tag read success rate threshold is >99%. Current telemetry data: seal pressure 1.03bar, temperature record -35℃~+15℃, RFID last 10 reads successful 9 times. The handover window has only 8 minutes left, and retesting requires 5 minutes.", + "question": "Based on the inspection criteria, can the handover be directly approved? If not, which issue should be prioritized for handling first? ", + "answer": "The handover cannot be directly approved. Prioritize handling the RFID read issue (success rate 90% < 99% threshold). Justification: 1) The pressure (1.03bar) and temperature (-35℃~+15℃) are both within the tolerance range; 2) RFID read failures may affect sample traceability, and it is necessary to retest to ensure a success rate >99%." + }, + { + "id": 617, + "scenario_code": "1.4", + "instruction": " When deploying scientific payloads in the permanently shadowed regions of the lunar south pole, it is necessary to allocate shared energy to three devices (seismometer, heat flow probe, neutron spectrometer). The system's total power budget is 120W, with each device's basic power consumption being: seismometer 15W (must operate continuously), heat flow probe peak 40W (operating cycle 30 minutes/2 hours), neutron spectrometer peak 60W (operating cycle 10 minutes/hour). The energy scheduling algorithm must ensure: 1) Continuous power supply to the seismometer; 2) Two periodic devices do not activate peak mode simultaneously; 3) Total power does not exceed the budget.", + "question": "If the heat flow probe is about to enter its peak operating phase, and the neutron spectrometer is currently in its basic power consumption state (20W), what is the remaining available power in the system at this time? ", + "answer": "65W" + }, + { + "id": 618, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform rock sampling, the Earth-Moon communication delay is 1.3 seconds. The current speed of the lunar rover is 0.2m/s, and it takes 5 seconds to deploy the robotic arm. After the operator issues a 'stop immediately' command, the control system uses a predictive algorithm to compensate for the delay: if the speed v>0 is detected when the command is issued, an additional braking distance d=0.26*v^2 (unit: meters) is automatically added. The boundary of the rock sampling area is 3 meters from the current position of the rover's front.", + "question": "Determine whether the lunar rover will exceed the boundary? Provide the calculation process.", + "answer": "It will exceed the boundary. Calculation process: braking distance d=0.26*0.2^2=0.0104m, distance moved during command transmission=0.2*1.3=0.26m, total displacement=0.0104+0.26=0.2704m<3m; but it takes 5 seconds to deploy the robotic arm, during which the distance moved=0.2*5=1m, cumulative displacement 1.2704m<3m (would not exceed the boundary if other factors are not considered)." + }, + { + "id": 619, + "scenario_code": "2.7", + "instruction": " The lunar rover receives a solar proton event warning while patrolling near the terminator, with radiation intensity expected to reach a dangerous threshold in 30 minutes. Current status:\n- 200 meters away from the safe cabin\n- Maximum safe driving speed 0.15m/s\n- Requires an additional 5 minutes to complete instrument retraction and system checks\nTerrain analysis shows that the shortest path has 3 craters with diameters >30cm that need to be bypassed, which is expected to add 40 meters to the journey. The safe cabin has a 50cm diameter entrance that needs to be precisely aligned.", + "question": "Calculate whether the lunar rover can return to the safe cabin before the radiation arrives? If time is insufficient, propose two emergency plans and analyze their feasibility.", + "answer": "Time analysis:\n1. Total distance to travel: 200 +40 =240 meters;\n2. Time required: (240m /0.15m/s)/60 +5 =26.67 +5 =31.67 minutes >30 minutes (cannot return on time).\nEmergency plans:\n1) Abandon bypassing and directly cross small craters (risk: possible damage to wheels);\n2) Skip the instrument retraction procedure to save 5 minutes (risk: loss of scientific data). Plan 1 is more optimal as it can protect core equipment." + }, + { + "id": 620, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the moon, located at coordinate point A (0,0), and needs to reach the scientific target point B (100,50) (unit: meters). Terrain data shows there are three optional paths between the two points:\n1. Direct path AB: 120 meters, average slope 5°, the wheel-soil mechanics model shows a rolling resistance coefficient of 0.2;\n2. Detour path ACB: via intermediate point C (60,20), total length 140 meters, average slope 3°, rolling resistance coefficient 0.15;\n3. Detour path ADB: via intermediate point D (40,60), total length 130 meters, average slope 8°, rolling resistance coefficient 0.25.\nIt is known that the motor efficiency of the lunar rover is 80%, the battery capacity is 500Wh, the current remaining power is 300Wh, and the driving power consumption formula is P = (10 + slope * 2 + resistance coefficient * 30) * distance / efficiency.", + "question": "If the mission requires at least 100Wh of power to be reserved for emergencies, which path should Yutu-2 choose to ensure it reaches the target point? Calculate the total power consumption for each path and provide the basis for the choice.", + "answer": "Calculate the power consumption for each path:\n1. AB path: P = (10 + 5*2 + 0.2*30)*120/0.8 = (10+10+6)*150 = 3900Wh > remaining power 300Wh (not feasible);\n2. ACB path: P = (10+3*2+0.15*30)*140/0.8 = (10+6+4.5)*175 = 3587.5Wh > 300Wh (not feasible);\n3. ADB path: P = (10+8*2+0.25*30)*130/0.8 = (10+16+7.5)*162.5 = 5437.5Wh > 300Wh (not feasible). Conclusion: The current power cannot meet the requirements of any path, and it is necessary to wait for charging or adjust the target point." + }, + { + "id": 621, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. It is known that: 1) the pressure inside the sealed can must be <10^-5Pa; 2) the RFID tag must work in an environment of -50°C to +80°C; 3) the handover process can last up to 15 minutes. Current telemetry shows the can temperature is -30°C, pressure is 5*10^-6Pa, but the RFID read/write success rate is only 85% (the standard should be ≥95%). Heating the RFID tag to +20°C can increase the success rate to 98%, but it will raise the pressure inside the can to 8*10^-6Pa (heating takes 5 minutes).", + "question": "Determine whether to perform the heating operation and calculate the remaining available complete inspection time.", + "answer": "Perform the heating operation: since 8*10^-6Pa is still below the pressure threshold, and the RFID success rate increases to the required level. Remaining time = total duration 15 minutes - heating 5 minutes = 10 minutes for other inspection items." + }, + { + "id": 622, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration in the Von Kármán crater, obtaining the following data: 1) High-resolution multispectral images from the Gaofen-7 satellite show a KREEP characteristic absorption peak 300 meters northeast; 2) The rover's near-infrared spectrometer detects ordinary basalt at the current location; 3) Topographic data indicates that the path to the target point has a 15-degree slope and a 2-meter wide fissure. The remaining power of the rover supports up to 4 hours of operation, with a flat ground movement speed of 5m/h, and a reduced speed of 2m/h when climbing. The scientific priority order is: KREEP rock > volcanic glass > breccia.", + "question": "Calculate whether the KREEP rock can be sampled before the power runs out? If not, propose an alternative plan and explain the reasons.", + "answer": "It cannot be completed. Time calculation: Climbing segment 300m/2m/h=150min, round trip requires 300min (5h) > 4h of power. Alternative plan: 1) Prioritize collecting volcanic glass along the path (if it exists), as its scientific value is higher than the current basalt; 2) Request an additional 1 hour of operation time to perform a one-way sampling only. Reason: Sampling of KREEP rock has the highest priority but is constrained by terrain and power limitations." + }, + { + "id": 623, + "scenario_code": "3.6", + "instruction": " The Yutu-2 rover needs to maintain the battery temperature above -40°C during the lunar night (-180°C). Insulation system parameters: 1) Equivalent thermal resistance of multi-layer insulation material R=8m²K/W; 2) Isotope heat source rated heat output Q_rhpu=15W; 3) Battery mass m=12kg, specific heat capacity c=900J/(kg·K); 4) Initial temperature T0=20°C; 5) Duration of the lunar night t_night=336 hours. Ignore other heat exchange paths.", + "question": "Verify if the isotope heat source alone can maintain the battery's safe temperature? If not, what is the minimum additional electrical heating power required (assuming 100% heating efficiency)?", + "answer": "Heat balance equation: Q_rhpu - (T_bat+40)/R * A = m*c*(dT/dt). At steady state, dT/dt=0, solving for T_bat = Q_rhpu*R/A -40. Assuming the battery surface area A≈0.6m², then T_bat=15*8/0.6 -40=160°C (unreasonable, indicating the model needs correction). In reality, the total heat supply must be ≥ heat loss: 15W + P_heater ≥ (20-(-180))/8 *0.6 → P_heater ≥ (200/8)*0.6 -15 ≈0W, but the initial cooling phase requires calculating the integral heat. The precise solution requires using the transient heat transfer equation, simplified to P_heater_min≈5W." + }, + { + "id": 624, + "scenario_code": "3.8", + "instruction": " In the Chang'e-6 sample return mission, the spacecraft needs to operate on the lunar surface for 48 hours, with the following power budget: 1) Scientific instruments: peak 120W (6 hours per day); 2) Drill: 800W (10 minutes per run, 3 runs planned); 3) Communication system: 280W during transmission (2 times per day, 30 minutes each time), 50W during reception; 4) Basic load: 80W (continuous). The lithium-ion battery pack has a total capacity of 45Ah, voltage 28V, and a discharge depth limit of 60%. The average daily power generation of the solar panels is 22kWh.", + "question": "Calculate the total energy consumption during the mission and the minimum safety margin of the battery capacity (considering the discharge depth limit), and determine if the operation plan needs to be adjusted.", + "answer": "Total energy consumption calculation: Scientific instruments=120W*6h*2=1.44kWh; Drill=800W*(10/60)h*3=0.4kWh; Communication=(280+50)W*0.5h*2 +50W*(48-1)h=0.33kWh+2.35kWh; Basic load=80W*48h=3.84kWh. Total≈8.36kWh. Solar power supply 22kWh/24h*48h=44kWh＞requirement. The battery needs to provide 0 energy (sufficient solar power), but must meet instantaneous power support: the maximum instantaneous load of 800W corresponds to a current≈28.57A (＜45Ah*60%=27A allowable discharge current). No need to adjust the plan." + }, + { + "id": 625, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the transfer of the sample container must be verified. Known: 1) The container weighs 2kg, with an RFID tag at the bottom; 2) The robotic arm has a maximum load of 3kg and positioning accuracy of ±1mm; 3) The handover process requires: a) reading the tag ID to match the mission database, b) pressure seal test > 1kPa, c) complete temperature recorder data. Current telemetry shows that the robotic arm has already grabbed the container, but the RFID read failure rate is 30%, the seal pressure is 0.8kPa, and the temperature data is normal. The transfer window has 8 minutes remaining.", + "question": "List the troubleshooting steps that must be executed immediately and the basis for judgment (in order of priority).", + "answer": "1) Re-adjust the posture of the robotic arm to align the RFID tag with the reader (to primarily resolve the identity matching issue); 2) Inspect the seal and re-pressurize to above 1kPa (insufficient pressure may lead to sample degradation); 3) If the first two steps fail and it is still unsuccessful after 3 minutes, initiate the emergency fixation procedure for direct transfer (to ensure the priority of the ascent window). Basis: RFID matching and sealing are basic requirements for sample traceability and preservation." + }, + { + "id": 626, + "scenario_code": "1.5", + "instruction": " The ground control center operates the lunar rover for rock sampling through a remote operation system, which uses a predictive control compensation algorithm. Given: the one-way communication delay between Earth and the Moon is 1.25 seconds, the maximum speed of the lunar rover is 0.1m/s, and the positioning accuracy of the robotic arm's end is ±5mm. The current mission requires moving 2 meters from the starting point to the target rock, during which the rover must avoid a crater 0.8 meters ahead (diameter 0.5 meters). The control command upload frequency is 4Hz, and the prediction model's estimation error of the lunar rover's position increases over time as e(t) = 0.01 * t (unit: meters, t in seconds).", + "question": "To ensure safe obstacle avoidance, at what minimum distance from the crater should the ground operator issue the turning command? Please provide the calculation basis.", + "answer": "0.225 meters. Calculation basis: 1) Total command effectiveness delay = communication delay + processing delay = 1.25 + (1/4) = 1.5 seconds; 2) Distance moved by the vehicle during this period = 0.1 * 1.5 = 0.15 meters; 3) Prediction error e(1.5) = 0.015 meters; 4) Safety margin taken as positioning accuracy 0.005 meters; Total advance = 0.15 + 0.015 + 0.005 = 0.17 meters; 5) Considering the crater radius of 0.25 meters, the actual required distance = 0.25 - 0.17 = 0.08 meters when entering the danger zone, so a decision should be made at a distance of (0.17 + 0.25)/2 = 0.225 meters from the edge." + }, + { + "id": 627, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. Analysis of the soil characteristics in this area shows: the top layer 0-30cm is loose fine particles (viscosity coefficient k=0.8 Pa·s), and 30-50cm contains high-hardness basalt fragments (Mohs hardness 6.5). The engineering team is equipped with three sampling tools: a rotary impact drill (suitable for hardness >5, power consumption 200W), a helical core sampler (suitable for viscosity <1 Pa·s, power consumption 80W), and an electric shovel (universal type, power consumption 150W). The current remaining energy of the probe is 1800Wh, and sampling must be completed within 2 hours.", + "question": "If it is required to obtain both the surface fine particles and the deep basalt samples simultaneously, which two tool combinations should be chosen to complete the task within the energy limit? Please calculate and explain.", + "answer": "Choose the helical core sampler (80W*2h=160Wh) and the rotary impact drill (200W*2h=400Wh), with a total energy consumption of 560Wh<1800Wh. The helical core sampler is suitable for the low-viscosity lunar soil on the surface, and the rotary impact drill can handle the high-hardness rocks at depth." + }, + { + "id": 628, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform rock sampling, the one-way communication delay between Earth and the Moon is 1.25 seconds. The current speed of the lunar rover is 0.2m/s, and there is an obstacle 3 meters ahead. The predictive control algorithm needs to send a braking command in advance, with a braking acceleration of -0.1m/s^2. There is no additional delay in signal transmission and command execution.", + "question": "To avoid a collision, at what distance from the obstacle should the ground control station send the braking command at the latest? (Round to two decimal places in the calculation.)", + "answer": "5.31 meters" + }, + { + "id": 629, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the soil in this area are: medium hardness (Mohs hardness 4-5), low viscosity, and high volatile content (about 0.1-0.3%). There are three sampling tools available: A-type rotary drill (suitable for rocks with hardness >6), B-type vibratory grab (suitable for loose lunar soil), and C-type scraper (suitable for sticky substances). The sampling system must meet the following constraints: 1) Sampling depth ≥30cm; 2) Volatile loss rate <5%; 3) Single sampling time ≤15 minutes. It is known that the volatile loss rate of the vibratory grab is 8%, the scraper is 3%, and the drill is 1%. The efficiency of the scraper decreases by 40% in medium-hardness lunar soil.", + "question": "Based on the above conditions and tool characteristics, which sampling tool combination should be chosen? Please explain the selection criteria and verify whether all constraints are met.", + "answer": "The C-type scraper should be chosen. Justification: 1) Hardness compatibility: the scraper can handle lunar soil with a Mohs hardness of 4-5; 2) Volatile control: a 3% loss rate meets the <5% requirement; 3) Depth requirement: the scraper can work to a depth of more than 30cm. Verification: Although the efficiency decreases by 40%, the task time constraint is ≤15 minutes per session, which is still sufficient to complete the sampling." + }, + { + "id": 630, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration within the Von Kármán crater and has obtained the following regional data: 1) Hyperspectral images show characteristic absorption peaks of KREEP rock at coordinates (12.3N, 45.6E); 2) LiDAR topographic data indicate that this point is on a 5° slope; 3) Panoramic camera shows that there are obstacles larger than 30cm in diameter on the path. The rover's movement parameters are: maximum climbing angle 10°, obstacle crossing height 20cm, and remaining power supports a total travel distance of 800 meters. The straight-line distance from the current point to the target point is 300 meters, and the safe detour path distance is 450 meters. The scientific priority ranking rule is: KREEP rock (weight 5) > volcanic glass (weight 3) > ordinary lunar soil (weight 1).", + "question": "Please calculate the scientific value weight of this sampling point and determine whether the rover should go to this point to collect samples? The decision-making basis needs to be explained.", + "answer": "The scientific value weight is 5 (KREEP rock). The rover should go to collect samples because: 1) Terrain passability: a 5° slope is less than the 10° limit and the detour path of 450 meters is within the 800-meter power limit; 2) Obstacle avoidance: the detour path can avoid stones larger than 30cm; 3) Highest scientific value (weight 5)." + }, + { + "id": 631, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 lander is located on the edge of an impact crater at 23.5° East longitude and 12.8° North latitude on the lunar near side. According to the lunar calendar, the current solar elevation angle during the lunar day is 15°, and the azimuth angle is 45° (0° is due north, increasing clockwise). The lander is equipped with two solar panels that can rotate in two dimensions, each with an area of 2.5m² and a photovoltaic conversion efficiency of 28%. The crater wall forms an obstruction in the azimuth range of 30°-60°, reducing the solar radiation intensity in the obstructed area to 0. It is known that the solar direct radiation intensity on the lunar surface is 1360W/m², and diffuse reflection is negligible.", + "question": "If the solar panels are currently fully aligned with the sun's azimuth (maximum power tracking without obstruction), calculate the actual power generation at this time (unit: watts). Consider the impact of terrain obstruction.", + "answer": "238W" + }, + { + "id": 632, + "scenario_code": "5.4", + "instruction": " During the lunar day, the Yutu-2 rover experienced an X-band communication interruption (lasting 15 minutes), diagnosed as caused by a solar flare leading to ionospheric disturbance. The rover's storage chip has 8GB of remaining capacity, the current scientific data generation rate is 12MB/min, and the emergency UHF backup link bandwidth is only 500kbps. Before the interruption, 3GB of data had been cached but not transmitted, with all data priorities divided as follows: engineering data (20%), high-value scientific data (50%), and routine exploration data (30%).", + "question": "Calculate which types of data should be prioritized for transmission in the first 30 minutes after communication is restored to ensure that critical information is not lost? Consider the risk of storage overflow (assuming a constant compression rate of 60%).", + "answer": "The remaining storage space can accommodate new data: 8GB - 3GB = 5GB; new data generated in 30 minutes: 12MB/min * 30 * 0.6 = 216MB. Prioritize transmitting high-value scientific data (50%) and engineering data (20%), totaling 3GB*70%=2.1GB. The UHF link can transmit 500kbps*1800s=1.125GB in 30 minutes, so all engineering data and part of the high-value scientific data (1.125GB-0.6GB=525MB) should be prioritized." + }, + { + "id": 633, + "scenario_code": "5.7", + "instruction": " The 128TB solid-state drive carried by the Chang'e-7 orbiter uses a NAND Flash architecture, with a block size of 4MB and an average write-erase life of 3000 cycles. The current wear-leveling algorithm employs a dynamic hot zone migration strategy, with daily write volumes fluctuating between 120~180GB (after compression), and the most active files accounting for 15% of the total. The storage has been operational for 400 Earth days, with an average daily write volume of 150GB.", + "question": "Calculate the remaining lifespan in the worst-case scenario (round to the nearest whole number), taking into account: ① 5% of the blocks must be reserved as spare; ② A warning is triggered when any block reaches 2500 write-erase cycles.", + "answer": "Total available blocks: 128TB/4MB * 95% = 31,250,000 blocks; Write-erase cycles per day for the most active blocks: 180GB*15%/4MB = 6,750 times/day; Remaining write-erase capacity: 2500 - (150*400*15%/4MB) = 2500 - 2250 = 250 times; Remaining lifespan = 250 / (6750/31,250,000) ≈ 1,157 days" + }, + { + "id": 634, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, a temporary power grid needs to be established. Currently, there are 3 devices: a seismometer (peak power 120W), a magnetometer (peak power 80W), and a drill (peak power 300W). The power module has a maximum output power of 400W and uses dynamic priority scheduling: drill > seismometer > magnetometer. When the total demand exceeds 400W, devices are shut down in descending order of priority. Now, the drill is in preheating mode (continuously consuming 150W), and the seismometer is calibrating (consuming 100W), at which point the magnetometer requests to start.", + "question": "Is the system allowed to start the magnetometer? If allowed, what is the actual power allocation for each device? ", + "answer": "The start-up is not allowed. Current total power consumption = Drill 150W + Seismometer 100W = 250W. If the magnetometer starts, the total demand = 250 + 80 = 330W < 400W, but the drill preheating may rise to 300W at any time, at which point the total demand = 300 + 100 + 80 = 480W > 400W. According to the priority, the magnetometer must be shut down. Therefore, the system will reject its start-up request to maintain stability margin." + }, + { + "id": 635, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover for rock sampling, the one-way communication delay between Earth and the Moon is 1.3 seconds. The current speed of the lunar rover is 0.2m/s, and a target rock is found 3 meters ahead. After the operator sends a braking command, the braking distance must not exceed 0.5 meters to ensure precise stopping. The maximum braking acceleration is 0.1m/s^2, and the control command transmission time is included in the communication delay.", + "question": "At what distance from the rock should the operator send the braking command at the latest? Consider the delay and braking distance.", + "answer": "The latest sending distance = distance traveled during communication delay + braking distance = (speed * delay time) + (speed^2 / (2 * acceleration)) = (0.2 * 1.3) + (0.2^2 / (2 * 0.1)) = 0.26 + 0.2 = 0.46 meters. Therefore, the command should be sent before the distance to the rock exceeds 3 + 0.46 = 3.46 meters." + }, + { + "id": 636, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander, while working at the edge of the Shackleton crater, suddenly receives a solar proton event warning: high-energy particle flow is expected to reach the moon in 30 minutes and last for 6 hours. Current status: 1) The lander is 2.8km away from the permanent shadow area shelter; 2) Maximum moving speed is 0.08m/s; 3) Turning or climbing requires an additional 20% time; 4) The shelter entrance faces 60° away from the current orientation, requiring a direction adjustment first.", + "question": "Determine whether the lander can complete the sheltering before the proton event arrives. Provide key time node calculations (turning time is counted as 5 minutes).", + "answer": "Cannot complete. Key nodes: 1) Turning time = 5 minutes; 2) Travel time = 2800m / (0.08m/s) = 35000s ≈ 583 minutes; 3) Total time required = 5 + 583 * 1.2 ≈ 705 minutes > 30-minute warning window." + }, + { + "id": 637, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. The known container mass is 2.4kg, and the RFID tag frequency is 13.56MHz±0.05MHz. The handover process requires: 1) The temperature recorder reading is within the range of -50℃~+30℃; 2) Sealing pressure > 10kPa; 3) RFID signal strength ≥ -60dBm. Current telemetry data: temperature -45℃, pressure 12kPa, RFID signal -58dBm@13.53MHz, container mass sensor shows 2.38kg.", + "question": "According to the handover standards, determine whether the current sample container meets the conditions for automatic handover? List all non-conformities (if any).", + "answer": "Meets handover conditions. Verification: 1) Temperature -45℃ is within the range; 2) Pressure 12kPa > 10kPa; 3) RFID frequency 13.53MHz is within the tolerance and the signal -58dBm ≥ -60dBm; 4) Mass deviation (2.38 vs 2.4kg) is within the normal sensor error range." + }, + { + "id": 638, + "scenario_code": "3.1", + "instruction": " Chang'e-7 rover is conducting exploration tasks at the lunar south pole, and its solar panels use a two-dimensional tracking algorithm. The current solar elevation angle is 15 degrees, and the azimuth angle is 30 degrees (with 0 degrees being due north). There is a rock 3 meters in front of the rover that is 2 meters high, blocking the view. The maximum output power of the solar panels P_max = 200W (when unobstructed), and the actual output power P_actual = P_max * cos(θ) * (1 - obstruction ratio), where θ is the angle of incidence of sunlight (angle with the normal). The current angle of incidence of sunlight θ = 20 degrees, the projection area of the rock on the solar panels is 1.2 square meters, and the total area of the solar panels is 2 square meters.", + "question": "Calculate the actual output power of the solar panels P_actual (保留两位小数, retain two decimal places).", + "answer": "148.38W" + }, + { + "id": 639, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander detects a warning of a solar proton event eruption at the edge of the Shackleton crater, which is expected to affect the current position in 30 minutes. The lander needs to urgently move to a permanently shadowed area 200 meters away for shelter. It is known that: 1) The current navigation system can only provide an absolute positioning accuracy of ±5 meters; 2) The moving speed is 0.1m/s; 3) 5 minutes need to be reserved for attitude adjustment for safe docking; 4) The IMU drift error is 0.1m/min.", + "question": "Determine whether the lander can complete the shelter before the proton event arrives? If not, how many minutes in advance at least is the warning needed to be issued for the lander to complete the shelter before the proton event arrives? ", + "answer": "Travel time = 200 / (0.1 * 60) ≈ 33.33 minutes; Total required time = 33.33 + 5 = 38.33 minutes > 30 minutes. A warning needs to be issued 38.33 - 30 = 8.33 minutes in advance." + }, + { + "id": 640, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S), and needs to communicate with the ground station via the Queqiao-2 relay satellite. It is known that:\n1. Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, about 65,000km from the Moon's center\n2. The Moon's radius is 1,737km\n3. The angle between the line connecting the relay satellite to the Moon's center and the line connecting the lander to the Moon's center at the current moment is 35°\n4. The elevation angle of the ground station antenna must be ≥10° to establish a stable link\n5. The average distance between the Earth and the Moon is 384,400km", + "question": "Please calculate whether the ground station can establish a dual-hop communication link with both Queqiao-2 and the lander at the current moment? The judgment basis needs to be explained step by step.", + "answer": "No. Judgment steps:\n1. Line of sight judgment from the lander to the relay satellite: The critical angle for lunar surface obstruction = arcsin(Moon's radius / relay satellite orbit radius) = arcsin(1737/65000) ≈ 1.53°, the current angle 35° > 1.53°, so there is a direct line of sight.\n2. Line of sight judgment from the relay satellite to the ground station: The Earth-Moon L2 point is always on the extension of the Earth-Moon line, the actual elevation angle of the ground station antenna is negative (needs to point towards the far side of the Moon), which does not meet the requirement of ≥10°." + }, + { + "id": 641, + "scenario_code": "3.1", + "instruction": " The Chang'e-5 lander is located near the Mons Rümker mountain at 43.06°N, 51.92°E on the near side of the Moon. During the lunar day, the solar elevation angle in this area varies from 5° to 35°, and the solar panels operate in a two-dimensional tracking mode (azimuth + pitch). It is known that: 1) the area of a single panel is 2.5m², with a photovoltaic conversion efficiency of 28%; 2) the surface reflectivity of the Moon is 0.12; 3) the solar constant is 1368W/m²; 4) terrain blocking reduces the effective sunlight exposure time by 18% daily. The current mission phase requires maintaining an average power output of at least 300W.", + "question": "If the solar elevation angle is 20°, considering the combined effect of direct sunlight and surface-reflected light, calculate whether the real-time power generation of a single panel meets the system requirements? (Hint: The effective incidence angle of reflected light is calculated as 60°.)", + "answer": "Not met. Calculation process: 1) Direct sunlight power = 1368*sin(20°)*2.5*0.28 = 322.6W; 2) Reflected light power = 1368*0.12*cos(60°)*2.5*0.28 = 57.6W; 3) Total power = (322.6+57.6)*0.82 = 311.7W < 600W (requirement for two panels)." + }, + { + "id": 642, + "scenario_code": "3.4", + "instruction": " The Yutu-2 rover performs the following tasks on the 3rd day of the lunar day: 1) Mobility operations: peak power of the drive motor is 180W, lasting 15 minutes; 2) Spectrometer detection: peak power is 250W, each time for 5 minutes, to be performed 3 times; 3) Data transmission: instantaneous power is 300W, each time for 8 minutes. Energy system constraints: the total power consumption in any 10-minute window must not exceed 400W, and the maximum discharge current of the lithium-ion battery pack is 20A (operating voltage 28V).", + "question": "Please design a task scheduling sequence that meets the energy constraints, requiring that the interval between spectrometer detections is no less than 30 minutes and all tasks are completed within 8 hours.", + "answer": "Example solution: 1) Mobility operations from 0-15 minutes (180W); 2) Spectrometer detection from 45-50, 135-140, and 225-230 minutes (250W); 3) Data transmission from 300-308 minutes (300W). Verification: Power consumption in any 10-minute window ≤ 400W, battery current ≤ 300/28 = 10.7A < 20A." + }, + { + "id": 643, + "scenario_code": "5.4", + "instruction": " During the lunar day, the Yutu-2 rover continuously transmitted exploration data when it encountered a solar conjunction interruption (the Sun was between the Earth and the Moon). Known facts:\n1. The transmission rate before the interruption was 256 kbps\n2. The remaining capacity of the solid-state storage is 8 GB\n3. The scientific data generation rate: panoramic camera 120 MB/hour, particle-induced X-ray spectrometer 60 MB/hour\n4. The expected duration of the interruption is 3 hours\n5. Using a lossy compression algorithm can reduce the data volume by 50% but will result in a 10% loss of scientific value", + "question": "To ensure that key data is not lost, how should the data transmission strategy be adjusted? Provide a specific calculation process.", + "answer": "Lossy compression should be enabled and high-value data should be transmitted first. Calculation process:\n1. Original data volume = (120 + 60) * 3 = 540 MB\n2. Remaining SSD capacity 8 GB >> 540 MB, no data needs to be discarded\n3. Compressed data volume = 540 * 0.5 = 270 MB < 8 GB\n4. Choosing the compression scheme can ensure storage safety and only result in a 10% loss of scientific value" + }, + { + "id": 644, + "scenario_code": "2.7", + "instruction": " The lunar rover receives a solar proton event warning while patrolling the Aristarchus plateau and needs to reach a 300-meter radius permanent shadow area for safety within 30 minutes. Current status: 1) Maximum safe speed 0.1m/s; 2) IMU shows a straight-line distance of 200 meters to the entrance of the safe area, but it is blocked by a 10-meter high cliff; 3) Detour options: East gentle slope (350 meters long) or West crater rim (320 meters long but requires crossing 3 sections with a 20° slope).", + "question": "Analyze the feasibility of the eastern and western routes (consider: a) whether the time is sufficient; b) whether the slope of the western route exceeds the 15° safety threshold), and provide a recommended route and rationale.", + "answer": "The eastern route takes 350/0.1=3500 seconds ≈ 58 minutes > 30 minutes; the western route takes 320/0.1=3200 seconds ≈ 53 minutes, still exceeding the limit, and the 20° slope exceeds the 15° safety threshold. Conclusion: Neither route is feasible, and the emergency on-site hibernation program must be initiated." + }, + { + "id": 645, + "scenario_code": "4.5", + "instruction": " When implementing a 2-meter deep water ice drilling in the lunar polar regions, the drilling system parameters are as follows: drilling speed 0.5cm/min (hard layer), 2cm/min (soft layer); drill head rated power 200W; the lunar soil profile shows 0-1.2m as the soft layer, 1.2-2m as the hard layer. The system energy consumption formula is E=P*t, where P is the real-time power, and t is the time. Assume the drill head always operates at full load.", + "question": "Calculate the total energy consumption (unit: joules) for completing this drilling task, and explain step by step the time spent and corresponding energy consumption for each layer.", + "answer": "Time spent on the soft layer: (120cm)/(2cm/min)=60min=3600s, energy consumption=200W*3600s=720000J; Time spent on the hard layer: (80cm)/(0.5cm/min)=160min=9600s, energy consumption=200W*9600s=1920000J; Total energy consumption=720000+1920000=2640000J" + }, + { + "id": 646, + "scenario_code": "1.2", + "instruction": " When deploying an integrated drilling and sampling device at the edge of the Shackleton crater in the lunar south pole, the geometric constraints of the equipment installation sequence must be considered. The main drill (120kg) must first be placed on the lunar surface reference platform (load-bearing limit 150kg) by the lander's robotic arm, followed by the installation of auxiliary stabilizing brackets (30kg) and solar panel arrays (20kg). All components must be installed in sequence, and a 15-minute stability check must be conducted after each robotic arm operation. The lander's power supply system can only support 90 minutes of continuous high-power robotic arm operation (including inspection time).", + "question": "If it is required to complete all deployments within a single power supply cycle, please verify whether the current installation sequence design (main drill → stabilizing bracket → solar panel) meets the time constraint? If not, propose an adjustment plan and explain the reasons.", + "answer": "Total time for the current design = 3 operations * 15 minutes of inspection + 2 transfer times (assuming each transfer takes 10 minutes) = 65 minutes, which meets the 90-minute constraint. No adjustment is needed." + }, + { + "id": 647, + "scenario_code": "1.4", + "instruction": " The lunar base energy grid needs to allocate peak power to 3 devices: the lunar soil analyzer (continuous demand of 80W), the mobile exploration vehicle charging station (instantaneous peak of 300W for each 10-minute charge), and the life support system (a must-guaranteed 100W). The grid has an output capacity of 400W, and the total load must not exceed 350W at any time to prevent voltage drops. The charging station needs to complete 6 charging operations daily, with intervals ≥1 hour.", + "question": "Design the operation schedule for the charging station, ensuring it meets the device requirements and grid constraints (provide at least 2 feasible time slot examples).", + "answer": "Example 1: Schedule the charging station to operate from 01:00-01:10 and 03:00-03:10 when the life support system and lunar soil analyzer are running (180W remaining); Example 2: Schedule the charging station to operate from 12:00-12:10 and 14:00-14:10 when the lunar soil analyzer is paused." + }, + { + "id": 648, + "scenario_code": "1.8", + "instruction": " When deploying the seismometer array, it was found that the local lunar soil bearing capacity is only 1/6 of the Earth equivalent. The original design used 4 circular load-bearing plates with a diameter of 20cm (individual pressure-bearing area of 314cm²), requiring the overall ground pressure to be ≤15kPa. The total mass of the seismometer is 60kg, and the lunar gravitational acceleration is 1.62m/s².", + "question": "Calculate whether the current design meets the bearing capacity requirements? If not, to what minimum diameter in centimeters (rounded to the nearest integer) should the individual load-bearing plates be expanded to meet the requirements? ", + "answer": "Current pressure = (60kg * 1.62m/s²) / (4 * 0.0314m²) = 774Pa < 15kPa, which meets the requirement. No expansion is needed." + }, + { + "id": 649, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 lander is located on the edge of an impact crater at 45° north latitude on the lunar near side. Its solar panels use two-dimensional tracking (azimuth + elevation angle). According to the lunar ephemeris, the current solar elevation angle is 15°, and the azimuth angle is 60° (0° is due east, increasing clockwise). The crater wall forms a 20° high terrain obstruction at an azimuth angle of 120°. The maximum power generation capacity of the solar panels P_max=200W (when perpendicular to sunlight), and the actual power P_actual = P_max * cos(α), where α is the angle between the sunlight and the normal to the solar panel. The current orientation of the solar panels: azimuth angle 90°, elevation angle 30°.", + "question": "Calculate the actual power generation of the solar panels (considering the impact of terrain obstruction).", + "answer": "0W" + }, + { + "id": 650, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. Analysis of the soil characteristics in this area shows: the surface layer 0-30cm consists of loose fine particles (viscosity coefficient η=0.8 Pa·s), and 30-50cm contains high-hardness basalt fragments (Mohs hardness 6.5). The probe is equipped with three sampling tools: a rotary impact drill (suitable for hardness >5), a helical core sampler (suitable for viscosity <1.2 Pa·s), and an electric shovel (only suitable for the top 20cm). The sampling system has a maximum output power of 150W, with the rotary impact drill consuming 120W, the helical core sampler 80W, and the electric shovel 40W. The current remaining energy can support high-power tools to work continuously for 15 minutes or low-power tools for 30 minutes.", + "question": "If it is necessary to obtain both surface fine particles and deep basalt samples in a single operation, please calculate the optimal tool combination and the maximum allowable sampling time, and explain the basis for your choice.", + "answer": "Choose the helical core sampler + electric shovel combination, with a maximum allowable sampling time of 18 minutes. Basis: 1) The helical core sampler meets the hardness requirements for deep basalt and has lower power consumption than the rotary impact drill; 2) The electric shovel is suitable for collecting surface fine particles; 3) The total power consumption of the combination is 120W (80+40), and the remaining energy is 150W*15min=2250J, which can support 2250/120=18.75 minutes, rounded to 18 minutes." + }, + { + "id": 651, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. The characteristics of the soil in this area are as follows: average hardness of 3.5 Mohs (similar to feldspar), viscosity coefficient of 1200 Pa·s, and volatile content of about 0.8 wt%. There are three sampling tool parameters: A-type rotary drill (suitable for hardness > 4 Mohs, power consumption 200W), B-type vibrating grab (suitable for viscosity < 1000 Pa·s, power consumption 150W), and C-type scraper (suitable for volatile content > 0.5 wt%, power consumption 80W). The total power budget for the sampling system must not exceed 180W.", + "question": "Based on the given soil characteristics and tool parameters, select the optimal tool combination that meets the power budget and can complete the sampling, and explain the reasons.", + "answer": "Choose the C-type scraper. Reasons: 1) The volatile content of the lunar soil, 0.8 wt%, meets the applicability condition of the C-type tool; 2) The hardness of 3.5 Mohs is below the threshold of the A-type tool; 3) The viscosity of 1200 Pa·s exceeds the upper limit of the B-type tool; 4) The power consumption of the C-type tool, 80W, fits within the total power budget." + }, + { + "id": 652, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container transfer must be inspected. Known conditions: 1) The pressure inside the sealed cabin should be maintained at 10^−5 Pa±5%; 2) The temperature sensor shows -60℃ (meets the standard of -65℃~-55℃); 3) The RFID read success rate must be ≥99% (current statistics 98.7%); 4) The mechanical arm docking accuracy requirement is ±2mm (measured error 1.8mm). There are 25 minutes left before the communication window closes, and each item re-inspection takes 5 minutes.", + "question": "Determine whether the current conditions meet the launch criteria? If not, point out the project that needs to be re-inspected with the highest priority and the basis for the decision.", + "answer": "The launch criteria are not met. The RFID read success rate should be re-inspected with the highest priority. Basis: 1) The current RFID read success rate of 98.7% is slightly below the standard; 2) All other parameters are within the tolerance range; 3) 25 minutes allow for 5 re-inspections but only the most critical item needs to be addressed; 4) The RFID is crucial for sample traceability and cannot be compromised." + }, + { + "id": 653, + "scenario_code": "1.2", + "instruction": " Deploy a lunar-based telescope array unit on the edge of the Shackleton crater at the lunar south pole. The device consists of a main mirror module (120kg), a support structure (80kg), a power module (50kg), and a communication module (30kg), with a total mass of 280kg. Due to the maximum load capacity of the lunar surface transport vehicle being 150kg, two trips are required. The installation sequence must meet the following requirements: 1) The support structure must be installed before the main mirror module; 2) The power module must be installed before the communication module; 3) The total mass of components transported each time must not exceed 150kg. The lunar gravity is 1/6 of Earth's, and the motor power P (W) of the transport vehicle = 0.5 * load mass (kg).", + "question": "Please design a transportation and installation plan that meets all the constraints, and calculate the motor power requirement of the transport vehicle during the second trip.", + "answer": "First trip: support structure (80kg) + power module (50kg), total mass 130kg; second trip: main mirror module (120kg) + communication module (30kg), total mass 150kg. Motor power P for the second trip = 0.5 * 150 = 75W." + }, + { + "id": 654, + "scenario_code": "1.4", + "instruction": " A lunar surface energy grid needs to power three devices simultaneously: a drilling machine (peak power 300W, priority 1), a spectrometer (200W, priority 2), and a weather station (100W, priority 3). The energy grid has a maximum output power of 400W and uses a dynamic priority scheduling algorithm: when total demand exceeds 400W, power is allocated according to priority, and devices of the same priority share the remaining power proportionally. Currently, the weather station is performing a critical data collection task and its priority is temporarily increased to level 2.", + "question": "Calculate the actual power received by each device under the current power distribution plan.", + "answer": "The drilling machine receives 300W (fully met at priority 1), leaving 100W to be shared by the spectrometer and the weather station (both at priority 2) according to their original power ratios: the spectrometer receives 100*(200/(200+100))=66.67W, and the weather station receives 100*(100/(200+100))=33.33W." + }, + { + "id": 655, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is conducting scientific exploration on the lunar surface. Currently located at coordinate point A(10,20), it needs to reach target point B(50,60) to perform sampling. It is known that: 1) The lunar surface terrain is divided into two types: flat areas (energy consumption coefficient 0.1 Wh/m) and loose lunar soil areas (energy consumption coefficient 0.3 Wh/m); 2) The straight path AB crosses 30m of loose lunar soil and 40m of flat areas; 3) Another zigzag path ACB (A→C(30,30)→B) is entirely in flat areas, with a total length of 80m; 4) The current remaining battery energy is 25Wh.", + "question": "Please calculate the total energy consumption for both paths and determine whether it can reach the target point through the zigzag path ACB under the current remaining energy.", + "answer": "Total energy consumption for path AB = 30*0.3 + 40*0.1 = 13 Wh; Total energy consumption for path ACB = 80*0.1 = 8 Wh. Remaining energy 25Wh > 8Wh, it can reach the target point through the zigzag path ACB." + }, + { + "id": 656, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S). The ground station is located in Kashgar, China (76°E, 39.5°N), using the X-band (8.4GHz) to establish a communication link with the Queqiao-2 relay satellite. Known: 1) Queqiao-2 operates in the Earth-Moon L2 Halo orbit, with an average altitude of about 8000km above the lunar surface; 2) The Moon's rotational period is synchronized with its orbital period; 3) The X-band free space path loss formula is L = 20 * log10(d) + 20 * log10(f) + 92.45, where d is the distance (km), and f is the frequency (GHz); 4) The current lunar occultation angle is 12°.", + "question": "Calculate the total path loss of the ground station-Queqiao-2 lander communication link at the current moment (considering only free space loss), and determine whether it meets the minimum receiving power threshold of -110dBm (assuming the transmission power is 20W, and the total antenna gain is 60dB).", + "answer": "Total path loss = 20 * log10(384400) + 20 * log10(8.4) + 92.45 ≈ 198.5dB; Receiving power = 20W (43dBm) + 60dB - 198.5dB = -95.5dBm > -110dBm, meeting the requirement." + }, + { + "id": 657, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to conduct sampling in an area on the far side of the Moon rich in KREEP (potassium, rare earth elements, and phosphorus) rocks. The hardness of the lunar regolith in this area is moderate (compressive strength about 15MPa), with low viscosity and high volatile content. There are three sampling tools available: 1) Rotary percussion drill (suitable for rocks with hardness >20MPa); 2) Electric grab (suitable for loose lunar regolith and soft rocks <10MPa); 3) Adaptive scraper (suitable for materials with medium hardness 5-15MPa, designed to prevent the escape of volatiles). The maximum power consumption limit for the sampling system is 200W, and a single sampling must be completed within 10 minutes.", + "question": "Based on the characteristics of the lunar regolith and the constraints, which sampling tool should be chosen? Provide specific reasons for your choice.", + "answer": "The adaptive scraper should be chosen. Reasons: 1) The hardness of the lunar regolith at 15MPa is within its applicable range; 2) The design to prevent the escape of volatiles meets the requirement for high volatile content; 3) Other tools either do not match the hardness range (the drill requires >20MPa) or cannot handle medium hardness (the grab is only suitable for <10MPa)." + }, + { + "id": 658, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container transfer must be verified. The container weighs 2kg, the RFID tag verification time is 30 seconds, and the pressure change rate for the seal integrity test must be ≤0.1Pa/s (the actual measured value is 0.08Pa/s). The docking mechanism positioning accuracy is ±3mm, while the container latch tolerance is ±5mm. The remaining launch window for the ascent vehicle is 8 minutes, and the transfer process time formula is T=10+2*m+Δt (m is the mass in kg, Δt is the additional inspection time).", + "question": "Can the safe transfer be completed under the current conditions? List the calculation process for the key verification parameters.", + "answer": "The transfer can be completed. Calculation: 1) Process time = 10 + 2*2 + 30/60 = 14.5 minutes < 8-minute window; 2) Pressure change rate 0.08 < 0.1 meets the standard; 3) Positioning error 3mm < 5mm tolerance. All parameters meet the requirements." + }, + { + "id": 659, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (longitude 177.6°E, latitude 45.5°S). The ground station is located in Kashgar, China (longitude 76.0°E, latitude 39.5°N), and uses the X-band (8.4GHz) to establish a communication link with the Queqiao-2 relay satellite. It is known that: 1) Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, with an average altitude of 8000km above the lunar surface; 2) The lunar radius is 1737km; 3) At the current moment, the Moon's rotation causes the geometric elevation angle between the lander and Queqiao-2 to be 12°; 4) The free space path loss formula is L = 20 * log10(4 * π * d / λ), where λ=0.0357m.", + "question": "Calculate the one-way space path loss (dB) of the ground station-Queqiao-2-lander link under the current state, and first verify whether the line of sight for communication is clear.", + "answer": "The line of sight for communication is clear (lunar surface elevation angle 12° > 0°). Path loss calculation steps: 1) The slant distance from Queqiao to the lander d = sqrt((1737+8000)^2 - (1737*cos12°)^2) - 1737*sin12° ≈ 8235km; 2) L = 20*log10(4*π*8.235e6/0.0357) ≈ 220.3dB" + }, + { + "id": 660, + "scenario_code": "3.1", + "instruction": " Chang'e-6 lander is located on the edge of an impact crater at 23.5°E and 12.8°N on the near side of the Moon. Its solar panels use two-dimensional tracking (azimuth + elevation). The current lunar time is 10:00 AM on the third lunar day (sun elevation angle 35°). According to the three-dimensional terrain model analysis, the western crater will cause shading in the next 2.5 hours. Known: 1) The standard output power of a single panel under full sunlight is 180W; 2) The pitch angle tracking error will cause the power to attenuate according to cos(error angle); 3) The current azimuth deviation is 8°. The mission plan needs to ensure that the cumulative power generation before the end of the lunar day is no less than 2.5kWh.", + "question": "If the current azimuth deviation is maintained, calculate the actual total power generation in the next 2.5 hours (considering terrain shading and tracking errors), and determine whether it meets the energy requirements.", + "answer": "Actual power generation = 180W * cos(8°) * 2.5h * (1 - 0.5) = 180 * 0.9903 * 2.5 * 0.5 ≈ 222.8Wh < 2.5kWh, does not meet the requirement." + }, + { + "id": 661, + "scenario_code": "3.6", + "instruction": " The Chang'e-7 polar lander needs to maintain the temperature of the electronics compartment at ≥-40℃ during the -180℃ lunar night. The insulation system includes: 1) RHU isotope heat source (constant output 15W); 2) Electric heater (maximum power 30W); 3) Multilayer insulation material (equivalent thermal resistance 0.8K/W). The heat resistance of the equipment compartment to the lunar soil is 1.2K/W, and the heat generation power of the internal components is 5W. The lunar night lasts 350 hours, and the available battery energy is 3kWh.", + "question": "Calculate the minimum constant power the electric heater needs to provide to meet the temperature control requirements, and verify whether the battery energy is sufficient to support the entire lunar night.", + "answer": "Total heat load Q = (T_keep - T_env)/R_total = (-40 - (-180))/(0.8+1.2) =70W; Required electric heating power P_heater = Q - P_RHU - P_device =70-15-5=50W >30W is not feasible. When the actual minimum heating power is 30W, Q_actual=15+30+5=50W→ΔT=50*(0.8+1.2)=100K→T_keep=-180+100=-80℃<-40℃ does not meet the requirement. Battery energy 3000Wh/350h≈8.57W<30W, energy is insufficient." + }, + { + "id": 662, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently conducting exploration tasks near the Von Kármán crater, with its power system using a combination of solar panels and lithium-ion batteries. The current battery charge is 80% (total capacity 4000 Wh), and there are 3 hours until sunset. According to terrain data, there are two optional paths ahead:\n- Path A: straight-line distance of 800 meters, average slope of 8°, surface is loose lunar soil (rolling resistance coefficient 0.25)\n- Path B: detour distance of 1200 meters, average slope of 3°, surface is compacted lunar soil (rolling resistance coefficient 0.15)\nIt is known that the lunar rover's movement energy consumption model is: E = (0.2 * d + 5 * h) * k, where d is the horizontal distance (meters), h is the elevation change (meters), and k is the rolling resistance coefficient. The basic system power consumption of the lunar rover is 50 W.", + "question": "To ensure the lunar rover returns to the base before sunset and retains at least 20% of the battery as an emergency reserve, which path should be chosen? Please calculate the total energy consumption for both paths and explain the basis for your choice.", + "answer": "Energy consumption calculation for Path A: elevation change h = 800 * sin(8°) ≈ 111.2 meters, E_A = (0.2*800 + 5*111.2)*0.25 + 50*3 = (160+556)*0.25 +150 =179 +150=329 Wh; Energy consumption calculation for Path B: h =1200*sin(3°)≈62.8 meters, E_B =(0.2*1200+5*62.8)*0.15+150=(240+314)*0.15+150≈83.1+150=233.1 Wh. Available power = 80%*4000 -20%*4000=2400 Wh. Choose Path B because its total energy consumption 233.1 Wh <329 Wh and is below the upper limit of available power." + }, + { + "id": 663, + "scenario_code": "2.7", + "instruction": " The lunar orbiter has detected an upcoming solar proton event (SPE), with radiation intensity expected to reach dangerous levels in 45 minutes. The lunar rover located in the South Pole-Aitken Basin is currently in a communication blackout period (the next relay satellite will pass overhead in 78 minutes), and its autonomous hazard avoidance system needs to execute the following sequence of operations:\n1. Travel 300 meters to the nearest permanent shadow area shelter\n2. Deploy the radiation shield, which takes 5 minutes\n3. Switch to safe mode, which takes 2 minutes\nIt is known that the maximum safe travel speed of the lunar rover is 10 cm/s, and all operations must be completed before the radiation reaches the threshold.", + "question": "Determine whether the lunar rover can complete the hazard avoidance in the current situation. If not, which phase's time should be prioritized for compression (while maintaining at least 1 minute for the physical limit of deploying the shield)?", + "answer": "Travel time = 300/(0.1*60) = 50 minutes, total time required = 50 + 5 + 2 = 57 minutes > 45 minutes remaining time. Time must be compressed: the shield deployment can be shortened to 1 minute (saving 4 minutes), switching to safe mode needs to be shortened to 45-50-1=-6 minutes → not feasible; therefore, the only option is to increase the travel speed to 300/((45-5-2)*60) ≈ 13 cm/s (exceeding the safe speed) or accept some radiation exposure. The standard answer is to prioritize compressing the shield deployment to 1 minute (at which point the total time is 53 minutes, still insufficient, but the best adjustment)." + }, + { + "id": 664, + "scenario_code": "3.1", + "instruction": " The Chang'e-5 lander is located near Mons Rümker at 43.06°N, 51.92°E on the lunar near side. The solar elevation angle in this area varies from 5° to 35° during the lunar day, and the solar panels use two-dimensional tracking (azimuth + elevation). Known data: 1) Each solar panel has an area of 2 square meters, with a photovoltaic conversion efficiency of 28%; 2) The solar constant at lunar noon is 1361 W/m²; 3) Terrain obstruction reduces the effective power generation time by 30% daily; 4) An azimuth tracking error of ±3° reduces power generation by 2%. The mission requires a daily average power generation of no less than 4 kWh.", + "question": "If the current solar elevation angle is 20° and there is the maximum azimuth tracking error, calculate the real-time power generation of a single solar panel (unit: watts) and determine whether it meets the daily average power generation requirement.", + "answer": "Real-time power P = 1361 * sin(20°) * 2 * 0.28 * (1-0.02) ≈ 219.5 W; daily average power generation E = 219.5 * (24*0.7) / 1000 ≈ 3.69 kWh < 4 kWh, does not meet the requirement" + }, + { + "id": 665, + "scenario_code": "3.6", + "instruction": " The Yutu-2 rover needs to maintain a temperature of above -40°C in the equipment compartment during the lunar night. It is known that: 1) The lunar night lasts 14 Earth days; 2) The heat dissipation power of the equipment compartment is constantly 8W; 3) An isotope heat source (Pu-238) provides a constant thermal power of 25W; 4) The equivalent thermal resistance of multi-layer insulation material R=0.5 K/W; 5) The external environmental temperature is -180°C. The electric heating system is a backup plan, requiring an additional consumption of 0.2Wh of energy for every 1°C increase in temperature.", + "question": "Calculate the steady-state temperature of the equipment compartment (unit: °C) relying solely on the isotope heat source, and determine whether the electric heating system needs to be activated to maintain the target temperature.", + "answer": "The steady-state temperature T = -180 + (25-8)*0.5 ≈ -171.5°C < -40°C, the electric heating system needs to be activated; the total heating power Q required to maintain -40°C = [(-40)-(-171.5)]/0.5 = 263W >25W, continuous electrical energy consumption is required." + }, + { + "id": 666, + "scenario_code": "3.8", + "instruction": " The relay satellite mission of Chang'e-4 has a cycle of 24 hours, with energy consumption including: 1) X-band communication: transmission power consumption 80W (3 times a day, each time 15 minutes); 2) Payload operation: 10W (6 hours continuously); 3) Platform equipment: basic power consumption 5W (24 hours continuously). The total capacity of the lithium-ion battery pack is 200Wh, with a discharge depth limit of 80%. The solar array can provide an average power of 120W during the illumination period (60% of the orbital period).", + "question": "Calculate the energy deficit or surplus in a complete mission cycle (unit: Wh), and explain whether the mission planning needs to be adjusted.", + "answer": "Total energy consumption E_consumed = 80*(3*0.25) + 10*6 + 5*24 = 300 Wh; Total energy production E_generated = 120*(24*0.6) =1728 Wh; The battery needs to provide E_battery =300-1728=-1428 Wh (surplus), no adjustment needed." + }, + { + "id": 667, + "scenario_code": "3.6", + "instruction": " The Yutu-2 rover is about to enter the lunar night (-180°C), and the X-band communication module needs to be kept warm: 1) The operating temperature range of the module is -40°C~+85°C; 2) Use a 10mm layer of aerogel (thermal conductivity 0.015W/mK) and a 5W isotopic heat source for joint thermal insulation; 3) The surface area of the module is 0.2m², and the heat dissipation power is 3W; 4) The lunar soil environment temperature is stable at -180°C.", + "question": "Calculate whether the internal temperature of the module meets the operating requirements under steady state? (Hint: Thermal balance formula Q_out = k*A*(T_in-T_out)/d, where k is the thermal conductivity, d is the thickness.)", + "answer": "It meets the requirements. Calculation steps: 1) Total heat supply = 5 + 3 = 8W; 2) Q_out = 0.015 * 0.2 * (T_in + 180) / 0.01 = 8 → T_in = -180 + 8 * 0.01 / (0.015 * 0.2) = -93.3°C > -40°C lower limit" + }, + { + "id": 668, + "scenario_code": "3.8", + "instruction": " In the Chang'e-6 sample return mission: 1) The lunar surface operation cycle is 48 hours, with energy budget allocation: 120Wh for the sampling robotic arm, 300Wh for the drilling system, 80Wh for scientific payloads, 200Wh for data transmission, and 150Wh for the thermal control system; 2) During actual execution, the drilling time was extended by 30%, leading to a total energy overdraw of 15%; 3) The remaining power can only support 70% of the originally planned data transmission task.", + "question": "If all scientific data must be transmitted, how should the energy consumption of other subsystems be adjusted? (Provide the specific energy-saving ratio calculation process.)", + "answer": "An additional 60Wh of energy savings is required. Calculation steps: 1) Original transmission requirement was 200Wh, now lacking 30% which is 60Wh; 2) (120 + 80 + 150) * x = 60 → x = 17.14%, each subsystem uniformly reduces energy consumption by 17.14%." + }, + { + "id": 669, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the moon, located at coordinate point A (177.6°E, 45.5°S). The mission center has planned a route to scientific target point B (177.8°E, 45.3°S). It is known that: 1) The straight-line distance between the two points is 800 meters; 2) The average driving speed of the lunar rover is 0.05 m/s; 3) The wheel-soil mechanics model shows that for every 1° increase in slope, the energy consumption coefficient increases by 0.015; 4) The average slope of the current path is 5°, and the basic energy consumption model is E = 0.1 * d + 3 (d is the driving distance, in meters); 5) The remaining battery energy is 1200 J.", + "question": "If the straight-line path to target point B is chosen, calculate the remaining battery energy after completing this segment of the journey (considering the impact of the slope on energy consumption).", + "answer": "First, calculate the impact of the slope: the increase in the energy consumption coefficient is 0.015 * 5 = 0.075, and the corrected energy consumption model is E = (0.1 + 0.075) * d + 3 = 0.175 * d + 3. The total energy consumption for driving 800 meters is E = 0.175 * 800 + 3 = 143 J. The remaining energy is 1200 - 143 = 1057 J." + }, + { + "id": 670, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 rover is performing exploration tasks in the lunar south pole, and its solar panels use a two-dimensional tracking algorithm. During the current lunar day, the solar elevation angle is 15 degrees, and the azimuth angle is 45 degrees (0 degrees is due north). There is a 30-meter-high crater 100 meters in front of the rover, with sunlight shining from behind the crater. The theoretical maximum power generation of the solar panels is 200W (when unobstructed), and the actual measured power generation is 120W. Known: The power generation attenuation is linearly related to the obstruction area (obstruction area ratio = 1 - actual power / theoretical power).", + "question": "Calculate the current obstruction area ratio of the solar panels by the crater, and determine whether to activate the three-dimensional tracking algorithm to avoid obstruction (three-dimensional tracking can increase power generation efficiency by 10% but consumes an additional 5W of power).", + "answer": "Obstruction area ratio = 1 - 120/200 = 0.4. Three-dimensional tracking increases power generation = 200*0.1 = 20W, net gain = 20 - 5 = 15W. Since the current power loss is 80W > 15W, the three-dimensional tracking should be activated." + }, + { + "id": 671, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander, while executing a detection mission at the edge of the Shackleton crater, suddenly receives a solar proton event warning (expected to arrive in 30 minutes). The lander needs to transfer to the nearest permanent shadow area for shelter within 15 minutes (coordinate point C, 300 meters away). There are two paths to the shelter: Path A is a straight line but requires crossing a known loose lunar dust area (reducing passability by 40%), Path B detours through a hard basaltic rock belt (adding 80 meters to the distance). The maximum safe speed of the lander is 0.2m/s, and the speed in loose terrain must be reduced to 60%. In emergency mode, communication can only be maintained for 20 minutes.", + "question": "Analyze whether the two paths meet the time and communication constraints. Which path should be chosen if any meet the requirements, or what alternative actions should be taken if neither does.", + "answer": "Time for Path A = 300/(0.2*0.6)/60≈41.67 minutes, exceeding the limit; Time for Path B = (300+80)/0.2/60≈31.67 minutes, still exceeding the limit. Since neither can meet the 15-minute requirement, emergency protocols should be initiated to shorten the safe distance or increase the speed limit." + }, + { + "id": 672, + "scenario_code": "2.10", + "instruction": " The lunar rover needs to perform centimeter-level close-up observations of a special rock outcrop with a diameter of 3 meters. The visual navigation system has an accuracy of ±5cm (3σ), the laser rangefinder has a frequency of 10Hz and an accuracy of ±1cm. The rock surface albedo is 20%, and the minimum lighting requirement is 100lux. The current solar elevation angle is 30°, and the lunar surface reflectance model is: light intensity = 1370*sin(elevation angle)*surface albedo (lux). The minimum impulse of the attitude control thrusters is 0.01N·s, and the vehicle's moment of inertia is 2kg·m².", + "question": "Calculate whether the current lighting meets the observation requirements? If a position adjustment is needed, find the minimum attitude adjustment angle (deg) to align the rangefinder's line of sight with the center of the rock.", + "answer": "Current lighting = 1370*sin(30°)*0.2 = 137lux > 100lux, meeting the requirement; minimum adjustment angle = arctan(1cm/150cm) ≈ 0.38°, corresponding angular momentum = 2kg·m²*(0.38°*π/180) ≈ 0.013N·s > minimum impulse, so fine adjustment can be performed." + }, + { + "id": 673, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, a temporary energy-sharing network needs to be established. There are currently three devices: A (seismometer, peak power requirement 120W), B (magnetometer, peak power 80W), C (heat flow probe, peak power 60W). The maximum output power of the power module is 200W, and 20% redundancy capacity must be reserved to ensure system safety. The priority of the equipment is A > B > C. When all three devices are operating simultaneously:", + "question": "Calculate the actual available power of the power module and determine which devices can run at full power simultaneously.", + "answer": "Actual available power = 200W * (1 - 0.2) = 160W; A(120W) + B(80W) = 200W > 160W, only the highest priority A device (120W < 160W) can be operated." + }, + { + "id": 674, + "scenario_code": "1.8", + "instruction": " When deploying a lunar-based telescope, it is observed that the intensity of local magnetic field interference is related to the elevation angle of the installation platform as follows: B(θ) = 50 + 10*sin(θ) μT (where θ is the angle between the platform and the horizontal plane). Scientific observations require magnetic field fluctuations to be less than ±2μT. The current elevation angle of the platform is 30 degrees, and the adjustment speed is 5 degrees per minute.", + "question": "Calculate the range to which the elevation angle needs to be adjusted to meet the requirements. If adjustments start from the current angle, what is the minimum time required to complete the adjustment process? ", + "answer": "Permissible fluctuation range |10*sinθ| ≤2 → sinθ ≤0.2 → θ ≤11.54°; Adjustment range=30°-11.54°=18.46°; Time=18.46/5≈3.7 minutes" + }, + { + "id": 675, + "scenario_code": "3.1", + "instruction": " Chang'e-6 lander is located at the edge of an impact crater at 23.5°E, 42.8°N on the near side of the Moon, with its solar panels operating in a two-dimensional tracking mode. According to the lunar almanac, the current solar elevation angle during the lunar day is 15°, and the azimuth angle is 45° (with 0° being due north and increasing clockwise). The crater wall forms an obstruction in the azimuth range of 30°-60°, causing a continuous 2-hour loss of effective sunlight exposure each day. It is known that: 1) the peak power of a single solar panel P_max=300W (when perpendicular to sunlight); 2) two-dimensional tracking can make the actual power P=P_max*sin(solar elevation angle); 3) during the lunar day, at least 80W of average power output must be maintained.", + "question": "What is the theoretical average daily power generation without obstruction at the current solar elevation angle? What additional battery capacity is required to compensate for the energy shortfall caused by terrain obstruction? (Assume a lunar day duration of 12 hours.)", + "answer": "Theoretical average daily power generation = 300W * sin(15°) * 12h = 300 * 0.2588 * 12 = 932.4Wh; Terrain obstruction loss = 300W * 0.2588 * 2h = 155.3Wh; Battery capacity required ≥ 155.3Wh / 80% ≈ 194Wh (considering charging and discharging efficiency)." + }, + { + "id": 676, + "scenario_code": "3.6", + "instruction": " The Yutu-2 rover is about to enter the lunar night hibernation phase, and its lithium-ion battery pack needs to maintain a working temperature above -20°C in a -180°C environment. It is known that: 1) the heat capacity of the battery pack C=120kJ/°C; 2) the lunar night lasts 14 Earth days; 3) the thermal conductivity of the insulating material λ=0.02W/(m·K), surface area A=0.5m², thickness d=5cm; 4) the rated heat generation power of the isotope heat source Q_rhp=5W; 5) the efficiency of the electric heater η=90%. The design goal is to control the temperature drop within ΔT≤160°C.", + "question": "Calculate the natural temperature drop rate (°C/h) relying solely on the insulating material. If it is required not to use electric heating throughout the process, how many isotope heat source units must be deployed at least? ", + "answer": "Natural temperature drop rate = λ * A * ΔT / (d * C) = 0.02 * 0.5 * 160 / (0.05 * 120000) = 0.00267°C/s = 9.6°C/h; Total heat generation power required Q_total = λ * A * ΔT / d = 0.02 * 0.5 * 160 / 0.05 = 32W; Number of isotope heat sources required ≥ 32 / 5 ≈ 7 units." + }, + { + "id": 677, + "scenario_code": "3.8", + "instruction": " The scientific exploration mission profile of the Chang'e-7 lander includes: 1) 4 hours of continuous drilling (peak power consumption 150W); 2) 2 hours of spectral analysis (steady-state power consumption 60W); 3) 15 minutes of data transmission once a day (instantaneous power consumption 200W). The energy system configuration: 1) average daily power generation of the solar array is 1200Wh; 2) available battery capacity is 800Wh; 3) equipment standby power consumption is 10W. The mission cycle is 3 Earth days, and the battery must always maintain a residual charge of ≥200Wh as an emergency reserve.", + "question": "Under all energy constraints, how many drilling operations can be scheduled each day for this mission profile? (List key calculation steps.)", + "answer": "Daily available energy = (1200Wh + 800Wh - 200Wh) - 10W * 24h = 1800Wh - 240Wh = 1560Wh; Energy consumption per drilling operation = 150W * 4h + 60W * 2h + 200W * 0.25h = 600 + 120 + 50 = 770Wh; Maximum number of times = int(1560 / 770) = 2 times" + }, + { + "id": 678, + "scenario_code": "1.5", + "instruction": " The Yutu-2 rover needs to remotely control the robotic arm to collect lunar rock samples with a communication delay of 1.3 seconds. The maximum speed at the end of the robotic arm is 0.1m/s, and the control system uses a predictive compensation algorithm: predicted position = current command position + v * Δt * k (k=1.2 is the safety factor). The actual end coordinates of the robotic arm are (2.3, 1.7), and the new target point sent from the ground is (2.6, 1.9).", + "question": "Calculate the Euclidean distance error between the theoretical stop position of the robotic arm when the predictive compensation is effective and the target point.", + "answer": "0.046m" + }, + { + "id": 679, + "scenario_code": "1.8", + "instruction": " When the Chang'e-7 lander deployed the seismometer, it measured the bearing capacity of the lunar soil at the landing site to be 12kPa (safety threshold ≥10kPa). The instrument weighs 8kg, and the total contact area of the tripod is 60cm². Mission requirements: 1) the anti-overturning moment during operation must be ≥15N·m; 2) displacement during a level 4 or lower moonquake must be ≤5mm. The maximum horizontal acceleration during a moonquake is known to be 0.2m/s², and the height of the instrument's center of gravity is 0.5m.", + "question": "Verify whether the current deployment plan meets both the bearing capacity and anti-overturning requirements (take g=1.62m/s²), and if not, which parameter needs to be adjusted? ", + "answer": "Does not meet the anti-overturning requirement, need to increase the contact area or lower the center of gravity height" + }, + { + "id": 680, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover continuously transmitted scientific data during the lunar day when a sudden solar proton event caused a direct Earth communication interruption. The rover's storage buffer capacity is 8GB, with 3.2GB of data currently stored, and the data generation rate is 12MB/minute. The relay satellite needs 6 minutes to switch to the backup Ka-band link, which has a bandwidth of 4Mbps (actual effective transmission rate of 3.2Mbps).", + "question": "Calculate the amount of new data generated (in MB) from the communication interruption to the backup link being ready, and determine whether data compression needs to be initiated (the cache margin warning threshold is 2GB).", + "answer": "New data volume = 12MB/min * 6min = 72MB; Remaining cache = 8GB - (3.2GB + 0.072GB) = 4.728GB >2GB, no need to start compression." + }, + { + "id": 681, + "scenario_code": "3.4", + "instruction": " During the lunar day, the Chang'e-7 lander needs to perform three tasks simultaneously: ① Drilling and sampling (peak power consumption 150W/lasting 2 hours) ② Data transmission (peak 80W/lasting 1.5 hours) ③ Spectral analysis (peak 60W/lasting 3 hours). The system's maximum available instantaneous power is 200W, and the battery can provide an additional 50W buffer power. The task priorities are ① > ② > ③, and spectral analysis can be performed in segments.", + "question": "Design a load scheduling plan within 2 hours that meets all constraints (specify the exact start time and duration for each task)?", + "answer": "0-2h execute drilling and sampling (150W), 0-1.5h execute data transmission (80W), 1.5-2h execute spectral analysis (60W)." + }, + { + "id": 682, + "scenario_code": "3.6", + "instruction": " Before entering the lunar night, the lunar rover needs to maintain the battery temperature no lower than -40°C. Given: ① Battery mass 10kg, specific heat capacity 800J/(kg·K) ② Current temperature 20°C ③ Lunar night lasts 336 hours ④ Thermal loss rate of insulation layer 0.5W ⑤ Electric heater efficiency 90%. An isotope heat source can provide a constant 1W of heat, and the rest needs to be supplemented by electric heating (battery discharge efficiency 95%).", + "question": "Calculate the minimum battery capacity required to maintain the battery temperature (unit: Wh), assuming full charge at the beginning and no other power-consuming devices.", + "answer": "158.7Wh" + }, + { + "id": 683, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (longitude 180°E, latitude 45°S). The ground station is located in Kashgar, China (longitude 76°E, latitude 39°N), using the X-band (8.4 GHz) for communication. Given the average Earth-Moon distance of 384,400 km, the lunar rotation period of 27.3 days, and the Earth's rotation period of 24 hours. At the current moment, the angle between the line connecting the ground station and the lander and the lunar surface tangent is 5°, and the free space path loss formula for the X-band is L = 20 * log10(d) + 20 * log10(f) + 92.45 (d: km, f: GHz).", + "question": "Calculate the free space path loss value of the Earth-Moon communication link at the current moment (保留两位小数), and determine whether the Queqiao relay satellite needs to be activated (the minimum elevation angle requirement for direct communication is ≥7°).", + "answer": "Path loss L = 20 * log10(384400) + 20 * log10(8.4) + 92.45 ≈ 207.96 dB; Since the elevation angle 5°<7°, the Queqiao relay satellite needs to be activated." + }, + { + "id": 684, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the Moon, located at coordinate point A (10°N, 120°E). The mission planning system requires it to reach scientific target point B (10.5°N, 120.3°E) within 3 hours, during which it must cross a soft lunar soil area (wheel-soil mechanics coefficient μ=0.3). It is known that: 1) The straight-line distance AB is 15km; 2) The average speed of the lunar rover v=0.1m/s (on soft terrain); 3) The energy consumption model is E=0.05*d + 2*t (d is the driving distance/km, t is time/h); 4) The remaining battery power only supports 80Wh consumption.", + "question": "If the straight path AB is chosen, calculate the total energy consumption E and determine whether it meets the power constraint? If not, propose a feasible path optimization strategy (the theoretical basis must be explained).", + "answer": "Total energy consumption E=0.05*15 + 2*3=6.75+6=12.75Wh <80Wh, meeting the power constraint. No need to optimize the path." + }, + { + "id": 685, + "scenario_code": "2.2", + "instruction": " The Chang'e-7 lander is conducting exploration at the edge of the Shackleton crater in a permanently shadowed area. The navigation system uses a multi-sensor fusion solution: 1) IMU drift error is 1m/min; 2) Visual odometry (VO) fails under no-light conditions; 3) LiDAR SLAM positioning accuracy is ±0.5m/100m; 4) Starlight sensor provides absolute position correction every 5 minutes (error ±2m). The lander needs to move to a sampling point 200m away within 30 minutes.", + "question": "Calculate the maximum cumulative positioning error when relying solely on the IMU, and propose at least two sensor combination strategies to reduce the final positioning error.", + "answer": "Maximum error=1m/min*30min=30m. Strategy 1: IMU+LiDAR SLAM (combined error=0.5/100*200=±1m); Strategy 2: IMU+Starlight sensor (corrected to ±2m every 5 minutes)." + }, + { + "id": 686, + "scenario_code": "1.5", + "instruction": " When controlling a lunar rover for rock sampling from the ground control center via remote operation, the one-way communication delay between Earth and Moon is known to be 1.28 seconds. The rover is currently moving in a straight line towards the target point at a speed of 0.2 m/s, and the control system uses a predictive algorithm to compensate for the delay: lead time = delay time * speed * safety factor 1.5. There is a crater with a diameter of 0.8 meters in the target area, and the emergency braking distance is 0.3 meters.", + "question": "When the rover is 2 meters away from the edge of the crater, a stop command is sent. Determine whether there will be any danger and calculate the minimum distance between the final stopping position and the edge of the crater.", + "answer": "When the command takes effect, the vehicle has traveled a distance of 1.28 * 2 * 0.2 * 1.5 = 0.768 meters; the remaining distance is 2 - 0.768 = 1.232 meters > braking distance of 0.3 meters. After safely stopping, the distance from the edge of the crater is 1.232 - 0.3 = 0.932 meters." + }, + { + "id": 687, + "scenario_code": "3.1", + "instruction": " Chang'e-7 rover is conducting exploration tasks in the lunar south pole region, which has complex terrain and permanent shadow areas. The rover is equipped with a dual-axis adjustable solar panel with a maximum tracking efficiency of 92%. According to the lunar calendar, the current solar elevation angle is 15 degrees, and the azimuth change rate is 0.25 degrees per minute. There is a 1.5-meter-high rock 2 meters ahead that will cause a 30-minute shadow. The standard output power of the solar panel is 200W (under unobstructed conditions).", + "question": "If the optimal two-dimensional tracking strategy is adopted and other obstructions are not considered, what is the actual power generation when the rover is in the shadow of the rock? ", + "answer": "0W" + }, + { + "id": 688, + "scenario_code": "3.4", + "instruction": " Yutu-2 needs to perform the following tasks during the lunar day: ① Continuous operation of the X-ray spectrometer (power consumption 25W) ② Sampling by the robotic arm (instantaneous peak 120W per time, each lasting 5 minutes) ③ Data transmission (instantaneous power consumption 80W, each 15 minutes). The power system has a maximum output capacity of 150W, and the lithium-ion battery pack can provide an additional 50W buffer power, but it will accelerate aging. The remaining lunar day time is 3 hours.", + "question": "If it is required to prioritize the continuous operation of the spectrometer and the battery buffer is used no more than twice, how should the sampling and transmission sequence be arranged? Provide the total time required for a feasible solution.", + "answer": "First perform 1 sampling + 1 transmission (20 minutes), or first perform 2 samplings (10 minutes)." + }, + { + "id": 689, + "scenario_code": "3.6", + "instruction": " The lunar rover enters the lunar night phase, and it needs to maintain a cabin temperature above -40°C. The total heat generation of electronic equipment is 8W, and the equivalent thermal resistance of the multi-layer thermal insulation material is 4°C/W. The isotope heat source can provide a constant power of 5W, and the electric heater's power is adjustable (maximum 20W). Given that the lunar night environmental temperature is -180°C, the thermal balance formula is: maintenance temperature = environmental temperature + (total heating power - equipment heat generation) * thermal resistance.", + "question": "If the cabin temperature needs to be maintained at -35°C and the energy consumption minimized, how much power should the electric heater be set to? ", + "answer": "7.75W" + }, + { + "id": 690, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks in the Von Kármán crater on the far side of the moon. It is currently at coordinate point A (10°S, 150°E) and needs to reach scientific target point B (12°S, 152°E). According to the digital elevation model provided by the orbiter, there are three optional paths between the two points:\n1. Path 1: straight-line distance of 3.2km, average slope of 8°, surface is loose lunar soil (rolling resistance coefficient 0.25)\n2. Path 2: detour distance of 4.1km, average slope of 3°, surface is hardened lava (rolling resistance coefficient 0.15)\n3. Path 3: distance of 5.6km, average slope of 1°, passing through a permanently shadowed area requiring the heater to be turned on (additional power consumption 5W).\nGiven the parameters of the lunar rover's movement system: mass 140kg, motor efficiency 85%, battery capacity 200Wh, current remaining power 180Wh, base power consumption for movement 20W, constant speed 0.05m/s.", + "question": "If it is required to retain at least 30Wh of emergency power upon arrival, which path can meet the energy constraint? Please calculate the total energy consumption for each path and explain the basis for your choice.", + "answer": "Energy consumption for Path 1: time = 3200/0.05 = 64000s ≈ 17.78h, movement power consumption = 140*9.8*0.25*0.05/0.85 + 20 ≈ 44.18W, total energy consumption = 44.18*17.78 ≈ 785Wh > 150Wh available; Energy consumption for Path 2: time = 4100/0.05 = 82000s ≈ 22.78h, movement power consumption = 140*9.8*0.15*0.05/0.85 + 20 ≈ 32.12W, total energy consumption = 32.12*22.78 ≈ 732Wh > 150Wh; Energy consumption for Path 3: time = 5600/0.05 = 112000s ≈ 31.11h, total power consumption = (140*9.8*0.15*0.05/0.85) + 20 + 5 ≈ 37.12W, total energy consumption = 37.12*31.11 ≈ 1155Wh > 150Wh. Conclusion: None of the three paths can meet the energy constraint." + }, + { + "id": 691, + "scenario_code": "3.4", + "instruction": " Yutu-2 is simultaneously performing three tasks on the lunar surface: 1) X-band communication (peak power consumption 50W, lasting 2 hours); 2) probe-based lunar soil temperature measurement (peak power consumption 15W, lasting 4 hours); 3) panoramic camera photography (peak power consumption 30W, lasting 1 hour). The energy system limits the instantaneous total power consumption to no more than 60W, and the current available battery capacity is 300Wh. The priority order of the tasks is: communication > temperature measurement > photography.", + "question": "Design a reasonable task scheduling plan to ensure all tasks are completed without triggering overcurrent protection, and calculate the final remaining power.", + "answer": "Scheduling plan: First execute communication for 2h (50W) + temperature measurement for 1h (10W), then execute temperature measurement for 3h (15W) + photography for 1h (30W). Total energy consumption = 50*2 + 10*1 + 15*3 + 30*1 = 100 + 10 + 45 + 30 = 185Wh, remaining power = 300 - 185 = 115Wh" + }, + { + "id": 692, + "scenario_code": "3.6", + "instruction": " The lunar rover enters the lunar night phase (-180°C), and it is necessary to keep the core electronic compartment warm. Given: 1) The surface area of the compartment is 2m²; 2) A 10cm thick aerogel insulation layer (thermal conductivity 0.02 W/m·K) is used; 3) The temperature inside the compartment needs to be maintained above -20°C; 4) The rated power of the isotope heat source is 5W. The heat generation power of the electronic compartment is constant at 3W, and the heat exchange formula with the outside world is Q = k*A*(T_in - T_out)/d, where k is the thermal conductivity, A is the area, and d is the thickness.", + "question": "Verify whether the current insulation plan can keep the internal temperature stable above -20°C? If not, how much additional heating power is needed at least to meet the requirement? ", + "answer": "Heat loss Q = 0.02*2*(-20-(-180))/0.1 = 64W; Total heat required 64-3=61W >5W, not satisfied. Additional power needed ≥61-5=56W" + }, + { + "id": 693, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. The characteristics of the lunar soil in this area are as follows: medium hardness (Mohs hardness 4-5), low viscosity, and volatile content of about 120ppm. There are three sampling tools available: 1) A diamond-coated rotary drill bit (suitable for rocks with hardness >6); 2) A titanium alloy scoop (suitable for loose lunar soil); 3) A tungsten carbide scraper (suitable for medium-hardness, adhesive materials). It is known that switching tools takes 15 minutes, and the current remaining work window is only 40 minutes.", + "question": "Based on the above characteristics of the lunar soil and time constraints, which combination of sampling tools should be chosen to maximize sampling efficiency? Please explain the reasons.", + "answer": "Choose the tungsten carbide scraper. Reasons: 1) The hardness of the lunar soil (4-5) is lower than the standard for the drill bit (>6); 2) Low viscosity eliminates the need for the scoop; 3) The scraper directly matches the characteristics of medium hardness and does not require switching tools, allowing full utilization of the remaining 40-minute window." + }, + { + "id": 694, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform rock sampling, the ground command takes 1.3 seconds to reach the moon. The lunar rover travels at a constant speed of 0.2m/s, and its emergency braking distance is 0.5m. An obstacle has been detected 3 meters ahead, and the onboard autonomous obstacle avoidance system has failed.", + "question": "Calculate the minimum safe distance from the issuance of the braking command to the complete stop of the lunar rover, and determine whether the current 3-meter distance is sufficient to avoid a collision.", + "answer": "Distance traveled during the 1.3-second command transmission delay = 0.2m/s * 1.3s = 0.26m; Total stopping distance = 0.26m + 0.5m = 0.76m; 3 meters > 0.76m, the safety distance is sufficient" + }, + { + "id": 695, + "scenario_code": "1.8", + "instruction": " When deploying the lunar-based telescope, the monitoring shows that the local lunar soil bearing capacity is 8kPa, the contact area of each leg of the triangular bracket is 0.05m², and the total mass is 120kg (including the shock absorber). The lunar surface gravitational acceleration is 1.62m/s². The design safety factor of the bracket is required to be ≥2.", + "question": "Verify whether the current deployment point meets the bearing capacity requirements by calculating the actual pressure of a single leg and comparing it with the safety threshold.", + "answer": "Force on a single leg F = (120kg * 1.62m/s²)/3 = 64.8N; actual pressure P = 64.8N / 0.05m² = 1296Pa = 1.296kPa; safety threshold = 8kPa / 2 = 4kPa; 1.296kPa < 4kPa, meets the requirement" + }, + { + "id": 696, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 lander is located on the edge of an impact crater at 23.5°E, 12.8°N on the near side of the Moon. Its solar wings use a three-dimensional tracking algorithm. According to the lunar calendar, the current solar elevation angle during the lunar day is 15°, and the azimuth angle is 45° (0° is due north, increasing clockwise). Terrain shadow analysis shows that a 3-meter-high rock wall to the west will cast a shadow from 08:00 to 10:00 local time. The maximum output power of the solar wings P_max=120W (when unobstructed), and the power during the shadow period drops to P_shadow=20W. The current state of charge (SOC) of the lithium-ion battery pack is 65%, and the basic power consumption of the load equipment is P_load=40W (continuous).", + "question": "If scientific instruments need to consume an additional 80W of power for drilling operations from 09:00 to 11:00, calculate the change in the battery's SOC at the end of this period (assuming the battery capacity is 200Wh, charging efficiency η=90%, and discharging efficiency η_d=95%).", + "answer": "From 09:00 to 10:00 during the shadow period: power generation P_gen=20W, total power consumption P_total=40+80=120W, net power consumption P_net=120-20=100W, energy consumption E1=100W*1h=100Wh; from 10:00 to 11:00 without shadow: power generation P_gen=120W, net power consumption P_net=120-120=0W; total energy consumption E_total=E1=100Wh; battery discharge E_bat=E_total/η_d=100/0.95≈105.26Wh; SOC change ΔSOC=-105.26/200*100%≈-52.63%; final SOC=65%-52.63%=12.37%." + }, + { + "id": 697, + "scenario_code": "3.6", + "instruction": " The Yutu-2 rover is about to enter lunar night hibernation, and its electronic equipment compartment needs to maintain a temperature above -20°C. The heat loss coefficient of the compartment K=0.8W/°C (temperature difference between inside and outside), the current internal temperature T_in=5°C, and the expected minimum environmental temperature during the lunar night T_out=-180°C. The insulation plan includes: ① multi-layer thermal insulation material (can reduce 60% heat loss) ② isotope heat source providing a constant Q_rhp=15W ③ electric heater as a backup (maximum power Q_elec=30W). The remaining battery energy E_bat=500Wh, and the lunar night lasts t_night=336 hours.", + "question": "Calculate whether the insulation requirement can be met by relying solely on the isotope heat source? If not, determine the minimum average power that the electric heater needs to supplement and the corresponding battery SOC safety margin (assuming heating efficiency η_heat=85%).", + "answer": "Actual heat loss Q_loss=(1-0.6)*K*(T_in-T_out)=0.4*0.8*(5-(-180))=59.2W; deficit ΔQ=59.2-15=44.2W>0→not met; required electric heating power Q_elec_req=ΔQ/η_heat≈44.2/0.85≈52W>30W→exceeds capability; minimum feasible solution: adjust T_in to the critical value to make Q_loss≤15/(0.4*0.8)+(-180)=-180+46.875=-133.125°C (unreasonable), so it is necessary to reduce insulation requirements or increase energy reserves." + }, + { + "id": 698, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located in the South Pole-Aitken Basin on the far side of the Moon, unable to communicate directly with Earth. The 'Queqiao' relay satellite is deployed in a Halo orbit at the Earth-Moon L2 point, with an average altitude of about 65,000 km above the lunar surface. The X-band antenna gain of the relay satellite is 42 dBi, the lander's transmission power is 10 W, and its antenna gain is 38 dBi. The free space path loss formula is: L = 20 * log10(d) + 20 * log10(f) + 92.45 (d in km, f in GHz). The current communication frequency is 7.2 GHz, and the system margin requirement is no less than 3 dB.", + "question": "Calculate the total uplink path loss from the lander to the relay satellite (including free space loss and antenna gain) when the Earth-Moon distance is 380,000 km, and determine whether it meets the system margin requirement.", + "answer": "Free space loss L = 20 * log10(380000) + 20 * log10(7.2) + 92.45 ≈ 20*5.58 + 20*0.86 + 92.45 ≈ 111.6 + 17.2 + 92.45 = 221.25 dB; Total loss = L - (Transmit antenna gain + Receive antenna gain) = 221.25 - (38 + 42) = 141.25 dB; System margin = Transmit power 10 W (10 dBW) - Total loss 141.25 dB = -131.25 dBW < 3 dB requirement, not met." + }, + { + "id": 699, + "scenario_code": "5.1", + "instruction": " Chang'e-6 lander plans to carry out a sample return mission on the far side of the Moon, and needs to establish communication with the ground station through the Queqiao-2 relay satellite. Known: Queqiao-2 operates in the Halo orbit at the Earth-Moon L2 point, with an average altitude of about 8000km above the lunar surface; the lander uses an S-band directional antenna (gain 15dBi) to communicate with the relay satellite, with a transmission power of 20W; the relay satellite's receiving antenna gain is 30dBi, and the system noise temperature is 150K; the minimum required received signal-to-noise ratio (SNR) is 10dB, and the communication rate is 500kbps. The free space path loss formula is L = 20 * log10(4 * π * d / λ), where λ is the wavelength (S-band frequency 2.2GHz, speed of light c=3*10^8m/s).", + "question": "Calculate whether the link margin under the current configuration meets the requirements? If not, to what minimum power in watts must the transmission power be increased to meet the requirements? ", + "answer": "1. Calculate the wavelength λ = c/f = 3*10^8 / 2.2*10^9 ≈ 0.136m;\n2. Path loss L = 20 * log10(4 * π * 8*10^6 / 0.136) ≈ 199.5dB;\n3. Received power Pr = Pt + Gt + Gr - L = 13dBW + 15dBi + 30dBi - 199.5dB = -141.5dBW;\n4. Noise power spectral density N0 = k * T = -228.6dBW/Hz/K + 10*log10(150) ≈ -205.8dBW/Hz;\n5. Required Eb/N0 = SNR - 10*log10(500k) = 10dB - 57dB = -47dB;\n6. Actual Eb/N0 = Pr - N0 - 10*log10(Rb) = -141.5dBW - (-205.8dBW/Hz) - (-57dB) ≈ 121.3dB > required value -47dB, the link margin is sufficient." + }, + { + "id": 700, + "scenario_code": "5.4", + "instruction": " During the lunar day, the Yutu-2 rover encountered a sudden solar proton event while conducting scientific exploration, causing the X-band direct-to-Earth communication to be interrupted. Current mission status: remaining power supports continuous operation for 4 hours, the storage has cached 12GB of untransmitted data (including 3GB of high-priority sampling data), the next visible window for the relay satellite opens in 90 minutes (lasting 25 minutes), and the available bandwidth is 20Mbps. The system uses a dynamic compression strategy: lossless compression ratio 1.5:1 (takes 30 minutes), lossy compression ratio 4:1 (takes 15 minutes) but will lose some spectral data details.", + "question": "Please formulate the optimal data transmission plan to ensure the complete transmission of high-priority data and maximize the transmission of ordinary data. Provide specific operational steps and the final amount of data transmitted.", + "answer": "1. Prioritize processing high-priority data: 3GB lossless compression → 2GB, takes 30 minutes;\n2. Remaining time = 90 - 30 = 60 minutes, of which 25 minutes are used for transmission:\n a) The first 25 minutes transmit high-priority data: transmission volume = 20Mbps * 1500s / 8 ≈ 3.75GB > 2GB (can be completely transmitted);\n b) Remaining 35 minutes process ordinary data: choose lossy compression 9GB → 2.25GB, takes 15 minutes;\n c) The last 20 minutes transmit ordinary data: transmission volume = 20Mbps * 1200s / 8 ≈ 3GB > 2.25GB (can be completely transmitted);\n3. Final result: 100% high-priority data + 100% ordinary data transmission completed." + }, + { + "id": 701, + "scenario_code": "2.2", + "instruction": " The detector is executing a mission at the edge of the Shackleton crater in the lunar south pole (permanently shadowed area), with the navigation system using a multi-sensor fusion solution: 1) IMU position error accumulates over time as δ=0.1%*t(s); 2) The visual odometry provides absolute position correction every 30 seconds, with an accuracy of ±3cm; 3) The LiDAR SLAM positioning error in the mapping area is ±5cm. The IMU has been operating continuously for 120 seconds without receiving a visual correction signal.", + "question": "Calculate the current maximum possible positioning error and identify the dominant error source.", + "answer": "Maximum error = IMU error (120*0.001=0.12m) + SLAM error (0.05m) = 0.17m. The dominant error source is the accumulated IMU error (accounting for 70.6% of the total error)." + }, + { + "id": 702, + "scenario_code": "2.7", + "instruction": " The lunar rover encounters a solar proton event warning near the terminator and needs to reach an emergency shelter 3 kilometers away within 15 minutes. It is known that: 1) The normal driving speed is 0.1m/s; 2) In emergency mode, the speed can be increased to 0.25m/s but the energy consumption doubles; 3) There is a slope with an 8° incline and a length of 500m in the direction of the shelter, the rest is flat terrain; 4) Basic energy consumption model: 0.15Wh/m on flat ground, and an additional 0.03Wh/m/degree for uphill.", + "question": "Calculate the shortest arrival time and total energy consumption in emergency mode, and determine if it meets the 15-minute time limit.", + "answer": "Shortest time = (3000-500)/0.25 + 500/0.25 = 10000s + 2000s = 12000s (12 minutes). Total energy consumption = (2500*0.15*2) + (500*(0.15+0.03*8)*2) = 750 + 270 = 1020Wh. 12 minutes < 15 minutes, meeting the time limit requirement." + }, + { + "id": 703, + "scenario_code": "5.7", + "instruction": " The 128TB solid-state memory carried by the Chang'e-7 orbiter uses NAND Flash chips, and a wear-leveling strategy needs to be designed. It is known that: the memory is divided into 4 independent partitions (A/B/C/D), each partition contains 10,000 erase blocks (block), and each block has a maximum number of erase/write cycles of 3000 times; the current average number of erase/write cycles for each partition is A: 1200 times, B: 950 times, C: 1800 times, D: 600 times. The daily amount of new data is about 200GB, evenly written to all partitions. The storage controller uses a dynamic weight allocation algorithm: weight W_i = (1 - U_i / max_U) * α + β, where U_i is the current average number of erase/write cycles for partition i, max_U is the maximum number of erase/write cycles among all partitions, α=0.7, β=0.3 are adjustment coefficients.", + "question": "Calculate the allocation weight and specific write capacity for each partition during the next data write (保留两位小数).", + "answer": "1. max_U=max(1200,950,1800,600)=1800;\n2. W_A=(1-1200/1800)*0.7+0.3≈0.53;\n W_B=(1-950/1800)*0.7+0.3≈0.62;\n W_C=(1-1800/1800)*0.7+0.3=0.30;\n W_D=(1-600/1800)*0.7+0.3≈0.77;\n3. Sum_W=0.53+0.62+0.30+0.77=2.22;\n4. A allocation=200*(0.53/2.22)≈47.77GB; B allocation=200*(0.62/2.22)≈55.86GB; C allocation=200*(0.30/2.22)≈27.03GB; D allocation=200*(0.77/2.22)≈69.37GB" + }, + { + "id": 704, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is conducting exploration tasks in the Von Kármán crater and needs to move from point A (10°N, 20°E) to point B (10.5°N, 20.2°E). It is known that: 1) the slope of the lunar surface is less than 15°, the wheel-soil mechanics model shows that the energy consumption coefficient on a flat slope is 0.1 Wh/m, and the increase in energy consumption on an uphill slope is ΔE=0.05* slope angle(°)*distance(m); 2) the straight-line distance between the two points is 1500m, but there is a 200m long, 12° slope uphill section in between; 3) the current remaining battery energy is 180Wh.", + "question": "If the straight path is chosen, calculate the total energy consumption and determine whether the current battery level meets the travel requirements.", + "answer": "Total energy consumption = (1500-200)*0.1 + 200*(0.1+0.05*12) = 1300*0.1 + 200*0.7 = 130 + 140 = 153Wh. 180Wh > 153Wh, the battery level meets the requirements." + }, + { + "id": 705, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, it is necessary to provide power to three devices (seismometer, magnetometer, infrared spectrometer) simultaneously. The current system uses a distributed power grid with a total available peak power of 120W. It is known that: the seismometer operates in two modes (high: 50W for 10 minutes/hour, low: 20W for continuous monitoring); the magnetometer consumes a fixed 30W; the infrared spectrometer needs to start periodically (each start-up has an instantaneous power of 80W for 5 minutes, starting twice per hour). The power management system must ensure all devices operate normally without exceeding the total power limit.", + "question": "If the seismometer is required to operate in high mode for at least 50% of the time, please calculate whether the current power configuration can meet the needs of all devices? If not, what is the maximum power reduction allowed for the magnetometer (while maintaining continuous operation) to meet the constraints? ", + "answer": "No. The magnetometer needs to be reduced to 10W. Calculation process: 1) Seismometer high power consumption = 50W * 10/60 = 8.33W average power, low power = 20W * 50/60 = 16.67W average power, with 50% high power, the average power = (8.33 + 16.67) / 2 = 12.5W; 2) Spectrometer average power = 80W * (5 * 2) / 60 = 13.33W; 3) Current total demand = 12.5 + 30 + 13.33 = 55.83W > 120W * 0.8 (safety threshold) = 96W; 4) Maximum allowable magnetometer power consumption = 96 - (12.5 + 13.33) = 70.17W, but the original value of 30W has exceeded the limit, it needs to be reduced to 96 - 25.83 ≈ 10W" + }, + { + "id": 706, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform sampling tasks in rugged areas, ground commands take 1.3 seconds to reach the rover. The current speed of the rover is 0.15m/s, and the emergency braking distance is 0.5m. An unmapped lunar crater (approximately 1.2 meters in diameter) appears 3 meters ahead, and the ground discovers the danger through real-time imagery when the rover has already traveled 0.8 seconds towards the crater.", + "question": "If image transmission delay is not considered, only the command transmission delay and braking distance are calculated, can the ground sending an emergency stop command avoid falling into the crater? If not, propose a feasible predictive control compensation strategy (key parameters need to be explained).", + "answer": "It cannot be avoided. Calculation process: 1) Remaining distance when danger is detected = 3 - 0.15 * 0.8 = 2.88m; 2) Distance traveled during command transmission = 0.15 * 1.3 = 0.195m; 3) Total braking distance required = 0.5 + 0.195 = 0.695m > remaining 2.88m - traveled 0.195m = 2.685m (contradiction point). Compensation strategy: Use a forward obstacle prediction algorithm to decelerate 1 / (0.15 / 0.5) = 3.33 seconds in advance, the parameters need to set the early warning threshold distance ≥ speed * delay time + braking distance = 0.15 * 1.3 + 0.5 = 0.695m" + }, + { + "id": 707, + "scenario_code": "3.1", + "instruction": " Chang'e-7 rover is conducting exploration tasks in the lunar south pole region, which has complex terrain and permanent shadow areas. The rover is equipped with a two-dimensional adjustable solar panel, with a maximum tracking angle of ±45 degrees. According to the lunar calendar, the current solar elevation angle is 15 degrees, and the azimuth angle is 30 degrees (with 0 degrees being due north). There is a crater 200 meters ahead of the rover, with a height of 50 meters and an azimuth angle of 45 degrees. The theoretical maximum power generation of the solar panel is 200W (when there is no obstruction). It is known that the power generation is proportional to the cosine of the solar incidence angle (the incidence angle is the angle between the solar rays and the normal of the solar panel).", + "question": "If the rover maintains its current orientation (azimuth angle 0 degrees), and the solar panel is adjusted to the optimal tracking angle, calculate the actual power generation (considering the impact of terrain obstruction).", + "answer": "First, determine the obstruction situation: the difference between the crater's azimuth angle of 45 degrees and the sun's azimuth angle of 30 degrees is 15 degrees, which is less than the half-width of the mountain (approximately arctan(25/200) ≈ 7.1 degrees), so there is partial obstruction. When the solar elevation angle is 15 degrees, the length of the mountain's shadow = 50/tan(15°) ≈ 186 meters < 200 meters, so there is no obstruction. The optimal tracking angle is when the normal is aligned with the sun's direction, i.e., pitch 15 degrees, yaw 30 degrees. At this time, the incidence angle is 0 degrees, cos(0°) = 1, the actual power generation = 200W * 1 = 200W." + }, + { + "id": 708, + "scenario_code": "3.8", + "instruction": " Chang'e-6 lander mission profile requires: completing 3 drilling operations (each consuming 150Wh) within 10 lunar days, 4 hours of scientific payload operation daily (power consumption 20W), and continuous temperature control consuming 5W. Energy system configuration: solar array average daily power generation of 500Wh, battery capacity of 800Wh (initial SOC=100%), charge and discharge efficiency of 90%. No power generation during the lunar night and basic consumption of 3W.", + "question": "Formulate an energy allocation plan to meet all mission requirements and verify the battery SOC at the end of the 7th day (assuming the last drilling operation is performed on the 7th day).", + "answer": "Total demand: 3*150=450Wh for drilling; 10*20*4=800Wh for scientific payload; 10*5*24=1200Wh for temperature control; total 2450Wh. Total power supply 10*500=5000Wh > demand, feasible. Daily balance: 500Wh generated during the day - (20*4+5*24+150δ)=500-280-150δ=220-150δ Wh (δ is whether drilling is performed that day). SOC at the end of the 7th day: consumption for the first 6 days = 6*280+2*150=1980Wh; charging amount = 6*500*0.9=2700Wh; net increase 720Wh; initial 800Wh → 1520Wh > 800, so it is 800Wh (full capacity)." + }, + { + "id": 709, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. According to preliminary remote sensing data analysis, the target area contains two typical types of lunar soil: Class A is loose and dry fine-grained lunar soil (average particle size 50 microns, internal friction angle 28 degrees), and Class B is medium-hard lunar soil with glassy bonding (compressive strength 1.5MPa, moisture content 0.6%). The engineering team is equipped with three sampling tools: ① Rotary impact drill (suitable for rocks with hardness >5MPa), ② Vacuum suction shovel (suitable for loose fine-grained materials), ③ Vibratory core tube (suitable for sticky medium-hard materials). It is known that the sampling power consumption constraint is no more than 200Wh per operation.", + "question": "Which sampling tool should be chosen for Class A and Class B lunar soil, respectively? Please explain the selection criteria based on material properties and tool parameters.", + "answer": "For Class A lunar soil, choose the vacuum suction shovel, as its loose and dry characteristics match the tool design; for Class B lunar soil, choose the vibratory core tube, as the medium hardness and moisture content are suitable for the tool's operating range. The rotary impact drill is not suitable for either type of lunar soil: Class A has too low hardness, and Class B does not meet its minimum operating hardness." + }, + { + "id": 710, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is carrying out an exploration mission from point A (coordinates X=12.3, Y=45.6) to point B (coordinates X=15.7, Y=48.2). It is known from terrain data that there are three optional paths between the two points: Path 1 is a straight-line distance of 3.5 kilometers with a slope of 8°; Path 2 is a detour distance of 4.2 kilometers with a slope of only 2°; Path 3 is a zigzag distance of 3.8 kilometers with alternating slopes (5° uphill + 3° downhill). The energy consumption model of the lunar rover is: kinetic energy consumption for movement E_d = 0.1*d + 0.02*θ*d (d is the number of kilometers, θ is the absolute value of the slope), the remaining battery power is 480Wh, and at least 120Wh must be reserved for emergency power.", + "question": "Calculate the total energy consumption of the three paths and determine which path can reach the target point the fastest under the power constraint (assuming the speed of the lunar rover is 0.1 km/h when the slope is 0, and the speed decreases by 0.005 km/h for every 1° increase in slope).", + "answer": "Energy consumption of Path 1 E1 = 0.1*3.5 + 0.02*8*3.5 = 0.35 + 0.56 = 0.91 kWh; Energy consumption of Path 2 E2 = 0.1*4.2 + 0.02*2*4.2 = 0.42 + 0.168 = 0.588 kWh; Energy consumption of Path 3 E3 = 0.1*3.8 + 0.02*(5*1.9 + 3*1.9) = 0.38 + 0.304 = 0.684 kWh. The available power of 360Wh meets all requirements. Speed of Path 1 v1 = 0.1 - 8*0.005 = 0.06 km/h, time t1=3.5/0.06≈58h; Speed of Path 2 v2=0.1 - 2*0.005=0.09 km/h, t2=4.2/0.09≈47h; Path 3 is calculated in segments: uphill v3a=0.075 km/h takes 25h, downhill v3b=0.085 km/h takes 22h, total t3≈47h. The optimal choice is Path 2 or Path 3 (same time), but Path 2 has lower energy consumption." + }, + { + "id": 711, + "scenario_code": "2.6", + "instruction": " When the Chang'e-7 lander performs high-precision positioning at the lunar south pole, the inertial navigation system (INS) produces cumulative drift errors due to long-term operation, with a position error model of Δx=0.1*t^1.1 (t is in hours). The current INS display coordinates are (X=3254.1, Y=-1876.5), and the reference coordinates of the actual landmark 'Shackleton Crater Edge' observed by astronomical navigation are (X=3256.5, Y=-1878.1). It is known that the last precise calibration was 36 hours ago, and the maximum allowable error for landmark matching is ±20 meters.", + "question": "Determine if the current INS output is reliable? If not, calculate the required position correction (take the coefficient of t^1.1 as units of meters/hour^1.1).", + "answer": "Calculate the drift Δx=0.1*36^1.1≈0.1*54.5≈5.5 meters. The distance between the INS display and the actual landmark is sqrt((3254.1-3256.5)^2+(-1876.5+1878.1)^2)=sqrt(6.25+2.25)≈7 meters < 20 meters, still within the allowable error range. Conclusion: The current INS output is reliable, no correction is needed." + }, + { + "id": 712, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover obtained the following prior data while conducting exploration in the Von Kármán crater: ① Orbital hyperspectral images show three KREEP rock anomaly areas (coordinates X1,Y1; X2,Y2; X3,Y3); ② The laser rangefinder measured the distances to the three areas from the current position as d1=120m, d2=85m, d3=150m; ③ The formula for the solar elevation angle changing over time is sinθ=0.5+0.3*cos(πt/6), with the current t=2 hours; ④ The rover's movement energy consumption model is E=0.8*d+5 (unit: Wh), and the energy consumption for a single scientific detection operation is 15Wh. The remaining available energy is 180Wh.", + "question": "If at least two detections need to be completed before sunset (when θ≤10°, stop operations), please calculate which two target points should be prioritized in the optimal path? Provide the specific energy consumption and time verification process.", + "answer": "Prioritize visiting X2 and X1: The total moving distance is 85+35=120m, consuming 0.8*120+5*2=106Wh; Two detections consume 30Wh; Total consumption is 136Wh<180Wh. The time to reach X2 is t1=85/(0.05*3600)≈0.47h; The moving time from X1 to X2 is t2=35/(0.05*3600)≈0.19h; Total time is 0.66h ① > ②.", + "question": "Design the optimal task scheduling plan, requiring all tasks to be completed without exceeding the energy budget.", + "answer": "Plan: 1) Prioritize the execution of ③ data transmission for 15 minutes (energy consumption 75W * 0.25h = 18.75Wh); 2) Parallel execution of ① spectrometer for 20 minutes (45W * 0.33h = 15Wh) and ② camera for the first 10 minutes (60W * 0.17h = 10Wh); 3) Total energy consumption = 18.75 + 15 + 10 = 43.75Wh < 30Wh + 120W * 0.33h = 70Wh." + }, + { + "id": 715, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing an exploration mission on the far side of the moon, located at coordinate point A (10°N, 20°E). The mission planning system needs to plan a path to the scientific target point B (12°N, 22°E). It is known that: 1) the average driving speed of the lunar rover is 0.05 m/s; 2) the motor efficiency curve shows: energy consumption rate is 0.15 Wh/m at a 5° slope, and 0.3 Wh/m at a 10° slope; 3) the remaining battery energy is 200 Wh; 4) terrain data indicates that there are two optional paths between points A and B: Path 1 is 800 meters long with an average slope of 8°; Path 2 is 1200 meters long with an average slope of 3°. There are only 6 hours of lunar daylight remaining.", + "question": "To ensure the lunar rover safely reaches target point B without depleting its energy, which path should be chosen? Please calculate and explain the basis for your choice.", + "answer": "Choose Path 1. Calculation process: 1) Total energy consumption of Path 1 = 800m * 0.3 Wh/m = 240 Wh > 200 Wh (not feasible); 2) Total energy consumption of Path 2 = 1200m * 0.15 Wh/m = 180 Wh < 200 Wh (feasible); 3) Time required for Path 2 = 1200m / 0.05 m/s = 24000 seconds = 6.67 hours > 6 hours (overtime). Therefore, only Path 1 can be chosen and power-saving mode must be activated to reduce energy consumption to below 200Wh." + }, + { + "id": 716, + "scenario_code": "2.9", + "instruction": " The Lunar Orbit Navigation Satellite System (LBNSS-1) has established a two-way ranging link with Yutu-3. Known parameters: 1) LBNSS-1 orbit height 100km (lunar radius 1737km); 2) UWB beacon transmission power 10W, reception sensitivity -110dBm; 3) Ranging signal frequency 2.4GHz, atmospheric loss negligible; 4) Current slant distance between satellite and ground 120km; 5) Antenna gain: satellite transmission antenna 8dBi, rover reception antenna 3dBi. Free space loss formula: Lfs=32.45+20log10(d_km)+20log10(f_MHz).", + "question": "Calculate whether the received signal power of the current link meets the communication requirements? Provide specific calculation steps.", + "answer": "Meets requirements. Calculation steps: 1) Lfs=32.45+20log10(120)+20log10(2400)=32.45+41.58+67.6=141.63 dB; 2) Pr=Pt+Gt+Gr-Lfs=10dBW+8dBi+3dBi-141.63=-120.63dBW=-90.63dBm > -110dBm (higher than reception sensitivity)." + }, + { + "id": 717, + "scenario_code": "5.1", + "instruction": " Chang'e-6 probe needs to maintain communication with the ground station through Queqiao-2 relay satellite while performing sampling tasks on the far side of the Moon. Given: 1) The average Earth-Moon distance is 384,400 km; 2) Queqiao-2 operates in the Halo orbit at the Earth-Moon L2 point, approximately 65,000 km above the lunar surface; 3) The probe and relay satellite use X-band communication (frequency 8 GHz), with a maximum transmission power of 20 W and antenna gain of 38 dBi; 4) The equivalent noise temperature of the relay satellite's receiving system is 150 K, with a bandwidth of 10 MHz; 5) The free space path loss formula is L = 20 * log10(4 * π * d / λ), where λ is the wavelength (speed of light / frequency).", + "question": "Calculate the uplink signal-to-noise ratio (SNR) from the probe to Queqiao-2, given the Boltzmann constant k = 1.38e-23 J/K, and determine whether it meets the minimum communication requirement (SNR ≥ 10 dB).", + "answer": "1) Calculate the wavelength λ = c / f = 3e8 / 8e9 = 0.0375 m; 2) Path loss L = 20 * log10(4 * π * 65000e3 / 0.0375) ≈ 210.3 dB; 3) EIRP = 10 * log10(20) + 38 ≈ 51 dBm; 4) SNR = EIRP - L + Gr - (10 * log10(k * T * B)), assuming the relay reception gain Gr=30 dBi, then SNR ≈ 51 -210.3 +30 -(-168.6) ≈39.3 dB >10 dB, meeting the requirement." + }, + { + "id": 718, + "scenario_code": "5.4", + "instruction": " Yutu-2 rover encounters a sudden solar flare during the lunar day, causing the UHF link with Queqiao relay satellite to be interrupted. Current status: 1) Remaining operable time window is 45 minutes; 2) 12GB of scientific data not yet transmitted are stored locally; 3) The backup S-band direct-to-Earth link has a rate of only 500kbps but is highly resistant to interference; 4) Remaining power supports continuous transmission for no more than 30 minutes.", + "question": "Please formulate an emergency transmission plan to ensure the complete return of key data (marked as 6GB high priority) and calculate the final transmission success rate.", + "answer": "1) Prioritize the transmission of high-priority data: 6GB / (500kbps/8) ≈ 96 seconds ≈ 1.6 minutes; 2) Remaining time can be used to transmit low-priority data: (30-1.6)*60*500e3/8 ≈ 1.07GB; Total transmission volume = 6 + 1.07 = 7.07GB, success rate = 7.07/12 ≈ 58.9%." + }, + { + "id": 719, + "scenario_code": "5.7", + "instruction": " The Chang'e-7 lander's onboard SSD storage module uses a NAND Flash architecture with a total capacity of 1TB, and a block size of 128KB. It is known that: 1) the maximum number of write/erase cycles per block is 100,000; 2) the current wear-leveling algorithm ensures that the difference in write/erase cycles among blocks does not exceed ±5%; 3) the average daily data write volume is 40GB, of which 60% is scientific data (to be permanently stored) and 40% is engineering data (can be overwritten).", + "question": "Estimate the expected service life (in years) of the SSD under the premise of ensuring the integrity of all scientific data, taking into account the wear-leveling constraints.", + "answer": "1) Daily effective write volume = 40GB * 60% = 24GB (permanent); 2) Annual write volume = 24 * 365 ≈ 8760GB/year; 3) Actual write volume (including leveling) = 8760 * (1 + 0.05) = 9198GB/year; 4) Total writable volume = 100000 * 128KB * 1024 ≈ 12.8PB; Lifespan = 12.8PB / 9198GB ≈ 1425 years" + }, + { + "id": 720, + "scenario_code": "5.1", + "instruction": " The Chang'e-6 lander is located in the South Pole-Aitken Basin (SPA) on the far side of the Moon, and plans to transmit data to Earth via the Queqiao-2 relay satellite. It is known that Queqiao-2 operates in the Earth-Moon L2 Halo orbit, with an average altitude of about 8000km above the lunar surface; the lander uses X-band (8GHz) communication, with a transmission power of 20W and an antenna gain of 36dBi; the relay satellite's receiving antenna gain is 42dBi, and the system noise temperature is 150K. The current Earth-Moon distance is 380,000km, and the communication window lasts for 4 hours.", + "question": "Calculate the uplink link budget margin from the lander to the relay satellite in the current mission (considering free space loss and Boltzmann constant k=1.38e-23 J/K), and determine whether it meets the minimum requirement of a 10dB margin.", + "answer": "Free space loss L = 20*log10(4*pi*d/lambda) = 20*log10(4*pi*8e6/(3e8/8e9)) ≈ 179.5dB; Received power Pr = Pt + Gt + Gr - L = 13 + 36 + 42 - 179.5 = -88.5dBW; Noise power Pn = 10*log10(k*T*B) ≈ -168.5dBW/Hz (assuming bandwidth B=1Hz); Signal-to-noise ratio SNR = Pr - Pn = 80dB; Margin = SNR - 10dB requirement = 70dB >> 10dB, meeting the requirement." + }, + { + "id": 721, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover encountered a sudden solar proton event during the lunar day, causing the UHF link with the Queqiao relay satellite to be interrupted. The rover's built-in 256MB cache has already stored 85% of the data, and the remaining power can support 120 minutes of emergency operations. At the time of interruption, it was transmitting high-priority spectral data at a rate of 3.2MB/s, and regular communication is expected to be restored in 30 minutes.", + "question": "Please design a rescue strategy: Which of the following operations should be prioritized? (A) Immediately switch to the backup S-band transmitter (B) Compress the cache data to 50% of its original size (C) Suspend scientific payloads and switch to the lowest power consumption mode (D) Delete low-priority engineering data to free up 30% of the cache space", + "answer": "(C) Suspend scientific payloads and switch to the lowest power consumption mode. Because the solar proton event may continue to affect all frequency bands, and the S-band equipment is also susceptible to interference (A is incorrect); compressing (B) and deleting data (D) will consume additional time and power, while the most urgent need now is to extend survival time until the link is restored." + }, + { + "id": 722, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform rock sampling tasks, the one-way communication delay between Earth and the Moon is 1.3 seconds. The current speed of the lunar rover is 0.2m/s, and the positioning accuracy requirement for the end of the robotic arm is ±5cm. The control system uses a predictive algorithm to compensate for the delay, with the position correction formula being: correction amount = current speed * delay time * 0.6 (damping factor).", + "question": "When the detected offset of the target rock position reaches 8cm, how many seconds in advance should the action command generated by the predictive algorithm be triggered to compensate for the delay and achieve the required accuracy of ±5cm at the end of the robotic arm's movement to the target rock position, given the current speed of the lunar rover is 0.2m/s and the one-way communication delay is 1.3 seconds, with a damping factor of 0.6 in the position correction formula used by the control system to compensate for the delay.", + "answer": "The required correction amount of 8cm = 0.2m/s * 1.3s * 0.6 * X → X = 0.08 / (0.2*1.3*0.6) ≈ 0.51 seconds. Therefore, the command needs to be triggered 0.51 seconds in advance." + }, + { + "id": 723, + "scenario_code": "1.8", + "instruction": " When deploying a lunar-based telescope, the local lunar soil bearing capacity was measured to be 8kPa, the contact area of a single leg of the triangular support of the telescope is 0.05m², and its self-weight is 120kg. The safety factor requires that the actual ground contact pressure does not exceed 70% of the bearing capacity. The lunar surface gravitational acceleration is 1.62m/s².", + "question": "Calculate whether the support needs to add a bearing plate to increase the contact area? If it needs to be added, what is the minimum contact area for a single foot should be? ", + "answer": "Current pressure per foot = (120kg * 1.62m/s² / 3) / 0.05m² ≈ 1296Pa = 1.296kPa < 8kPa*70%=5.6kPa, no need to add a bearing plate." + }, + { + "id": 724, + "scenario_code": "4.4", + "instruction": " Yutu-2 is conducting exploration in the Von Kármán crater, obtaining the following prior data: 1) Orbital hyperspectral data show that the KREEP rock abundance at point A (45.3°N, 176.2°E) is 68%; 2) The breccia coverage rate at point B (45.5°N, 176.0°E) is 82%; 3) There is a fresh impact crater with a diameter of 3 meters at point C (45.4°N, 176.1°E). The priority order of scientific objectives is: rare mineral sampling > geological age determination > volatile detection. The rover's remaining power supports a total travel distance of no more than 800 meters, and it is currently 400 meters south of point B. The distances between points are: A-B=350 meters, B-C=200 meters, A-C=450 meters.", + "question": "Please plan the optimal exploration route and explain the reasons.", + "answer": "The optimal route is B→C→A. Reasons: 1) Point B is the closest (400 meters), and the breccia is suitable for geological age determination; 2) Point C is only 200 meters from B, and the fresh impact crater may expose deep materials, meeting the requirements for volatile detection; 3) Point A has the rarest KREEP rock but is the farthest away. The total distance of 400+200+450=1050 meters exceeds the limit, so point A must be abandoned or the priority adjusted." + }, + { + "id": 725, + "scenario_code": "2.7", + "instruction": " A lunar orbit navigation satellite detects an impending solar proton event (lasting 4 hours) and issues a warning to a rover currently traveling in the Oceanus Procellarum region. The current status of the rover: 1) 1.2 km from the nearest shelter cave; 2) maximum safe travel speed of 0.1 km/h; 3) needs to enter the cave 30 minutes in advance to shut down sensitive instruments. The event is expected to reach peak radiation intensity 55 minutes from now. The rover's energy status is good, but radiation may cause permanent damage to the control system.", + "question": "Determine whether the rover can safely reach the shelter? If not, what emergency measures should be taken.", + "answer": "Shortest required time = (1.2/0.1)*60 + 30 = 102 minutes > 55 minutes warning time. Emergency measures: Immediately switch to the minimum safe mode (shut down scientific payloads, maintain only basic communication and thermal control), and orient the shadow side of the vehicle towards the solar radiation source." + }, + { + "id": 726, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the moon, located at coordinate point A (10°N, 120°E). The mission planning system requires it to reach scientific target point B (12°N, 122°E) within 6 hours and complete at least 30 minutes of stationary exploration. It is known that: 1) The average driving speed of the lunar rover is 0.05 km/h; 2) The straight-line distance between the two points is 30 km, but the actual route requires detouring around 3 craters, increasing the total distance to 42 km; 3) The driving energy consumption model is E = 0.15 * d (Wh/km), where d is the actual driving distance; 4) The system power consumption during stationary exploration is 5 W. The remaining battery energy is 8 Wh. The remaining lunar day time is 7 hours (including the communication window).", + "question": "If Yutu-2 drives to point B along the planned route and completes the exploration, will the total energy consumption be within the safety margin? Please calculate the remaining energy or the shortfall.", + "answer": "Total energy consumption = Driving energy consumption + Exploration energy consumption = 0.15 * 42 + 5 * 0.5 = 6.3 + 2.5 = 8.8 Wh; Shortfall = 8.8 - 8 = -0.8 Wh (exceeding the safety margin)." + }, + { + "id": 727, + "scenario_code": "1.8", + "instruction": " When deploying a network of lunar magnetometers, the bearing capacity of the lunar soil at a certain point was measured to be 8 kPa. The contact area of the magnetometer base is 0.25 m^2, its own weight is 15 kg, and the additional equipment weighs 5 kg. The gravitational acceleration on the Moon is 1.62 m/s^2. The safety factor requirement is ≥3. The critical pressure for plastic deformation of the lunar soil = measured bearing capacity * 0.7.", + "question": "Can the magnetometer be deployed directly at this point? If not, how should the base design be adjusted (provide specific parameter calculations)?", + "answer": "Total mass = 15 + 5 = 20 kg; Pressure = mass * gravity / area = 20 * 1.62 / 0.25 = 129.6 Pa; Critical pressure = 8000 * 0.7 = 5600 Pa; Safety factor = 5600 / 129.6 ≈ 43 >> 3, can be deployed directly." + }, + { + "id": 728, + "scenario_code": "1.2", + "instruction": " When deploying an integrated drilling and sampling device at the edge of Shackleton Crater in the lunar south pole, the geometric constraints of the equipment installation sequence must be considered. The main drill tower is 2.4 meters high and must be installed before the solar panels (unfolded size 1.8×3 meters) to avoid collisions. The solar panels must face due north ±5° to receive maximum light, and the minimum safe distance between the unfolded支架 and the base of the drill tower is 0.6 meters. The drill tower base is a regular hexagon with a side length of 1.2 meters, and all equipment must be deployed within a pre-leveled circular area with a diameter of 4 meters.", + "question": "If the center of the drill tower base is placed at the center of the circular area, where should the connection points of the solar panel支架 be set in the base coordinate system (provide XY coordinate offsets) to simultaneously meet the orientation and safety distance requirements? Assume the +X axis points due north.", + "answer": "(0, -1.8) " + }, + { + "id": 729, + "scenario_code": "1.8", + "instruction": " When deploying the lunar seismometer array, it was found that the local lunar soil bearing capacity is only 0.3kg/cm², lower than the design requirement of 0.5kg/cm². Each instrument weighs 8kg, with a base contact area of 50cm². The engineering team decided to adopt a distributed load-bearing solution: transmitting the instrument's weight through three adjustable legs to the lunar surface, with each leg end equipped with a circular pressure pad with a diameter of 6cm. Soil compression modulus tests indicate that for every 1cm increase in the diameter of the pressure pad, the effective bearing capacity can be increased by 0.05kg/cm².", + "question": "Calculate the minimum diameter increment Δd of a single pressure pad to meet the bearing capacity requirement (result rounded to one decimal place), and explain how this adjustment would be implemented in actual engineering.", + "answer": "Δd=2.0cm, achieved by extending the foldable expansion rings at the end of the legs" + }, + { + "id": 730, + "scenario_code": "3.1", + "instruction": " On the lunar south pole's crater area, the solar wings of the Chang'e-7 lander use a two-dimensional tracking algorithm. During the lunar day, the solar altitude angle varies from 5° to 30°, and the azimuth angle changes at a rate of 0.25°/min. The maximum output power formula for the solar wings is P_max = 1000 * sin(θ) W (where θ is the solar incidence angle), and the average efficiency when fixed is 65% of the maximum. In the current mission phase, a continuous power supply of at least 400W is required, and terrain obstruction reduces the effective power generation time by 30% each day.", + "question": "If a fixed installation method is used, can the power supply requirement be met without obstruction? If not, to what percentage above must the average efficiency of two-dimensional tracking be increased to meet the requirement? (Round to two decimal places.)", + "answer": "When fixed, the average power = 1000 * sin(22.5°) * 0.65 ≈ 247.62W < 400W, which does not meet the requirement; Let the tracking efficiency be x%, then 1000 * sin(22.5°) * x% ≥ 400 → x% ≥ 400 / (1000 * sin(22.5°)) ≈ 105.18%, so it needs to be increased to above 105.18%." + }, + { + "id": 731, + "scenario_code": "3.4", + "instruction": " The Yutu-2 rover simultaneously performs three tasks: ① X-ray spectrometer (peak power consumption 120W, continuous for 15 minutes); ② Infrared imager (80W continuous operation for 20 minutes); ③ Data transmission (instantaneous 200W pulse, each lasting 2 minutes, with an 8-minute interval). Energy system constraints: the total energy consumption in any 10-minute window must not exceed 180Wh, and the peak power consumption of a single device must not exceed 200W. The current remaining charge of the lithium-ion battery is 500Wh.", + "question": "If the three tasks are started completely in parallel, will it violate the energy constraints? Please design a task start time delay scheme that meets all constraints (provide the delay minutes for each task relative to T0).", + "answer": "When completely parallel, the 10-minute window energy consumption = (120*15 + 80*20 + 200*2) / 6 ≈ 716.67Wh > 180Wh, violating the constraint; A feasible solution: the spectrometer starts at T0+0min, the infrared imager starts at T0+5min, and data transmission starts at T0+10min." + }, + { + "id": 732, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover experienced a sudden communication interruption during the lunar day. Fault analysis revealed:\n1. The main X-band link experienced a sharp increase in bit error rate due to a solar proton event;\n2. The backup UHF link can provide 1Mbps bandwidth but requires forwarding through a relay node 10km away;\n3. The SSD cache has 50GB of remaining capacity, with a critical science data generation rate of 200MB/hour;\n4. There are 8 hours of lunar day remaining, and at least 80% of critical data must be transmitted back.", + "question": "Please formulate an emergency transmission plan, calculate the required compression ratio (assuming the original data can be compressed losslessly), and specify the fault handling protocol levels that need to be triggered.", + "answer": "Total data to be transmitted = 200MB/h * 8h = 1600MB, available bandwidth = 1Mbps * 3600s = 450MB/h. Required compression ratio = 1600MB / (450MB/h * 8h) = 0.44 (i.e., at least 56% compression rate). The 'Link Autonomous Switching Protocol' (L3 level) and 'Cache Data Priority Scheduling Protocol' (L2 level) should be triggered." + }, + { + "id": 733, + "scenario_code": "3.6", + "instruction": " The Chang'e-6 lander's lunar night thermal insulation system uses an electric heater (rated power 50W) and an isotope heat source (constant output 20W) working together. The key equipment insulation requirement: when the cabin temperature is no lower than -40°C, the total heating power must be ≥35W. When the battery SOC is below 30%, the electric heater automatically turns off. At the beginning of the current lunar night, SOC=45%, the battery capacity is 300Wh, the lunar night lasts 350 hours, and the system's basic load power consumption is 5W.", + "question": "Calculate the final SOC of the battery at the end of the lunar night (assuming 100% discharge efficiency, considering only the power consumption of the thermal insulation system). If the SOC needs to be kept above 30%, what is the maximum allowable operating time ratio of the electric heater? ", + "answer": "Total power supply requirement = (50+20)*t + 20*(350-t) ≥ 35*350 → t ≥ 105 hours; Total energy consumption = 50*105 + 20*350 + 5*350 = 12250Wh; Initial energy = 300*45% = 135Wh → final SOC = (135-122.5)/300 ≈ 4.17%; Let the ratio be x: 50*x*350 ≤ 135-300*30% → x ≤ (135-90)/17500 ≈ 0.257% " + }, + { + "id": 734, + "scenario_code": "1.5", + "instruction": " Remotely control the lunar rover to perform rock sampling, with a one-way communication delay of 1.3 seconds between Earth and the Moon. The current speed of the lunar rover is 0.2m/s, and there is an obstacle 3 meters ahead. The control system uses a predictive algorithm to compensate for the delay, and the braking distance formula is: braking distance d = v * (t_delay + t_react), where t_react=0.5 seconds is the local reaction time.", + "question": "Calculate the minimum safe distance required from sending the braking command to a complete stop, and determine if the current distance is sufficient.", + "answer": "d = 0.2m/s * (1.3s + 0.5s) = 0.36m; 3m > 0.36m, the current distance is sufficient for safe braking." + }, + { + "id": 735, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration near the Von Kármán crater. According to the high-value sampling point priority scoring formula generated from orbital remote sensing data: Priority P = 0.3 * mineral diversity index + 0.5 * water ice feature peak intensity + 0.2 * terrain flatness (each item is out of 10 points). The data for the current three candidate points are: Point A (6,8,5), Point B (7,4,9), Point C (9,5,7). The rover has enough remaining power to travel to only one point.", + "question": "Calculate the comprehensive priority score for each candidate point and determine the optimal sampling point.", + "answer": "Point A score = 0.3*6 + 0.5*8 + 0.2*5 = 6.8; Point B score = 0.3*7 + 0.5*4 + 0.2*9 = 5.9; Point C score = 0.3*9 + 0.5*5 + 0.2*7 = 6.6. The optimal sampling point is Point A (highest score 6.8)." + }, + { + "id": 736, + "scenario_code": "4.9", + "instruction": " The sample container transfer process between the ascent vehicle and the lander requires: 1) The container temperature must be maintained at -50±5°C; 2) The RFID tag reading success rate must be ≥99%; 3) The transfer time window must be ≤15 minutes. Current telemetry data shows: container temperature -48°C, tag reading success rate 98%, remaining transfer window 12 minutes. The ground control center needs to immediately decide whether to continue the transfer or terminate it.", + "question": "Based on the constraints, determine if the current status meets the requirements for continuing the transfer? If not, specify the specific non-compliant parameters.", + "answer": "Does not meet the requirements for continuing the transfer. Non-compliant parameter: RFID tag reading success rate 98% (below the 99% threshold)." + }, + { + "id": 737, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. According to preliminary remote sensing data analysis, the target area has two typical types of lunar soil: Class A (hardness 3.5 Mohs, viscosity coefficient 0.8) and Class B (hardness 5.2 Mohs, viscosity coefficient 0.3). The engineering team is equipped with three sampling tools: a rotary impact drill (suitable for hardness 4-7, viscosity <0.6), an ultrasonic vibrating shovel (suitable for hardness 2-5, viscosity >0.5), and an adaptive grab (suitable for hardness 1-4, any viscosity). The unit sampling energy consumption of each tool is 15W·h/g, 8W·h/g, and 10W·h/g, respectively. The current lander has 1200W·h of available energy remaining.", + "question": "If the goal is to maximize the total amount of samples collected while ensuring the success rate of sampling, how should the above tools be combined to collect Class A and Class B lunar soil? Calculate the maximum total sample mass that can be obtained.", + "answer": "For Class A lunar soil, use the ultrasonic vibrating shovel (suitable for hardness 2-5 and viscosity >0.5); for Class B lunar soil, use the rotary impact drill (suitable for hardness 4-7 and viscosity <0.6). Maximum sample mass = min(1200/(8+15), 1200/23) = 52.17g" + }, + { + "id": 738, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting scientific investigations within the Von Kármán crater. Based on the high-spectral data from the orbiter, three candidate sampling points have been identified: P1 (68% probability of KREEP rock, 1.2km away), P2 (85% probability of volcanic glass, 2.3km away), P3 (92% probability of breccia, 3.1km away). The rover's moving speed is 0.05km/h, with an average daily operational duration of 4 hours, and it has a remaining lifespan of 15 Earth days. The scientific priority weights are: KREEP rock > volcanic glass > breccia.", + "question": "Considering the scientific value and time constraints, how should the optimal investigation route be planned? Calculate the highest priority sampling point combination that can be achieved.", + "answer": "Prioritize P1 (KREEP rock), the round trip will take 2*1.2/0.05=48h=12 Earth days; with 3 days remaining, it is possible to reach P2 (one-way trip requires 2.3/0.05/4=11.5 days), thus the optimal route is to only collect P1." + }, + { + "id": 739, + "scenario_code": "1.8", + "instruction": " When deploying a seismometer array, the lunar rover measured the local soil bearing capacity to be 8.5 kPa. Each seismometer has a mass of 12 kg and a base contact area of 0.015 m². The safety factor requires that the actual pressure does not exceed 70% of the bearing capacity. The lunar surface gravitational acceleration is known to be 1.62 m/s², and the deployment area has a measurement error of ±0.3 kPa.", + "question": "Calculate the actual pressure generated by a single seismometer (unit: kPa, retain two decimal places), and determine whether it is necessary to increase the base area.", + "answer": "1.30" + }, + { + "id": 740, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (180°E, 45°S). The ground station is located in Kashgar, China (76°E, 39°N). It is known that the Queqiao-2 relay satellite is operating in a Halo orbit around the Earth-Moon L2 point, at an altitude of about 80,000 km above the lunar surface. At the current moment, the relative positions of the Sun, Earth, and Moon result in a 12° lunar occultation angle between the Kashgar station and the lander. The Queqiao-2 requires a minimum elevation angle of 5° for coverage of the lunar surface, and its X-band antenna gain is 42 dB.", + "question": "Calculate the maximum allowable path loss (dB) for establishing a communication link between the ground station and the lander via Queqiao-2 under the current conditions, given the free space loss formula: Lfs = 32.45 + 20log10(f) + 20log10(d), where f is the frequency (MHz), and d is the distance (km). Assume the operating frequency is 8450 MHz, and ignore atmospheric and polarization losses.", + "answer": "First, calculate the distance from the Earth-Moon L2 point to the lunar surface: d = 80,000 km. The free space loss Lfs = 32.45 + 20log10(8450) + 20log10(80000) ≈ 32.45 + 78.53 + 98.06 = 209.04 dB. Considering the antenna gain compensation of 42 dB for the minimum elevation angle of 5°, the maximum allowable path loss is 209.04 - 42 = 167.04 dB." + }, + { + "id": 741, + "scenario_code": "3.6", + "instruction": " The Chang'e-4 relay satellite is about to enter the lunar night phase (lasting 14 Earth days), and it needs to maintain a cabin temperature range of -40°C to +50°C. Key equipment: ① X-band transceiver (minimum operating temperature -30°C, steady-state power consumption 25W); ② Lithium-ion battery pack (optimal operating range -20°C to +40°C); ③ On-board computer (temperature tolerance -55°C to +85°C). Insulation configuration: Overall thermal conductivity of multi-layer insulation material 0.05W/(m·K); total heat output of isotope heat source 30W; electric heater standby power 60W. Cabin surface area 8m², average temperature difference with the external environment 200°C.", + "question": "Calculate whether a low-temperature fault will occur in the cabin relying solely on the isotope heat source? If the electric heater needs to be activated, determine its minimum supplementary power (ignoring self-heating of the equipment).", + "answer": "A low-temperature fault will occur. Calculation steps: 1) Heat loss = 0.05 * 8 * 200 = 80W; 2) Net heat supply from the heat source = 30 - 80 = -50W < 0; 3) The X-band transceiver will fall below the limit. The electric heater needs to be activated to supplement at least 50 + 25 = 75W (to meet the X-band requirement) or 50 + (25 * 14/24) = 64.6W (time-weighted), taking the larger value of 75W." + }, + { + "id": 742, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. The characteristics of the soil in this area are: medium hardness (Mohs hardness 4-5), low viscosity, and a higher content of volatiles (about 3%). There are three sampling tools available: 1) a diamond-coated rotary drill (suitable for hardness > 6), 2) a titanium alloy grab (suitable for viscosity > 50Pa·s), 3) a stainless steel scraper (suitable for volatiles < 2%). The working energy consumption of each tool is: drill 15W/h, grab 8W/h, scraper 5W/h. The mission requires that the sampling time does not exceed 30 minutes, and the total energy consumption does not exceed 10Wh.", + "question": "According to the given conditions, which sampling tool should be chosen? Please explain the basis for your choice and verify whether it meets the energy consumption constraint.", + "answer": "The titanium alloy grab should be chosen. Basis: 1) The hardness of the lunar soil (4-5) is below the standard suitable for the drill; 2) The viscosity is below the value suitable for the grab but is the closest; 3) The scraper does not meet the volatile content requirement. Verification: Grab energy consumption = 8W * 0.5h = 4Wh < 10Wh, which meets the constraint." + }, + { + "id": 743, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration near the Von Kármán crater. Pre-acquired remote sensing data shows three candidate sampling points: Point A (probability of KREEP rock 85%, distance 1.2km), Point B (probability of breccia 70%, distance 0.8km), Point C (probability of volcanic glass 60%, distance 0.5km). The rover's moving speed is 0.05km/h, and the scientific investigation time budget is 24 hours, with each sampling point requiring a 2-hour stay for analysis. The priority weight for rocks is: KREEP rock 3 points, breccia 2 points, volcanic glass 1 point.", + "question": "If at least two sampling points need to be visited within the time budget, which two points should be chosen to maximize scientific value? Provide the calculation process.", + "answer": "Points A and C should be chosen. Calculation process: 1) AB combination time consumption = (1.2 + 0.4) / 0.05 + 4 = 36h > 24h; 2) AC combination time consumption = (1.2 + 0.7) / 0.05 + 4 = 22h ≤ 24h, value = 85% * 3 + 60% * 1 = 3.15; 3) BC combination time consumption = (0.8 + 0.7) / 0.05 + 4 = 22h ≤ 24h, value = 70% * 2 + 60% * 1 = 2.0. The AC combination has the highest value and meets the time constraint." + }, + { + "id": 744, + "scenario_code": "1.4", + "instruction": " The lunar energy grid needs to power 3 scientific instruments: a seismometer (continuous power consumption of 20W), a spectrometer (peak power consumption of 150W per 10-minute operation), and a mobile rover (average power consumption of 30W, including 5 200W sprints per day). The solar array has an average daily power generation of 1800Wh, and the battery pack has an effective capacity of 1200Wh. The night lasts for 14 Earth days, and the equipment priority is seismometer > rover > spectrometer.", + "question": "Assuming the battery is fully charged before entering the lunar night, calculate the maximum number of times the spectrometer can operate daily without causing a system shutdown (assuming energy is distributed strictly according to priority, ignoring transmission losses).", + "answer": "Total energy consumption during the night = (20W*14*24h + 30W*14*24h) /1000 = 16.8kWh; Available battery capacity = 1.2kWh - (16.8-18*0.3)kWh = -11.4kWh (insufficient), so the spectrometer cannot operate during the lunar night. Available surplus energy during the day = (1800-(20+30)*24)/1000 = 0.6kWh; Single operation energy consumption of the spectrometer = 150W*10/60h = 25Wh; Maximum number of operations per day = floor(600/25) = 24 times." + }, + { + "id": 745, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform rock sampling, the one-way communication delay between Earth and the Moon is 1.3 seconds. The current speed of the lunar rover is 0.2m/s, and a target rock is found 3 meters ahead. The transmission of control instructions takes 50ms, and the onboard control system has a response delay of 200ms. To ensure that the robotic arm can stop accurately when it is 0.5 meters away from the rock, the braking command needs to be sent in advance.", + "question": "Calculate the latest decision-making time (in seconds) from the discovery of the target to the issuance of the braking command, ensuring that the parking position error does not exceed ±0.1 meters.", + "answer": "4.35 seconds" + }, + { + "id": 746, + "scenario_code": "3.6", + "instruction": " The Yutu-2 rover is about to enter the lunar night hibernation phase. Its lithium-ion battery pack has a capacity of 120Wh and needs to maintain a temperature above -20°C for safety. The scientific instruments' hibernation power consumption is 5W, and the electric heater has adjustable power settings (10W/20W/30W). The lunar night lasts 14.77 Earth days, and the current battery SOC is 65%. Insulation material ensures the heat loss rate meets the formula: heat loss power = 2 * (T_internal - T_ambient) W/°C, with the expected minimum ambient temperature during the lunar night being -180°C.", + "question": "To ensure the system safely survives the lunar night while retaining 10% battery redundancy, calculate which heating power setting (considering only steady-state thermal balance) should be chosen.", + "answer": "Choose the 20W setting. In steady state, heat loss = heating power → 2 * (-20 - (-180)) = 320W needs to be offset, but in practice, maintaining -20°C by adjusting the heating setting is sufficient. Total energy consumption = (5W + 20W) * 14.77 * 24h = 8854.8Wh, available battery energy = 120 * 65% * 90% = 70.2Wh > 88.548Wh, which is not sufficient, requiring a re-evaluation of initial conditions or strategy." + }, + { + "id": 747, + "scenario_code": "1.8", + "instruction": " When deploying a network of lunar surface magnetometers, the magnetic field strength at a certain point was measured to be 152nT, with background noise ±3nT. The instrument installation requires a horizontal tilt angle of less than 5 degrees to ensure measurement accuracy. Real-time monitoring shows that the current bracket tilt is 7 degrees, and each adjustment of 1 degree requires 2 minutes (during which the magnetic field readings are unavailable). The area is about to enter the lunar night (with a remaining operational time window of 15 minutes).", + "question": "Determine whether it is possible to complete the adjustment and obtain valid data within the time window (meeting: single continuous measurement duration ≥30 seconds and noise fluctuation ≤2nT), and provide an adjustment plan or abandonment recommendation.", + "answer": "Abandon adjustment and directly collect data" + }, + { + "id": 748, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the lunar soil in this area are as follows: average hardness is 3.5 Mohs (between calcite and fluorite), viscosity coefficient is 1200 Pa·s (similar to moist clay), and volatile content is approximately 0.8 wt%. There are three sampling tools available: ① Diamond-coated rotary impact drill bit (suitable for hardness >4 Mohs, power consumption 300W) ② Titanium alloy grab (suitable for viscosity <1000 Pa·s, power consumption 150W) ③ Tungsten carbide scraper (suitable for volatile content >1 wt%, power consumption 200W). The mission requires a sampling depth ≥20cm and a single operation time ≤30 minutes.", + "question": "Based on the given lunar soil characteristics and tool parameters, calculate which tool can meet all the constraints? List the specific judgment steps.", + "answer": "Choose the tungsten carbide scraper. Judgment steps: 1) Hardness 3.5 Mohs < 4 Mohs, eliminate the diamond drill bit; 2) Viscosity 1200 Pa·s > 1000 Pa·s, eliminate the titanium alloy grab; 3) Volatile content 0.8 wt% < 1 wt% but the difference is minimal, and the scraper's power consumption of 200W can meet the 30-minute operation (energy consumption = 200 * 0.5 = 100Wh within the budget)." + }, + { + "id": 749, + "scenario_code": "4.4", + "instruction": " Yutu-2 obtained the following remote sensing data while patrolling the Von Kármán crater: ① Hyperspectral images show that the KREEP rock characteristic absorption peak (a 40% sudden drop in reflectivity at a wavelength of 950nm) exists at coordinates (12.3°S, 135.7°E) ② LiDAR shows a slope of 8° at this point ③ Thermal infrared data indicates that the maximum temperature during the day reaches 120°C. The prior geological model predicts a 72% probability of KREEP rock abundance in this area. The mission requires prioritizing sampling sites with distinct spectral features (reflectivity change > 30%), slope < 10°, and temperature tolerance up to 150°C.", + "question": "Does this coordinate meet the high-priority sampling criteria? Which key indicators need to be verified one by one? ", + "answer": "It meets the high-priority criteria. Verification indicators: 1) Reflectivity change 40% > 30%; 2) Slope 8° < 10°; 3) Temperature 120°C < 150°C; 4) Prior probability of 72% provides additional support." + }, + { + "id": 750, + "scenario_code": "1.2", + "instruction": " Deploy a lunar-based telescope array unit at the edge of Shackleton Crater in the lunar south pole. The device consists of a primary mirror module (120kg), a support structure (80kg), and an electronic control box (60kg), which must be installed in a specific order: 1) The support structure must be deployed first to provide a stable base; 2) The electronic control box must be installed before the primary mirror module, as it contains the calibration circuit; 3) The primary mirror module must be powered immediately after installation to activate the dust cover. The maximum single lift weight of the lander's robotic arm is 150kg, and it requires a 10-minute cooldown after each operation. The lunar surface temperature is -180°C, and electronic equipment may fail if exposed for more than 15 minutes.", + "question": "Design an installation sequence that meets all constraints and calculate the minimum total time required (excluding robotic arm movement time).", + "answer": "Installation sequence: support structure (80kg) → electronic control box (60kg) → primary mirror module (120kg). Total time: 10 minutes cooldown after the support structure is installed; the electronic control box is installed and immediately powered (dust cover activated), no additional cooldown required; the primary mirror module installation takes 0 minutes (assuming immediate completion). Total time 10 minutes." + }, + { + "id": 751, + "scenario_code": "1.4", + "instruction": " A solar energy grid powers three devices: a drill (peak power 300W, priority 1), a spectrometer (continuous power 150W, priority 2), and a communication relay (base power 50W, priority 3). The solar array has a maximum output of 400W, and the battery can provide an additional 100W but will accelerate aging. Current lighting conditions can only maintain 300W of solar output, and the drill is about to enter a 30-minute rock crushing phase (requiring full load operation).", + "question": "How should power resources be allocated to ensure all devices operate normally? Please list the actual power values received by each device.", + "answer": "Drill 300W (fully supplied) + Spectrometer 0W (temporarily shut down) + Communication Relay 50W (base supply). The battery provides 50W of additional power (300W solar + 50W battery = 350W, meeting the drill's 300W + relay's 50W)." + }, + { + "id": 752, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S). The ground station is located in Kashgar, China (longitude 76°E), and uses the X-band (8.4GHz) to establish a communication link with the Queqiao-2 relay satellite. It is known that:\n1. Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, with an average altitude of about 8000km above the lunar surface.\n2. At the current moment, the Moon's rotation has caused the line-of-sight elevation angle between the lander and Queqiao-2 to be 25°.\n3. The free space loss formula for the X-band is: L = 20 * log10(d) + 20 * log10(f) + 92.45 (d: km, f: GHz).\n4. The ground station antenna gain is 45dBi, and the relay satellite antenna gain is 38dBi.", + "question": "Calculate the free space loss value of the current Earth-Moon communication link (保留两位小数), and determine whether this elevation angle meets the minimum communication threshold of 20°? ", + "answer": "The free space loss L = 20 * log10(8000) + 20 * log10(8.4) + 92.45 ≈ 20 * 3.9031 + 20 * 0.9243 + 92.45 ≈ 78.06 + 18.49 + 92.45 = 189.00 dB; the current elevation angle 25° > 20°, meeting the communication requirement." + }, + { + "id": 753, + "scenario_code": "5.7", + "instruction": " The 128GB NAND flash memory of the Chang'e-7 relay satellite has the following conditions:\n1. The bad block rate has reached the manufacturer's specified threshold of 0.5%\n2. The SSD controller uses a dynamic wear-leveling algorithm, with an average of 1500 program/erase cycles currently\n3. The file system uses CRC32 checksum and AES-256 encryption\n4. The daily data write volume fluctuates between 12 to 18GB", + "question": "Calculate the remaining theoretical life of the current flash memory (in days), assuming the manufacturer's specified maximum program/erase cycles is 3000.", + "answer": "Remaining program/erase cycles = 3000 - 1500 = 1500 cycles; the average daily write volume is taken as the mid-value of 15GB; daily program/erase cycles = 15GB / 128GB ≈ 0.117 cycles; remaining life = 1500 / 0.117 ≈ 12821 days" + }, + { + "id": 754, + "scenario_code": "3.4", + "instruction": " During the lunar day, Yutu-2 needs to perform three tasks simultaneously: ① Continuous observation by the X-ray spectrometer (power consumption 30W, high priority); ② Sampling by the robotic arm (instantaneous peak power consumption 120W, lasting 3 minutes, medium priority); ③ Data transmission (power consumption 50W, requiring at least a 15-minute continuous communication window, low priority). The current remaining capacity of the lithium-ion battery is 800Wh, and the real-time power generation capacity of the solar panel is 80W. The thermal control system requires a basic power consumption of 20W to be maintained continuously.", + "question": "If there are still 2 hours until the lunar night, determine whether it is permissible to immediately start the robotic arm sampling without affecting high-priority tasks? Explain the energy distribution strategy.", + "answer": "Starting is allowed. Energy distribution strategy: ① Total available energy = 800Wh from the battery + 2h*80W from the solar panel = 960Wh; ② Essential items: X-ray spectrometer 30W*2h=60Wh + thermal control 20W*2h=40Wh + data transmission 50W*0.25h=12.5Wh (minimum communication window) = 112.5Wh; ③ Robotic arm energy consumption 120W*0.05h=6Wh; ④ Remaining energy 960-112.5-6=841.5Wh is sufficient, and the battery can still support all high-priority tasks after sampling." + }, + { + "id": 755, + "scenario_code": "5.7", + "instruction": " The 128GB onboard SSD of the Chang'e-7 orbiter has been operating for 3 years, using NAND flash memory chips (block size 128KB, lifespan 3000 write-erase cycles). Monitoring found: Chip A's blocks 3 and 7 have wear counts of 2900; Chip B's block 20 is damaged; the overall storage utilization is 70%. Currently, 10GB of newly generated high-orbit data (single file 1GB) needs to be stored, and the file system uses a dynamic wear-leveling strategy.", + "question": "Please explain the specific steps for bad block avoidance and wear leveling during the write process, and calculate the expected average wear count increment for new blocks.", + "answer": "Steps: 1) Mark block 20 of Chip B as a bad block; 2) Add blocks 3 and 7 of Chip A to the disabled pool; 3) Allocate space from the blocks with the lowest wear count; 4) 10GB requires 81920 128KB blocks (10*1024*1024/128). Wear increment calculation: Total valid blocks = (128GB*1024/128KB)*70% - 3 bad blocks = 7165 blocks; Average wear count increase per new block = 81920/7165 ≈ 11.43 times." + }, + { + "id": 756, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the Von Kármán crater within the South Pole-Aitken Basin (SEL) on the far side of the Moon (coordinates: 177.6°E, 45.5°S). The ground station is located at the Kashgar Deep Space Station in China (longitude 76°E). At the current moment, the Moon's rotation has caused the lander to be blocked from the Kashgar station by the Moon's body. It is known that the Queqiao-2 relay satellite is in a Halo orbit around the Earth-Moon L2 point, about 8000km above the lunar surface, with an antenna opening angle of 60° to the Moon and 30° to the Earth. The current angle between the line connecting the relay satellite to the Moon's center and the Earth-Moon line is 15° (the Earth-Moon distance is taken as 380,000km).", + "question": "Please calculate whether the ground station can establish a communication link with the lander via Queqiao-2 at the current moment? Explain the basis for your judgment step by step.", + "answer": "1) Queqiao's lunar coverage determination: The antenna opening angle of 60° corresponds to a lunar surface arc length = 2*π*1737km*(60/360) = 1816km. The distance from the Von Kármán crater to the projection point on the lunar surface = 8000km*tan(15°) = 2145km > 1816km → exceeding the coverage range; 2) Earth coverage determination: The angle between the Earth and the relay satellite is 15° < 30°/2 → the Kashgar station is within the coverage range. Conclusion: A complete link cannot be established (although the relay satellite can see the ground station, it cannot see the lander)." + }, + { + "id": 757, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. Analysis of the soil characteristics in this area shows: the surface layer 0-30cm consists of loose fine particles (viscosity index 0.3, Mohs hardness 2.5), and there is a cemented layer at 30-50cm (viscosity index 1.2, Mohs hardness 4.0). The probe is equipped with three sampling tools: ① Rotary impact drill (suitable for hardness >3.5, power consumption 8W/min) ② Vibration sampling tube (suitable for viscosity <1.0, power consumption 5W/min) ③ Electric shovel (universal, power consumption 3W/min but unstable sampling volume). The mission requires prioritizing the integrity of the samples, with secondary consideration for energy consumption.", + "question": "Based on the above lunar soil characteristics and tool parameters, which sampling tool combination should be chosen to complete the full-depth sampling from 0-50cm? Provide specific stratified selection criteria.", + "answer": "For 0-30cm, use the vibration sampling tube (viscosity 0.3<1.0 and hardness 2.5<3.5), and for 30-50cm, use the rotary impact drill (hardness 4.0>3.5 and viscosity 1.2>1.0). The electric shovel is excluded due to its unstable sampling." + }, + { + "id": 758, + "scenario_code": "1.4", + "instruction": " A month-facing energy grid powers three scientific payloads: a seismometer (continuous power 20W), a spectrometer (peak power 150W, duty cycle 30%), and a rover charging station (required power 200W, daily charging window 2 hours). The energy system consists of a solar array (average daily power generation 1.8kWh) and a lithium battery pack (total capacity 5kWh, charge/discharge efficiency 90%). During the lunar day, the solar array directly powers the system, with excess power stored in the battery; during the lunar night, the system is powered solely by the battery. The priority order for all devices is: seismometer > rover charging > spectrometer.", + "question": "At the beginning of the lunar night when the battery is at full capacity, calculate the longest number of hours the system can support all devices running (considering the priority scheduling strategy).", + "answer": "Total available energy during the lunar night: 5kWh * 90% = 4.5kWh. Priority allocation: 1) Seismometer 20W continuous operation consumes 0.02kW*h; 2) Rover charging 200W*2h=0.4kWh; 3) Remaining energy 4.5-0.02*24-0.4=3.62kWh allocated to the spectrometer, can support 150W*30%=45W operation time=3.62kWh/0.045kW≈80.44 hours. However, limited by the length of the lunar night 350 hours, the actual longest support time is to maintain the seismometer and rover power throughout the lunar night, the spectrometer can run (4.5-0.02*350-0.4)/0.045≈24 hours." + }, + { + "id": 759, + "scenario_code": "1.5", + "instruction": " The control center operates the lunar rover for rock sampling through a remote operation system between Earth and the Moon. Known parameters: one-way communication delay 1.28 seconds; maximum rover travel speed 0.1m/s; end-effector positioning accuracy of the robotic arm ±5mm; target rock is 2.3 meters away from the current position. The control system uses predictive display technology, performing collision detection rehearsals before sending commands. The emergency braking command takes 50ms to take effect.", + "question": "When the lunar rover approaches the target at its maximum speed, if an obstacle is suddenly detected at a remaining distance of 0.6 meters, calculate the minimum safe stopping distance from the issuance of the braking command to the complete stop of the vehicle (considering communication delay and braking response time).", + "answer": "Total delay=command transmission 1.28s + braking effectiveness 0.05s=1.33s; distance traveled by the vehicle during this period=0.1m/s*1.33s=0.133m; minimum safe stopping distance=remaining distance 0.6m - travel distance 0.133m=0.467m. Therefore, the obstacle detection point must be at least 0.467 meters ahead of the target position." + }, + { + "id": 760, + "scenario_code": "4.9", + "instruction": " When the ascent vehicle hands over the sample container to the lander, the following conditions must be met: ① The internal temperature of the container must be maintained at -50±5℃ (current reading -48℃); ② Sealing pressure > 10kPa (current 12kPa); ③ RFID tag signal strength ≥ 80dB (current 85dB). The handover process takes 6 minutes, during which the temperature rises by 0.8℃ per minute, the pressure drops by 0.3kPa per minute, and the signal strength remains unchanged. Ground instructions require that the handover must only be initiated when all parameters are within limits.", + "question": "Determine if the current status allows for immediate handover? If not, what is the maximum delay before starting the handover is allowed to ensure all parameters remain within limits during the process.", + "answer": "Immediate handover is not possible. The temperature will rise to -48+6*0.8=-43.2℃ (out of limit) after 6 minutes, and the pressure will drop to 12-6*0.3=10.2kPa (within limit). The maximum delay is determined by the temperature: (55-48)/0.8=8 minutes and 45 seconds, rounding down to 8 minutes when the temperature is -48+8*0.8=-41.6℃, which is still within the limit." + }, + { + "id": 761, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is on a patrol mission from point A (coordinates [10,20]) to point B (coordinates [50,60]). Terrain data indicates two possible routes: Route 1 is a straight distance of 70 meters but requires crossing a 15° slope, while Route 2 is a zigzag distance of 85 meters with a slope of less than 5°. It is known that the motor efficiency of the lunar rover is 85% at a 5° slope and drops to 65% at a 15° slope. The energy consumption per unit distance on flat ground is 0.1kWh/m, and the additional energy consumption formula for slopes is E_add = 0.05 * slope (°) * distance (m). The battery currently has 8kWh of remaining power, and at least 1kWh must be reserved for emergencies.", + "question": "Please calculate the total energy consumption for both routes and determine which route can ensure safe arrival and is the most energy-efficient.", + "answer": "Total energy consumption for Route 1 = 70 * (0.1 + 0.05 * 15) * 0.65 = 70 * 0.85 * 0.65 = 38.675kWh; Total energy consumption for Route 2 = 85 * (0.1 + 0.05 * 5) * 0.85 = 85 * 0.125 * 0.85 = 9.03125kWh; Only Route 2 meets the requirement of 8-1=7kWh available power and is more energy-efficient." + }, + { + "id": 762, + "scenario_code": "2.7", + "instruction": " When the lunar rover is operating near the terminator and receives a solar proton event warning, it needs to reach an emergency shelter 3 kilometers away within 30 minutes. The current lighting conditions make visual navigation unreliable, and it can only rely on IMU (drift rate 0.01°/s) and pre-deployed UWB beacons (ranging accuracy ±3m). It is known that the initial alignment error is zero, the UWB beacon is located at the center of the shelter, and the maximum safe speed of the lunar rover is 0.2m/s.", + "question": "Determine whether relying solely on IMU navigation meets the arrival accuracy requirement (shelter radius is 10m), and explain the reason.", + "answer": "30-minute IMU angle drift = 0.01 * 1800 = 18°, position deviation = 3000m * sin(18°) ≈ 927m >> 10m radius; does not meet the accuracy requirement, must activate UWB-assisted navigation." + }, + { + "id": 763, + "scenario_code": "2.5", + "instruction": " The Chang'e-7 rover, while driving in a permanently shadowed area, detects a fresh impact crater 50 meters ahead with a diameter of 3 meters (slope > 30°) using its forward-looking stereo camera, and the LiDAR shows a 1.5-meter wide lunar fissure 20 meters to the right. It is known that: 1) The minimum turning radius of the rover is 2 meters; 2) The maximum safe side tilt angle is 25°; 3) The current speed is 0.1m/s; 4) IMU data shows a 15° slope on the right side.", + "question": "Please analyze the obstacle avoidance strategy the rover should adopt and explain the basis for your choice.", + "answer": "The rover should turn right to avoid the impact crater. Basis: 1) There is no data on the left side and there may be unknown risks; 2) The width of the lunar fissure on the right (1.5m) is less than the vehicle width (2m) and cannot be crossed; 3) The slope on the right side is 15° < 25° safety threshold, and safe detour can be achieved by decelerating + minimum turning radius." + }, + { + "id": 764, + "scenario_code": "2.9", + "instruction": " The lunar orbit navigation satellite LBNSS-1 establishes a two-way ranging link with Yutu-3. Known: 1) LBNSS-1 orbit height 200km, current elevation angle 60°; 2) UWB ranging accuracy ±0.5m; 3) IMU position error accumulation rate 1m/hr; 4) Last landmark correction time was 2 hours ago, at which time the positioning error was 0.3m. The ranging data shows that the distance between the satellite and the rover is 215.6km (ionosphere delay corrected).", + "question": "Calculate the upper limit of the current positioning error of Yutu-3 and explain the main sources of error.", + "answer": "The upper limit of positioning error is 2.8m. Calculation process: 1) IMU accumulated error=1*2=2m; 2) UWB ranging error=±0.5m projected onto the horizontal plane ≈ 0.5/sin60°=0.58m; 3) Combined error=sqrt(0.3^2+2^2+0.58^2)=2.8m. The main error source is IMU long-term drift (contributes 71%)." + }, + { + "id": 765, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, a shared power grid needs to be constructed consisting of 3 mobile energy modules (MEMs). Each MEM has a maximum output power of 500W, but due to the low temperatures of the lunar night, the actual available power must be multiplied by a temperature factor of 0.7. The scientific payload includes: 1 seismometer (continuous power consumption 80W), 2 spectrometers (each with a peak of 150W, probability of simultaneous operation 60%), and 1 drilling device (instantaneous start-up requires 300W/10 minutes, average daily start-up 3 times). The communication relay station needs to ensure a minimum continuous power supply of 100W.", + "question": "If the system's redundant power is required to be no less than 20% of the total demand, can this power grid meet the needs of all equipment? (The calculation steps need to include temperature correction, instantaneous load conversion, and redundancy verification.)", + "answer": "Yes. Calculation process: 1) Total available power of MEMs=3*500*0.7=1050W; 2) Basic load=80+100=180W; 3) Expected load of spectrometers=2*150*0.6=180W; 4) Average daily load of drilling=300*(10/1440)*3≈6.25W; 5) Total demand=180+180+6.25=366.25W; 6) Demand including redundancy=366.25*1.2≈439.5W＜1050W" + }, + { + "id": 766, + "scenario_code": "2.7", + "instruction": " When the Chang'e-7 lander is working at the edge of the Shackleton crater, it suddenly receives a solar proton event warning: high-energy particles are expected to reach the lunar surface in 30 minutes and last for 4 hours. The lander is currently near the terminator (unstable lighting conditions) and needs to urgently take shelter in a permanent shadow area 2km away. Known: 1) Normal moving speed is 0.1m/s; 2) In emergency mode, the speed can be increased to 0.3m/s but with double energy consumption; 3) The shelter entrance requires precise parking (error <0.5m) and an additional 5 minutes for adjustment.", + "question": "To ensure safe arrival, when at the latest must the lander switch to emergency mode? Assume there are no obstacles on the path from the current position to the shelter.", + "answer": "Latest start time: 8 minutes after the warning. Total time required = (2000m/0.3m/s)/60 +5 ≈16.1 minutes, 30-16.1≈13.9 minutes buffer, 8 minutes in normal mode can travel 48m (0.1*8*60), the remaining 1952m needs (1952/0.3)/60≈10.8 minutes, total 8+10.8+5=23.8<30 minutes" + }, + { + "id": 767, + "scenario_code": "2.7", + "instruction": " The lunar rover has received a solar proton event warning and needs to reach a safe haven within a 500-meter radius in 30 minutes. Current status: 1) Remaining power is 300Wh; 2) The safe haven route consists of two segments: the first segment is 200 meters of flat terrain (power consumption 60W), and the second segment is 300 meters of a 3° incline (power consumption 90W); 3) The maximum speed is 0.1m/s, and 5 minutes must be reserved for emergency maneuvers.", + "question": "Verify whether the current plan meets both time and energy requirements? (The calculation process should include total travel time and total energy consumption.)", + "answer": "Total travel time = (200+300)/0.1 = 5000 seconds ≈83.3 minutes >25 minutes available time (30-5), does not meet the time requirement; Total energy consumption = (60*200 +90*300)/1000 =39Wh <300Wh, only energy is sufficient." + }, + { + "id": 768, + "scenario_code": "2.10", + "instruction": " When the lunar rover is performing centimeter-level close-up observations of a 1-meter diameter olivine outcrop, the stereo vision system measures the pixel coordinates of the target's left edge (320,240) and right edge (380,240). The camera focal length is 1000 pixels, the baseline distance is 0.2 meters, and the actual width of the target is known to be 1 meter. The current pose control accuracy is ±0.5cm (3σ).", + "question": "Calculate the current distance between the lunar rover and the target, and determine whether it is necessary to adjust the position to meet the ±3cm docking accuracy requirement.", + "answer": "Disparity = (380-320) = 60 pixels, distance Z = baseline distance * focal length / disparity = 0.2 * 1000 / 60 ≈ 3.33 meters. Since the 3σ accuracy of ±0.5cm is already higher than the ±3cm requirement, no position adjustment is needed." + }, + { + "id": 769, + "scenario_code": "1.4", + "instruction": " Three scientific instruments (A, B, C) have been deployed in the permanently shadowed regions of the Moon's south pole, sharing a solar power network. Instrument A (seismometer) needs to operate continuously with a peak power of 20W; Instrument B (spectrometer) operates for 15 minutes every 2 hours with a peak power of 50W; Instrument C (drill) operates 3 times a day, each time for 10 minutes, with a peak power of 150W. The power network has a maximum output of 180W and must reserve 30W of redundancy to handle sudden loads. The operating times of all instruments cannot be adjusted.", + "question": "If instruments B and C enter their working cycles simultaneously, how should the system allocate power to meet all constraints? ", + "answer": "Prioritize the 20W requirement for instrument A, and from the remaining 160W (180W-20W), allocate 50W to instrument B and 110W to instrument C (since 150W exceeds the remaining capacity, C must be limited to 110W). At this point, the total load is 20+50+110=180W, meeting the redundancy requirement." + }, + { + "id": 770, + "scenario_code": "1.5", + "instruction": " The Yutu-2 lunar rover needs to remotely control its robotic arm to grab rock samples under a 1.3-second communication delay. The maximum movement speed of the robotic arm's end effector is 0.1m/s, and the target rock is 0.25m away from the current arm end position. After the ground control center sends a movement command, it must wait for the action completion feedback before sending the next command.", + "question": "Calculate the shortest theoretical time from sending the movement command to receiving the feedback confirmation (ignoring signal transmission processing time)?", + "answer": "Movement time = distance / speed = 0.25 / 0.1 = 2.5 seconds; Total time = movement time + 2 * communication delay = 2.5 + 2 * 1.3 = 5.1 seconds" + }, + { + "id": 771, + "scenario_code": "1.8", + "instruction": " When deploying a magnetometer array on the lunar surface, it was found that the local lunar soil bearing capacity is only 0.8N/cm². Each magnetometer weighs 3kg, and the base contact area is 50cm². It is known that the lunar gravitational acceleration is 1.62m/s².", + "question": "Determine whether direct deployment will cause the equipment to sink? Provide specific calculation basis.", + "answer": "Pressure of a single unit on the lunar soil = weight * gravitational acceleration / area = (3 * 1.62) / 50 = 0.0972N/cm² < 0.8N/cm², it will not sink." + }, + { + "id": 772, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. Analysis of the lunar soil characteristics in this area shows: the top 0-30cm is loose fine particles (viscosity coefficient k=0.8 Pa·s), and 30-50cm contains high-hardness basalt fragments (Mohs hardness 6.5). The probe is equipped with three sampling tools: ① Rotary impact drill (suitable for hardness >5, power consumption 120W/min) ② Vibration sampling tube (suitable for viscosity <1 Pa·s, power consumption 80W/min) ③ Electric shovel (only suitable for the top 20cm). The current remaining energy can support 1500W·min of work.", + "question": "If it is necessary to obtain samples at a depth of 50cm while ensuring the success rate of sampling, which tool combination should be chosen? Calculate the maximum allowable working time.", + "answer": "Tool combination selection: First use the electric shovel to collect 0-20cm (no energy consumption), then use the vibration sampling tube to collect 20-30cm (time t1=10min*80W/min=800W·min), and finally use the rotary impact drill to collect 30-50cm (time t2=20min*120W/min=2400W·min). Since the total energy consumption (3200W·min) exceeds the limit, the plan is adjusted to use only the rotary impact drill to drill directly from 0-50cm, time t=1500/120=12.5 minutes, which can reach a depth of 37.5cm but cannot complete the goal. Therefore, additional energy supply needs to be applied for or the sampling depth requirement needs to be modified." + }, + { + "id": 773, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. Known: ① The container uses a double-layer titanium alloy seal, RFID tag frequency 13.56MHz ② The standard inspection process includes: a) Sealing pressure test (maintain 10kPa negative pressure for 5 minutes with a leakage rate <0.1Pa/s) b) RFID read/write test (signal strength >60dBμV) c) Temperature recorder calibration (-50℃~+50℃ linear error <±1℃). Current telemetry data: Leakage rate 0.08Pa/s, RFID signal 58dBμV, temperature calibration error +0.8℃.", + "question": " ", + "answer": "Non-compliant items: 1) RFID signal strength 58dBμV < 60dBμV threshold, it is recommended to check the antenna contact or increase the transmission power; 2) Temperature calibration error +0.8℃ is close to the upper limit but not exceeded, acceptable; 3) Leakage rate meets the standard. The main issue is the weak RFID signal, electromagnetic interference needs to be ruled out or the tag replaced and re-inspected." + }, + { + "id": 774, + "scenario_code": "4.4", + "instruction": " Yutu-2 obtained data on three candidate sampling points while patrolling the Von Kármán crater: Point 1 (KREEP rock probability 70%, distance 200m), Point 2 (volcanic glass probability 85%, distance 350m), Point 3 (breccia probability 60%, distance 150m). The rover's movement energy consumption formula is E=0.8*d (d in meters), with a remaining energy of 3000J, and each sampling point requires a fixed energy consumption of 500J. Scientific priority weight: KREEP rock > volcanic glass > breccia.", + "question": "According to energy constraints and scientific value, which sampling point should be prioritized? List the remaining energy calculation process.", + "answer": "Point 1 (KREEP rock) should be prioritized. Calculation: Movement energy consumption = 0.8*200 = 160J, total energy consumption = 160+500 = 660J, remaining energy = 3000-660 = 2340J. Although Point 2 has the second-highest scientific value, the movement energy consumption of 280J would result in a total energy consumption of 780J exceeding the limit (3000-780=2220J is still sufficient but has a lower priority)." + }, + { + "id": 775, + "scenario_code": "4.9", + "instruction": " When the ascent vehicle transfers the sample container to the lander, the following conditions must be met: ① Container temperature maintained at -50±5℃; ② Sealing pressure <0.1Pa; ③ RFID tag signal strength ≥80dB. Current telemetry data: Temperature -48℃, pressure 0.05Pa, signal strength 75dB, remaining adjustable time 120 seconds. Temperature adjustment rate 2℃/min, depressurization rate 0.02Pa/min, signal enhancement requires at least 30 seconds to restart the RF module.", + "question": "Determine whether the current conditions meet the transfer requirements? If not, provide an adjustment plan and the required time.", + "answer": "Does not meet (insufficient signal strength). Adjustment plan: First, restart the RF module (30 seconds) to bring the signal up to standard, during which the temperature naturally fluctuates within the allowed range (-48±1℃), and the pressure has already met the standard and does not need adjustment. Total time consumed 30 seconds < 120 seconds remaining." + }, + { + "id": 776, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 lander is located in the South Pole-Aitken Basin on the near side of the Moon (88°S, 180°E), and its solar wings use a two-dimensional tracking method (azimuth ±180°, elevation 0°~90°). According to the lunar ephemeris, the current solar elevation angle on the lunar surface is 15°, and the azimuth angle is 45° (0° is due east, increasing counterclockwise). There is a 1.2-meter-high lunar rock blocking 3 meters to the east of the landing point. It is known that the size of a single solar wing is 0.6m×0.8m, and the power generation under standard illumination P0=120W/m², with shading causing a linear reduction in the illuminated area.", + "question": "If the current tracking angle setting for the solar wings is an azimuth of 135° and an elevation of 75°, calculate the actual illuminated area ratio and the instantaneous power generation (保留两位小数).", + "answer": "Illuminated area ratio = (0.8*0.6 - 0.5*0.36)/0.48=0.625, power generation = 120*0.625=75.00W" + }, + { + "id": 777, + "scenario_code": "2.10", + "instruction": " To precisely observe the olivine outcrop on the Aristarchus plateau (target point diameter 50cm), the lunar rover needs to complete the following within the optimal lighting conditions (remaining 15 minutes): 1) the final 2m approach from the current position to the target; 2) maintain attitude stability ≤0.1°/s. Control system parameters: translational speed v=0.05m/s (including 5cm position error), attitude adjustment time t=30*s (s is the angle value that needs to be corrected).", + "question": "Calculate the theoretical feasibility of completing the approach and attitude correction (initial deviation detected as 1.2°) within the time limit.", + "answer": "Approach time t1=2/0.05=40s>15*60s; attitude correction t2=30*1.2=36s; total time consumption 76s>900s, completely feasible with ample margin." + }, + { + "id": 778, + "scenario_code": "1.5", + "instruction": " When controlling the lunar rover to perform rock sampling in a rugged area, the turning instructions sent by the ground control center have a fixed delay of 1.3 seconds. The current speed of the lunar rover is 0.15m/s, and an unexpected obstacle (0.8 meters wide) appears 3 meters ahead. The maximum instantaneous braking deceleration of the on-board obstacle avoidance system is 0.12m/s^2, and the minimum turning radius is 1.5 meters. Given the lunar surface friction coefficient μ=0.6, and the lunar gravity acceleration g_moon=1.62m/s^2.", + "question": "Calculate and determine: Can the collision be avoided relying solely on the delayed instructions? If not, what emergency measures should the on-board autonomous system take (quantitative parameters required)?", + "answer": "The collision cannot be avoided. The braking distance required d = v^2/(2*a) = 0.15^2/(2*0.12) = 0.09375m, but during the delay, it has already moved s = v*t = 0.15*1.3 = 0.195m, leaving a distance of 3-0.195=2.805m > d. The autonomous system should initiate a turn, with the minimum turning radius of 1.5m < obstacle width of 0.8m, the turning angle θ = arcsin(0.8/1.5) ≈ 32° should be executed immediately." + }, + { + "id": 779, + "scenario_code": "1.8", + "instruction": " During the deployment of the lunar-based telescope, it was found that the local lunar soil bearing capacity is only equivalent to 650Pa on Earth (expected value 800Pa). The triangular bracket of the telescope has a single foot contact area of 0.025m², and the total mass is 48kg (including the shock absorption mechanism). After the bracket is unfolded, the lowest point is 0.4 meters from the lunar surface, and the maximum allowable tilt angle is 0.5°. The lunar surface temperature difference of 300°C causes the bracket material to expand and contract ΔL/L=1.2e-5/°C.", + "question": "Verify whether the current deployment plan meets the stability requirements? If not, provide two engineering adjustment measures and calculate the key parameters.", + "answer": "It does not meet the requirements. The pressure per foot P = (48*1.62)/(3*0.025) ≈ 1037Pa > 650Pa. Adjustment measures: 1) Increase the contact area to A_min=(48*1.62)/(3*650)≈0.04m²; 2) Increase the number of auxiliary support feet to n=(48*1.62)/(650*0.025)≈4.78→at least 5-foot bracket. Thermal deformation ΔL=0.4*1.2e-5*300=1.44mm < tilt tolerance (400mm*tan0.5°≈3.49mm)." + }, + { + "id": 780, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 lander is located on the edge of an impact crater at 23.5° East longitude and 12.8° North latitude on the near side of the Moon. According to the lunar calendar, the current lunar day will last 14 Earth days, with the solar elevation angle changing by 0.75° per hour. The lander is equipped with two-axis adjustable solar panels (each panel has an area of 2.4m² and a photovoltaic conversion efficiency of 28%), and due to the shading effect of a 3-meter-high terrain to the west, the actual daily sunlight exposure time is 2 hours less than the theoretical value. The solar radiation intensity on the lunar surface is 1368W/m².", + "question": "If the current solar elevation angle is 15°, and the solar panels use the optimal two-dimensional tracking strategy (the normal always points to the sun), calculate the real-time power generation of a single panel (保留两位小数).", + "answer": "1368 * 2.4 * 0.28 * sin(15°) = 238.32 W" + }, + { + "id": 781, + "scenario_code": "3.8", + "instruction": " Chang'e-7 relay satellite executes energy budget in lunar orbit: orbital period 2 hours, shadow period accounts for 30%. Payload normal power consumption 80W (instantaneous peak 150W during data transmission), platform equipment basic power consumption 50W. Lithium-ion battery pack available capacity 200Wh, charge-discharge efficiency 95%. During shadow period, at least 40Wh emergency margin must be guaranteed, and the average daily power generation of solar panels must reach 110% of the budget.", + "question": "Calculate the allowed peak working time of the payload within a single orbital period (in minutes), assuming that shutting down non-essential platform equipment can save 30W during peak periods.", + "answer": "(200*0.95-40-50*2*0.3)/(150-(50-30)) = 1 hour = 60 minutes" + }, + { + "id": 782, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing exploration tasks inside the Von Kármán crater, located at coordinate point A(10,20). The science team requires it to travel to coordinate point B(45,35) to collect basalt samples. It is known that: 1) when the lunar surface slope exceeds 15°, a detour is required; 2) the energy consumption model is E = 0.12*d + 2.5*|Δh| (d is horizontal distance/km, Δh is elevation change/m); 3) the elevation at point A is -1930m, and at point B is -1945m; 4) the direct path AB is 3.2km but includes a 18° slope area, while the detour path ACB is 4.1km with a maximum slope of 12°.", + "question": "To meet the optimal energy constraint, which path should Yutu-2 choose? Calculate the total energy consumption difference between the two paths (result rounded to 1 decimal place).", + "answer": "Choose the detour path ACB. Direct path AB energy consumption: E_AB = 0.12*3.2 + 2.5*|-15| = 0.384 + 37.5 = 37.9 Wh; Detour path ACB energy consumption: E_ACB = 0.12*4.1 + 2.5*|-15| = 0.492 + 37.5 = 38.0 Wh. Energy consumption difference 0.1 Wh." + }, + { + "id": 783, + "scenario_code": "2.2", + "instruction": " The Chang'e-4 lander is conducting navigation tests in the South Pole-Aitken Basin. Current combined navigation system parameters: visual odometry position error ±3m/100m, IMU drift rate 0.1°/h, LiDAR SLAM absolute accuracy ±0.5m. The mission requires positioning error not to exceed 5m. Known: 1) Continuous travel for 120 minutes without landmark correction; 2) Initial IMU alignment error 0.05°; 3) Average travel speed 0.1m/s.", + "question": "Determine whether the current system still meets the positioning accuracy requirements? Provide the main sources of error and the total error estimate (assuming linear error accumulation).", + "answer": "Does not meet the requirements. Main errors: 1) IMU angular drift error = 0.1°/h * 2h = 0.2°, leading to position error = tan(0.2°) * (0.1m/s * 7200s) ≈ 5.03m; 2) SLAM error ±0.5m; 3) Visual odometry error = ±(3/100)*72 = ±2.16m. Total error ≈ 5.03 + 0.5 + 2.16 = 7.69m > 5m." + }, + { + "id": 784, + "scenario_code": "2.7", + "instruction": " When the lunar rover is operating near the terminator, it receives a solar proton event warning and needs to reach a permanently shadowed area within a 500m radius in 30 minutes. Current status: 1) Remaining power supports a maximum travel distance of 800m; 2) The terrain map shows a 17° slope obstacle 300m to the north, and an 8° gentle slope passage 450m to the northeast; 3) The emergency communication relay window opens every 15 minutes, with the next opening in 7 minutes.", + "question": "Plan the optimal risk-avoidance route and explain the decision-making basis (considering travel time, energy consumption, and communication needs).", + "answer": "Choose the 450m gentle slope passage to the northeast. Basis: 1) The 17° slope exceeds the safe slope (>15°); 2) The 450m distance meets the power constraint (<800m) and time constraint (at a speed of 0.1m/s it would take 75 minutes, but in emergency mode, it can reach 0.25m/s, requiring only 30 minutes); 3) It can reach the safe area before the next communication window (22 minutes later) and send a status confirmation." + }, + { + "id": 785, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform rock sampling: ① The one-way communication delay between Earth and the Moon is 1.3 seconds; ② The current speed of the lunar rover is 0.2m/s; ③ The positioning accuracy requirement for the end of the robotic arm is ±5cm; ④ A target rock is found 3 meters ahead. After the operator issues a 'stop immediately' command, the braking distance of the lunar rover must not exceed the positioning accuracy tolerance. It is known that the maximum braking acceleration of the lunar rover is 0.08m/s^2.", + "question": "Calculate the theoretical minimum displacement from the time the command is issued until the vehicle comes to a complete stop (including the effect of communication delay), and determine whether it meets the accuracy requirement.", + "answer": "Minimum displacement = communication delay segment displacement (0.2 * 1.3 = 0.26m) + braking segment displacement (v^2 / (2a) = 0.2^2 / (2 * 0.08) = 0.25m → total displacement 0.51m > 5cm, does not meet the requirement." + }, + { + "id": 786, + "scenario_code": "1.8", + "instruction": " When deploying the seismometer array, the following issues were found: ① The actual bearing capacity of the lunar soil in the designated area is 4.8kPa, lower than the design requirement of 5kPa; ② The contact area of the base of each instrument is 0.12m^2, with a mass of 22kg; ③ The gravitational acceleration on the lunar surface is 1.62m/s^2. The engineering team decided to adapt by increasing the contact area, with the new base using the same material but changing the geometric shape.", + "question": "Calculate the minimum contact area required for the new base (保留两位小数), and indicate which key parameters must remain unchanged when changing the shape? (Note: 保留两位小数 means '保留 to two decimal places')", + "answer": "Minimum area=(22*1.62)/(4800)=0.07m^2; The height of the base's center of gravity and the uniformity of the ground pressure distribution must remain unchanged." + }, + { + "id": 787, + "scenario_code": "5.4", + "instruction": " Yutu-2 rover experienced an X-band communication interruption during the lunar day, with fault diagnosis indicating that the ionosphere was disturbed by a solar flare. At this time:\n1. Remaining operable time window: 2 hours\n2. UHF backup link rate: 16kbps (only 1/8 of the X-band)\n3. Data in the buffer waiting to be transmitted: 50MB of engineering telemetry + 200MB of scientific data\n4. DTN protocol overhead accounts for 15%\n5. The system requires at least the transmission of all engineering telemetry and 30% of scientific data to ensure mission integrity", + "question": "Determine whether the minimum transmission requirements can be met under the current conditions? List the formula for calculating the effective data transmission volume.", + "answer": "Yes. Effective transmission volume = 16kbps * 7200s * (1 - 15%) = 97.92MB > (50MB + 200MB * 30%) = 110MB" + }, + { + "id": 788, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. Analysis of the soil characteristics in this area shows: the surface layer 0-30cm consists of loose fine particles (shear strength <5kPa), 30-60cm contains cemented breccia (shear strength 15-20kPa), and below 60cm there is a high-hardness basalt layer (compressive strength >100MPa). The probe is equipped with three sampling tools: 1) a rotary hollow drill (suitable for hardness <50MPa, power consumption 300W); 2) an impact coring drill (suitable for hardness 50-200MPa, power consumption 800W); 3) an electric shovel (only suitable for loose surface layers, power consumption 150W). The probe's solar panels can provide a continuous 200W power during the lunar day, and the battery pack can support a peak power of 1000W (not exceeding 10 minutes).", + "question": "If it is necessary to complete continuous sampling from the surface to a depth of 1 meter within a single lunar day cycle, please design a reasonable sequence of tool usage and corresponding operation time allocation (assuming each 10cm advance takes: 2 minutes for the electric shovel, 5 minutes for the rotary drill, 8 minutes for the impact drill).", + "answer": "Tool sequence: Electric Shovel (0-30cm) → Rotary Drill (30-60cm) → Impact Drill (60-100cm). Time allocation: Electric Shovel 6 minutes (3 segments * 2min), Rotary Drill 15 minutes (3 segments * 5min), Impact Drill 32 minutes (4 segments * 8min), total time 53 minutes. Power constraint: The impact drill phase requires activation of the battery to support a peak power of 800W." + }, + { + "id": 789, + "scenario_code": "3.4", + "instruction": " Yutu-2 needs to perform three tasks simultaneously during the lunar day: ① X-ray spectrometer (peak power consumption 80W, lasting 20 minutes); ② Laser rangefinder (instantaneous pulse 120W, working 10 seconds every 5 minutes); ③ Data transmission (stable power consumption 50W, lasting 15 minutes). The power system uses a dynamic load scheduling strategy: when the instantaneous total power consumption exceeds 150W, the lowest priority task is automatically delayed. The task priority order is ② > ① > ③. The current available battery capacity is 300Wh.", + "question": "Determine if the three tasks can be completed without triggering load scheduling? If not, provide the task execution sequence that meets the power constraints and the total time required (ignoring equipment cooling time).", + "answer": "Cannot be completed directly. Optimized execution order: first execute ② Laser rangefinder (12 minutes energy consumption = 120*(12*60/300)*10/60 +50*15/60=4+12.5=16.5Wh), then execute ③ Data transmission (15 minutes energy consumption = 50*15/60=12.5Wh), finally execute ① X-ray spectrometer (20 minutes energy consumption = 80*20/60≈26.67Wh). Total time 47 minutes, total energy consumption 55.67Wh<300Wh, and peak power consumption ≤150W at all times." + }, + { + "id": 790, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the transfer of the sample container must be verified. The container weighs 2kg, and the maximum acceleration the transfer mechanism can bear is 5m/s². The diameter of the ascent vehicle's docking ring is 40cm, with horizontal positioning accuracy of ±3cm and a vertical cushioning stroke of 10cm. The total length of the sample transfer path is 80cm (including a 30° inclined section), the rated power of the transfer mechanism is 20W, and the coefficient of friction μ=0.15. Environmental constraints: lunar gravity 1.62m/s², the transfer process must be completed within 120 seconds to avoid excessive solar radiation.", + "question": "Verify the feasibility of the transfer plan: calculate the minimum required driving power and the maximum allowable transmission speed (consider the kinetic energy formula E_k=0.5*m*v^2 and the power to overcome the inclined component P=(m*g_sinθ + μ*m*g_cosθ)*v).", + "answer": "The inclined component force F_slope=2*1.62*(sin30°+0.15*cos30°)≈2.14N; the minimum power P_min=F_slope*v_max≥20W → v_max≤9.35m/s; but the acceleration constraint a_max≤5m/s² and the time constraint t_min=80cm/(9.35m/s)=85ms meet the requirements. In practice, choosing v=80cm/120s≈0.67cm/s corresponds to P≈1.43W, which is much lower than the rated power, making the plan feasible." + }, + { + "id": 791, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 rover is conducting exploration tasks in the South Pole-Aitken Basin of the Moon, an area with complex terrain and multiple highlands blocking the view. The rover is equipped with a two-dimensional solar panel, whose power generation model is: P = P_max * cos(θ) * (1 - 0.02*dust), where θ is the angle of incidence of sunlight, and dust is the lunar dust accumulation coefficient (current value is 0.15). The lunar surface time is noon 12:00, with a solar elevation angle of 30° and an azimuth angle of 45°. The current orientation of the solar panel: pitch angle 20°, yaw angle 60° (0° is the true north direction). It is known that P_max=200W.", + "question": "Calculate the actual power generation of the current solar panel (保留两位小数), and determine whether the angle of the solar panel needs to be adjusted to improve power generation efficiency (assuming adjustment can make θ≤10°)?", + "answer": "The actual power generation is 138.79W, and the angle needs to be adjusted. Calculation steps: 1) Calculate the relative solar angle: pitch angle difference=30°-20°=10°, yaw angle difference=45°-60°=-15°; 2) Incidence angle θ=arccos(cos(10°)*cos(15°))=18.19°; 3) P=200*cos(18.19°)*(1-0.02*0.15)=138.79W. Since the current θ>10°, efficiency can be improved after adjustment." + }, + { + "id": 792, + "scenario_code": "3.4", + "instruction": " Yutu-2 rover plans to perform three tasks simultaneously during the 8th Earth day of the lunar day: ① Continuous X-ray spectrometer detection (peak power consumption 80W, lasting 2 hours) ② Robotic arm sampling (instantaneous impact current 15A@24V, each lasting 5 minutes) ③ High-speed data transmission (peak 120W, each 30 minutes). The power bus has a rated capacity of 10A, and the lithium-ion battery pack has a maximum instantaneous output capacity of 8A. The system uses a priority scheduling strategy: sampling > data transmission > detection.", + "question": "When the third sampling by the robotic arm overlaps with the data transmission task, how should the equipment operation sequence be adjusted to meet the power constraints? ", + "answer": "Suspend the data transmission task. Since the sampling instantaneous current of 15A has exceeded the bus capacity (10A), and the sampling has the highest priority, the lower priority data transmission task needs to be temporarily interrupted." + }, + { + "id": 793, + "scenario_code": "3.6", + "instruction": " When the Chang'e-7 lander enters the lunar night phase, its scientific payload cabin needs to maintain a working temperature of -20°C to +30°C. The cabin thermal loss coefficient K=1.2W/°C, and the external environmental temperature is -180°C. The electric heater efficiency η=85%, and the radioisotope heat source (RHU) can provide a constant 5W of heat. The temperature control requirement formula is: heating power Q = K*(T_target - T_env) - Q_RHU.", + "question": "Calculate the minimum input power required by the electric heater under the most stringent conditions (maintaining +30°C)?", + "answer": "Q = 1.2*(30-(-180)) -5 = 247W; Electric heater input power = 247/0.85 ≈ 290.6W" + }, + { + "id": 794, + "scenario_code": "1.4", + "instruction": " The lunar base power grid needs to allocate peak power to 3 devices: X-ray spectrometer (continuous demand 80W), laser communication terminal (instantaneous pulse demand 200W per 10 seconds), and mobile exploration vehicle charging station (base demand 30W, can be delayed). The system's total power supply capacity is 240W, and when the pulse device is working, the power of other devices must be ≤40W. The laser communication is triggered every 2 hours and has the highest priority.", + "question": "If the spectrometer is performing a critical observation (cannot be interrupted), and the communication terminal starts a pulse at this time, calculate the maximum allowable power of the charging station at this moment? And provide a power allocation plan that meets the constraints.", + "answer": "Maximum allowable power = min(240-200-80, 40) = 40W; effective plan: Communication 200W + Spectrometer 80W + Charging station 40W = 320W > 240W does not hold. The actual maximum charging power = 240-200-80 = -40W < 0, so the charging station must stop power supply." + }, + { + "id": 795, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. Known: ① The container seal pressure must be maintained at 85±5kPa ② The temperature recorder shows -60℃ to +50℃, all within the permitted range ③ The success rate of RFID tag reading is related to the distance as P=1-0.2*d (d in meters). Current inspection data: seal pressure 83kPa, temperature -55℃, handover distance 1.2 meters. The mechanical arm of the ascent vehicle can withstand a maximum of 3 repeated operations.", + "question": "Determine whether the current sample container meets the handover standards? If not, how many times can adjustments be attempted at most？", + "answer": "Meets the standards. Based on: ① Pressure 83kPa within the 80-90kPa range ② Temperature -55℃ within the permitted range ③ RFID read success rate P=1-0.2*1.2=76%> minimum requirement of 70%. No adjustment operations needed." + }, + { + "id": 796, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S), and needs to establish a communication link through the Queqiao-2 relay satellite. It is known that Queqiao-2 operates in the Earth-Moon L2 Halo orbit, with an average distance of about 65,000 km from the Moon's center. The lander uses an X-band (8 GHz) directional antenna (gain 38 dBi), and the relay satellite's receiving antenna gain is 42 dBi. At the current moment, the Moon's rotation causes the geometric elevation angle between the lander and the relay satellite to be 12°, and the free space path loss formula is: L = 20 * log10(4 * π * d / λ), where λ is the wavelength (speed of light c=3*10^8 m/s).", + "question": "Calculate the free space path loss value of the current Earth-Moon communication link (unit: dB), and determine whether it meets the minimum receiving power threshold of -110 dBm (assuming a transmission power of 10 W).", + "answer": "Wavelength λ = c / f = 3*10^8 / (8*10^9) = 0.0375 m; distance d = 65,000 km = 6.5*10^7 m; path loss L = 20 * log10(4 * π * 6.5*10^7 / 0.0375) ≈ 214.3 dB. Received power Pr = Pt + Gt + Gr - L = 40 dBm + 38 dBi + 42 dBi - 214.3 dB ≈ -94.3 dBm > -110 dBm, meets the requirement." + }, + { + "id": 797, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. The characteristics of the soil in this area are as follows: average hardness of 3.5 on the Mohs scale (similar to feldspar), viscosity coefficient of 0.8, and volatile content of about 120 ppm. There are three sampling tool parameters: ① Rotary impact drill (suitable for hardness > 4, power consumption 25W/min) ② Vibratory grab (suitable for viscosity < 1.0, power consumption 18W/min) ③ Scraper (universal, power consumption 15W/min). The mission requires prioritizing the integrity of the sample, with secondary consideration for power consumption.", + "question": "Based on the characteristics of the lunar soil and the mission requirements, which sampling tool should be selected? Provide specific selection criteria.", + "answer": "Choose the vibratory grab. Justification: ① The lunar soil viscosity of 0.8 meets the grab's suitability condition (<1.0) ② The hardness of 3.5 does not meet the drill's requirement (>4) ③ Although the scraper is universal, the grab is more suitable for the current lunar soil characteristics ④ The grab's power consumption of 18W/min is lower than the drill's 25W/min" + }, + { + "id": 798, + "scenario_code": "4.4", + "instruction": " Yutu-2 is conducting exploration in the Von Kármán crater, obtaining the following remote sensing data: ① KREEP rock distribution probability heatmap (resolution 100m) ② Laser altimeter topographic data (accuracy ±0.5m) ③ Multispectral mineral identification results. It is known that the priority for sampling KREEP rocks is the highest, but the current power level only supports movement of 300 meters. The current position at point A has a KREEP rock probability of 65%, with flat terrain; point B has a probability of 82% but requires climbing a 2° slope (increasing power consumption by 20%); point C has a probability of 58% and passes through a loose lunar soil area (speed must be reduced to 0.8 times).", + "question": "Calculate the reachability index within the effective exploration radius for each candidate point (formula: index = KREEP rock probability / (base distance * terrain correction factor), terrain correction factor: flat ground is 1, slope is 1.2, soft area is 1.15), and determine the optimal path target point.", + "answer": "Index for point A = 65 / (300 * 1) = 0.217; Index for point B = 82 / (300 * 1.2) = 0.228; Index for point C = 58 / (300 * 1.15) = 0.168. The optimal target point is point B (highest index 0.228)." + }, + { + "id": 799, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover continuously transmits scientific data to the Queqiao relay satellite during the lunar day. A sudden solar proton event causes the X-band link signal-to-noise ratio to drop by 6 dB. The original link design margin was 4 dB, and the (255,223)RS encoding can correct 16 bytes of errors. When the current bit error rate rises to 10^-3, 12 bytes of uncorrectable errors are generated per second. The remaining local cache capacity of the rover is 50 MB, and the data generation rate is 1.2 Mbps.", + "question": "Determine whether the emergency caching mode needs to be activated, and calculate the maximum sustainable operating time (ignoring switching delay).", + "answer": "The signal-to-noise ratio degradation of 6 dB exceeds the design margin of 4 dB, so the caching mode needs to be activated. Effective data rate = 1.2 Mbps * (223/255) ≈ 1.05 Mbps; Error data volume = 12 B/s * 8 = 96 bps; Net rate = 1.05 Mbps - 96 bps ≈ 1.049 Mbps; Operating time = (50*8 Mb) / 1.049 Mbps ≈ 381 seconds ≈ 6 minutes 21 seconds." + }, + { + "id": 800, + "scenario_code": "5.7", + "instruction": " The 128 GB NAND flash memory of the Chang'e-7 orbiter uses a wear-leveling algorithm, with a maximum of 100,000 erase/write cycles per block. The current file system divides the entire disk into 4 independent partitions (A: Engineering data 30 GB, write frequency 10 times/day; B: Scientific data 60 GB, write frequency 4 times/day; C: Logs 15 GB, write frequency 50 times/day; D: Backup 23 GB, write frequency 0.1 times/day), with each erase block size being 2 MB.", + "question": "Calculate the expected lifespan of partition C (unit: years), assuming that the daily write data is evenly distributed and no bad blocks are generated.", + "answer": "Partition C's average daily write volume = 50 times/day * 15 GB = 750 GB/day; Average daily erase cycles per block = (750 GB / 2 MB) / (15 GB / 2 MB) = 50 times; Expected lifespan = 100,000 times / (50 times/day) / 365 ≈ 5.48 years." + }, + { + "id": 801, + "scenario_code": "1.4", + "instruction": " The lunar base energy grid needs to allocate peak power to three devices: a lunar soil smelting furnace (continuous demand of 500W), a spectrometer (instantaneous peak of 800W for each 10-minute session), and a mobile exploration vehicle charging station (demand of 300W). The total output limit of the power grid is 1000W, and the spectrometer must exclusively use 800W when operating. The priority order of the devices is: spectrometer > smelting furnace > charging station. Currently, the smelting furnace is operating at 400W, and the charging station is running at full load.", + "question": "If the spectrometer is about to start a 10-minute operation, how should the power grid adjust the power of each device to meet the constraints? ", + "answer": "Shut down the charging station (release 300W), reduce the smelting furnace to 200W (total 200+800=1000W), ensuring the spectrometer has exclusive use of 800W." + }, + { + "id": 802, + "scenario_code": "2.7", + "instruction": " When the lunar rover is operating near the terminator and receives a solar proton event warning, it needs to reach a 3-kilometer distant emergency shelter within 15 minutes. Terrain analysis shows: the straight path requires crossing a lunar rille with a 20° slope (the wheel-soil mechanics model shows that the maximum safe speed at this slope is 0.05m/s), while the detour along a flat path is 4 kilometers long (maximum speed 0.15m/s). Safety protocols require arriving 3 minutes early.", + "question": "Please verify through calculations which path choice can meet the safety time requirement? Provide the specific calculation process.", + "answer": "Straight path time: crossing the rille segment at a speed limited by the slope to 0.05m/s, assuming the rille width is 300 meters, it takes 300/0.05=600 seconds=10 minutes; the remaining 2700 meters at the maximum speed of 0.15m/s takes 2700/0.15=18000 seconds=5 minutes; in total, 15 minutes to arrive, but this violates the requirement to arrive 3 minutes early. Detour along the flat path: 4000/0.15≈26667 seconds≈7 minutes 24 seconds<12 minutes (15-3), meeting the requirement. The detour along the flat path should be chosen." + }, + { + "id": 803, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, allocate shared energy to three devices (seismometer, magnetometer, spectrometer). The total output power of the energy system is 120W, with the basic power consumption of each device as follows: seismometer 20W (requires continuous operation), magnetometer 30W (operates for 30 minutes every 2 hours), spectrometer 50W (operates 3 times a day, each time for 1 hour). During the lunar day, solar power supply is stable, while during the lunar night, it relies on batteries, ensuring that the key device, the seismometer, operates uninterruptedly for 14 days. The total capacity of the battery is 10kWh, with a charge and discharge efficiency of 90%.", + "question": "If the battery is fully charged at the start of the lunar night, and only considering the power consumption of the seismometer, can the battery support its continuous operation for 14 days? If not, to what minimum power (in watts) must the seismometer's power consumption be reduced to ensure continuous operation for 14 days during the lunar night without additional power sources or interruptions in operation due to power limitations? ", + "answer": "It can support. Calculation process: Seismometer energy consumption for 14 days = 20W * 24h * 14 = 6720Wh; Available battery energy = 10000Wh * 0.9 = 9000Wh > 6720Wh. Therefore, there is no need to reduce power consumption." + }, + { + "id": 804, + "scenario_code": "1.8", + "instruction": " When deploying the drilling equipment, it was found that the local lunar soil bearing capacity is only 4kPa (lower than the expected 8kPa). The original design of the support frame has a contact area of 0.25m², a self-weight of 50kg, and a maximum operational load of 200kg. The safety factor requirement is ≥2. The lunar gravitational acceleration is known to be 1.62m/s².", + "question": "If the support frame design is not changed, what is the maximum allowable operational load in kilograms under the current site conditions? (Round the result to the nearest whole number.)", + "answer": "Maximum allowable load = (bearing capacity * area / g - self-weight) / safety factor = (4000 * 0.25 /1.62 -50)/2 ≈ (617-50)/2 ≈283kg. However, due to the original design limit of 200kg, 200kg is taken." + }, + { + "id": 805, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover establishes an X-band communication link (256kbps) with the ground station via a relay satellite during the lunar day. When the rover moves into the shadow of a crater, a sudden communication interruption occurs, at which point there are 12MB of untransmitted scientific data in the cache. Known facts:\n1. Remaining lunar day time: 40 minutes;\n2. Outside the shadow area, a 512kbps link can be restored;\n3. The DTN protocol allows the minimum transmission unit per communication window to be 64kB;\n4. The remaining write-erase life of the SSD storage chip is 500 cycles.", + "question": "Design the optimal data rescue plan, including the basis for selecting the transmission strategy and the consumption of the remaining write-erase life.", + "answer": "1. Strategy selection: Block transmission (12MB/64kB=187 blocks), utilizing short windows each time out of the shadow area for transmission\n2. Theoretical time required: 12MB/512kbps=187 seconds (3 minutes) <40 minutes → feasible\n3. SSD consumption: Each 64kB write consumes 1 write-erase cycle → total consumption 187 times <500 times" + }, + { + "id": 806, + "scenario_code": "5.8", + "instruction": " The intelligent spectrometer deployed at the lunar research station generates 50GB of raw data per hour. The onboard AI processor uses a hybrid CNN+Transformer model for feature extraction. Known facts:\n1. AI processing can reduce the data volume to 5% of the original;\n2. The processing time of the CNN module is proportional to the data volume (coefficient 0.2s/MB);\n3. The Transformer module has a fixed processing time of 8 seconds;\n4. The maximum continuous operation time allowed for the payload computer is 30 minutes.", + "question": "Calculate the theoretical total processing time for a single 50GB data set and determine whether batch processing needs to be activated. If batch processing is required, provide the minimum number of batches and the corresponding upper limit of data volume per batch.", + "answer": "1. CNN processing time: 50GB*1024MB/GB*0.2s/MB=10240 seconds >30 minutes (1800 seconds)\n2. Batch processing must be activated → minimum number of batches = 10240/1800 ≈ 5.7, rounded up to 6 batches\n3. Upper limit per batch = 50GB/6 ≈ 8.33GB" + }, + { + "id": 807, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration within the Von Kármán crater. There are three candidate sampling points: ① Highland anorthosite area (spectral analysis shows strong Al absorption peak); ② Suspected KREEP rock outcrop (Th content reaches 15 ppm); ③ Recent impact ejecta blanket (contains glassy melt). The rover has enough remaining power to operate for a maximum of 3 hours. The time required to move to each point is: ① 20 minutes, ② 35 minutes, ③ 15 minutes. In-situ analysis time required: XRF 25 minutes per point, LIBS 15 minutes per point. Scientific priority weights: KREEP rock > anorthosite > ejecta.", + "question": "Formulate the optimal exploration path, taking into account both scientific value and time constraints (the calculation logic must be explained).", + "answer": "Optimal path: ②→①. Calculation logic: 1) Total time = movement 35+20+analysis (25+15) = 95 minutes < 180 minutes; 2) Maximize scientific benefits: prioritize exploration of high-weight KREEP rock ②; 3) With 145 minutes remaining, it is possible to complete the XRF+LIBS analysis of anorthosite ① (40 minutes), but not enough to explore ③." + }, + { + "id": 808, + "scenario_code": "5.4", + "instruction": " During the scientific exploration tasks of the Yutu-2 rover during the lunar day, a sudden solar proton event caused the X-band communication with the Queqiao relay satellite to be interrupted. The rover's internal buffer can store 8 hours of raw data (at a rate of 500 kbps), and the backup UHF band link has a bandwidth of only 50 kbps but is highly resistant to interference. Mission priority rules specify: engineering telemetry data (30% of the total) must be transmitted in real-time, and scientific data can be delayed for transmission but with a maximum tolerance of 12 hours.", + "question": "Please design a recovery strategy for the interruption: 1) Calculate whether the UHF link can transmit all cached data within 12 hours; 2) If not, how should the data transmission priority be adjusted? ", + "answer": "1) UHF link transmission volume in 12 hours = 50 kbps * 3600s * 12 = 2160 Mb; total cache = 500 kbps * 3600s * 8 = 14400 Mb > 2160 Mb, unable to complete transmission. 2) Prioritize the transmission of engineering telemetry data (14400 Mb * 30% = 4320 Mb), and selectively compress or discard low-priority data packets of the remaining scientific data to meet the 2160 Mb limit." + }, + { + "id": 809, + "scenario_code": "3.1", + "instruction": " The Chang'e-5 lander is executing a sample return mission in the pre-selected landing area at 43.06°N, 51.92°W on the near side of the Moon. During the lunar day, the solar elevation angle in this area varies between 15° and 75°. The solar panel uses a two-dimensional drive mechanism (azimuth ±180°, elevation 0° to 90°). According to the three-dimensional reconstruction data of the terrain, there is a crater 10 meters high 200 meters to the due west, which will cause an obstruction from 10:00 to 14:00 local time. The maximum output power of the solar panel under standard test conditions (AM0, 25°C) is 1200W. An azimuth tracking error can result in a 5%/10° power loss, and an elevation tracking error can result in a 3%/10° power loss. The current system uses an open-loop tracking strategy based on the lunar ephemeris.", + "question": "If at 12:00 local time, the solar azimuth is 225° and the elevation angle is 60°, and the actual azimuth deviation is +15° and the elevation deviation is -5° due to delayed control commands, what is the actual power generation considering the combined effects of terrain obstruction and tracking errors at this time? ", + "answer": "The actual power generation is 0W (as the terrain completely blocks the sunlight)." + }, + { + "id": 810, + "scenario_code": "4.4", + "instruction": " During its patrol in the Von Kármán crater, Yutu-2 obtained data from three candidate sampling points: Point A (probability of KREEP rock 85%, distance 1.2km), Point B (probability of volcanic glass 72%, distance 0.8km), and Point C (probability of breccia 65%, distance 2.1km). The remaining power of the rover supports a total travel distance of 3km, with scientific priority weights being: KREEP rock (1.5) > volcanic glass (1.2) > breccia (1.0). Sampling and return must be completed within 2 hours.", + "question": "Based on scientific value and time constraints, which two points should be prioritized for sampling? Calculate whether the total travel distance of the optimal path meets the requirement.", + "answer": "Prioritize sampling from Points A and B. The optimal path is base → B (0.8km) → A (1.2-0.8=0.4km) → base (1.2km), total distance = 0.8+0.4+1.2=2.4km < 3km, meeting the requirement." + }, + { + "id": 811, + "scenario_code": "4.9", + "instruction": " When the ascent vehicle docks with the return capsule, the sample container must meet the following conditions: ① Temperature maintained at -50±5℃; ② Internal pressure <10^-3Pa; ③ RFID tag read success rate ≥99%. Current telemetry data shows the container temperature is -48℃, pressure is 5*10^-4Pa, but the RFID read success rate is only 95%. The docking window has 8 minutes remaining, and the following measures can be taken: A) Heat to -45℃ (takes 3 minutes) B) Secondary vacuum (takes 5 minutes) C) Restart the RFID reader (takes 2 minutes).", + "question": "To ensure all three indicators meet the standards and do not exceed the time limit, which measures should be taken? Explain the execution order and total time required.", + "answer": "Execution order: C→A. First, restart the RFID reader (2 minutes) to bring the read rate up to standard, then heat to -45℃ (3 minutes) to adjust the temperature. Total time required is 5 minutes < 8 minutes, and the pressure is already up to standard, so no action is needed." + }, + { + "id": 812, + "scenario_code": "3.1", + "instruction": " The Chang'e-7 lander is located at the edge of the Shackleton crater in the lunar south pole (latitude 88.5°S), and its solar panels use a three-dimensional tracking algorithm. Given that it is currently lunar noon, the solar elevation angle is 12°, and the azimuth angle is 180° (due south). The maximum power generation capacity of the solar panels P_max=300W (when perpendicular to sunlight), the actual power generation P_actual=P_max*cos(θ), where θ is the angle between the sunlight and the normal to the solar panel. The lander's power system needs to maintain at least 200W of power output, but due to terrain obstruction, the solar panels can only be adjusted to an azimuth angle of 150° and a pitch angle of 30°.", + "question": "Calculate whether the current actual power generation of the solar panels meets the minimum requirement? If not, to what minimum pitch angle must it be adjusted to meet the requirement? (Given cos(30°)=0.866, cos(20°)=0.94, cos(15°)=0.966).", + "answer": "1) The current angle θ=arccos[cos(30°)*cos(180°-150°)]=arccos(0.866*0.866)=30°, P_actual=300*cos(30°)=259.8W > 200W; 2) No adjustment needed." + }, + { + "id": 813, + "scenario_code": "3.6", + "instruction": " The Yutu-2 rover is about to enter lunar night hibernation, with a battery pack capacity of 400Wh and a health state SOH=90%. The lunar night lasts 14 Earth days, and it needs to maintain a constant temperature of -40°C. Known: 1) The basic power consumption of the thermal insulation system is 5W; 2) The electric heating power requirement Q_heat=10*(T_out+180)/14 (W), where T_out is the external temperature; 3) 50Wh of power must be retained upon awakening. The current external temperature will drop to -180°C.", + "question": "Verify if the existing battery can support the entire lunar night? If not, how many isotope heat sources (each can reduce 20% of Q_heat) need to be activated at least? ", + "answer": "1) Q_heat=10*(-180+180)/14=0W, total energy consumption=(5W*336h)+50Wh=1730Wh > 400Wh*90%=360Wh; 2) Let n be the number of heat sources: (5+0.8^n*0)*336+50≤360 → n≥2" + }, + { + "id": 814, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. The characteristics of the soil in this area are: medium hardness (Mohs hardness 4-5), low viscosity, and volatile content of about 120ppm. There are three sampling tools available: A-type rotary percussion drill (suitable for rocks with hardness >6), B-type vibratory grab (suitable for soils with viscosity >500cP), and C-type scraper (suitable for loose, dry soil). The sampling system uses force/position hybrid control, with a maximum allowable contact force of 50N and position control accuracy of ±2mm.", + "question": "Based on the given soil characteristics and tool parameters, which sampling tool should be selected? Please explain the selection criteria and the force control parameter range that needs to be set.", + "answer": "The C-type scraper should be selected. Reasons: 1) The soil hardness of 4-5 is below the standard suitable for the A-type drill; 2) The viscosity of 120ppm is much lower than the standard suitable for the B-type grab; 3) The C-type is specifically designed for loose, dry soil. The force control parameters should be set to 10-30N (to avoid exceeding the 50N upper limit and ensure sampling efficiency)." + }, + { + "id": 815, + "scenario_code": "2.9", + "instruction": " In the Lunar Beacon Navigation Satellite System (LBNSS), the real-time ranging data for beacons M1 and M2 are as follows:\n- Distance from M1 to the lunar rover d1=120km±50m (1σ)\n- Distance from M2 to the lunar rover d2=80km±30m (1σ)\n- Baseline distance between the two beacons L=150km±10m. It is known that the lunar rover and the two beacons are approximately coplanar, and the current joint positioning algorithm uses the weighted least squares method, with weights inversely proportional to the square of the ranging error.", + "question": "Please calculate the optimal positioning coordinates (x,y) of the lunar rover relative to the baseline of beacons M1-M2, assuming M1 is the origin (0,0) and M2 is located on the positive x-axis (150,0).", + "answer": "Let the weights w1=1/(50^2)=0.0004, w2=1/(30^2)≈0.0011. Solve the system of equations:\n(x-0)^2 + (y-0)^2 =120000^2\n(x-150000)^2 + (y-0)^2 =80000^2\nUsing the weighted least squares method, the optimal solution is x≈96240m, y≈±79800m (take the positive value)." + }, + { + "id": 816, + "scenario_code": "4.9", + "instruction": " During the transfer phase of the ascent vehicle and the return capsule's sample container, the following conditions must be met: 1) The internal temperature of the container must be maintained at -50±5°C; 2) The RFID tag reading success rate must be ≥99.9%; 3) The axial deviation of the docking must be <3°. Current telemetry shows the container temperature is -48°C, the RFID has successfully read 10 times in a row (historical success rate 100%), and the docking mechanism feedback indicates an axial deviation of 2.7°. The ascent vehicle has 120 seconds of remaining adjustable time, a temperature regulation rate of 0.1°C/s, and a posture adjustment rate of 0.02°/s.", + "question": "Based on the current status, determine whether the transfer conditions are met? If there are critical parameters, calculate whether adjustments can be completed within the remaining time.", + "answer": "The transfer conditions are met. The basis for the judgment is: 1) The temperature of -48°C is within the range of -55 to -45°C; 2) The RFID reading rate is 100% > 99.9%; 3) The axial deviation is 2.7° < 3°. No adjustment is needed: The temperature regulation margin is ±2°C, and the posture adjustment margin is 0.3° (requires 15 seconds) which is far less than the remaining 120 seconds." + }, + { + "id": 817, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander, while performing exploration tasks at the edge of the Shackleton crater, suddenly receives a solar proton event warning signal. According to the contingency plan, the rover needs to move to a pre-selected safe area 500 meters away within 30 minutes. The safe area is located due east, and the route involves crossing a slope with an average gradient of 12°. The maximum climbing speed of the lunar rover is 5 cm/s (10 cm/s on flat ground), and the current remaining power can support continuous operation for 40 minutes. It is known that the length of the slope section is 200 meters, and the rest is flat ground.", + "question": "Calculate whether the lunar rover can complete the safety move before the power runs out? If not, what emergency measures should be taken? (Hint: Calculate the total moving time and compare it with the power supply duration.)", + "answer": "Time spent on the slope = 200 / (0.05 * 100) = 40 minutes; Time spent on flat ground = (500 - 200) / (0.10 * 100) = 30 minutes; Total time spent is 70 minutes, exceeding the 40-minute power limit. Emergency measures should include: 1) Request ground instructions to switch to the lowest power consumption mode 2) Prioritize power supply to key equipment 3) Look for temporary safe points along the way." + }, + { + "id": 818, + "scenario_code": "2.10", + "instruction": " The lunar rover needs to perform close-up imaging with millimeter-level accuracy on a special basalt outcrop (coordinates X=3254.12, Y=1876.55). It is currently located at X=3253.85, Y=1876.30, with a positioning error of ±3cm (3σ) from the onboard visual navigation system, and an IMU drift error of 0.1°/hour. During the approach, the angle between the solar panel and the sun must be kept ≥30°, and the current solar azimuth is 125°. The yaw angle of the scientific camera in the vehicle coordinate system is 5°, and the pitch angle is -2°.", + "question": "Calculate the maximum allowable heading angle deviation range during the final approach phase to ensure that the position deviation of the scientific camera's line of sight center from the target point does not exceed 1cm. (Hint: Consider positioning error, installation error, and approach distance.)", + "answer": "Approach straight-line distance = sqrt((3254.12-3253.85)^2 + (1876.55-1876.30)^2) = 0.39m; Comprehensive error budget: Positioning error 3cm + target accuracy 1cm = 4cm; Maximum allowable angle deviation = arctan(0.04/0.39) ≈ 5.9°; After deducting the camera installation yaw angle of 5°, the actual heading control needs to be maintained within ±0.9°." + }, + { + "id": 819, + "scenario_code": "3.1", + "instruction": " Chang'e-7 lander is located near the lunar south pole (latitude 85°S), and its solar panels use a two-dimensional tracking algorithm (azimuth + elevation). According to the lunar ephemeris, it is currently lunar noon, with a solar elevation angle of 5°. There are permanently shadowed craters in this area, with the nearest crater wall 50 meters from the lander and 10 meters high. The maximum output power of the solar panels is 500W (when unobstructed), with an azimuth tracking error of ±3° and an elevation tracking error of ±1°. The lunar surface albedo is 0.12.", + "question": "Calculate the actual power generation of the solar panels at present (considering terrain obstruction, tracking errors, and the contribution of the lunar surface reflection), and provide the specific derivation steps.", + "answer": "1. Terrain obstruction judgment: when the solar elevation angle is 5°, the shadow length = 10/tan(5°) = 114.3m > 50m, so there is obstruction; 2. The obstructed proportion = (114.3-50)/114.3 = 56.3%; 3. Effective received power = 500*(1-0.563) = 218.5W; 4. Efficiency reduction due to tracking errors: cos(3°)*cos(1°) = 0.9986*0.9998 ≈ 0.9984; 5. Reflection contribution = 500*0.12*0.3 (assuming a diffuse reflection coefficient) = 18W; 6. Total power = (218.5*0.9984) + 18 ≈ 236W" + }, + { + "id": 820, + "scenario_code": "3.6", + "instruction": " The Yutu-2 rover is about to enter lunar night hibernation. Its lithium-ion battery capacity is 120Wh, and it needs to maintain a temperature above -40°C. It is known that: 1) the battery heat capacity is 150J/°C, 2) the lunar night lasts 14 Earth days, 3) the equivalent thermal conductivity of the insulation layer is 0.05W/m·K, 4) the surface area is 0.8m², the temperature difference between inside and outside is 200K, 5) the electric heating efficiency is 90%, 6) the standby power consumption of scientific instruments is 2W. The isotope heat source provides a constant 3W of heat.", + "question": "Calculate the minimum heating energy required to ensure the battery safely survives the lunar night and verify whether it is within the battery capacity range.", + "answer": "1. Heat loss = 0.05*0.8*200/0.02 = 400W → actual heat flow through the insulation layer = 400*(273-233)/200 = 80W; 2. Heat to be supplemented = 80W - 3W = 77W; 3. Electric heating power = 77/0.9 ≈ 85.6W; 4. Total energy consumption = (85.6 + 2)*14*24 ≈ 29.4kWh >> 120Wh → need to optimize the insulation layer or activate deep hibernation mode" + }, + { + "id": 821, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the handover inspection of the sample container must be completed. The known container mass is 500g, and the RFID tag frequency of 13.56MHz ± 5% is considered qualified; the sealing pressure should be maintained at 1-1.2kPa; the temperature recorder requires the entire process to be within the -50°C to +30°C range. Current telemetry data: RFID frequency 12.9MHz, sealing pressure 1.05kPa, temperature record shows it once reached -55°C but is currently -20°C. The handover agreement stipulates that a level three alarm will be triggered if any key parameter exceeds the standard.", + "question": " ", + "answer": "Handover is not allowed. Non-conformities: RFID frequency deviation = (13.56 - 12.9) / 13.56 = 4.87% (close but not exceeding the 5% threshold); temperature once reached -55°C, exceeding the lower limit by 10% (|-55 + 50| / 50 * 100% = 10%). The reason for triggering the alarm is the temperature exceeding the standard." + }, + { + "id": 822, + "scenario_code": "3.8", + "instruction": " In the Chang'e-6 sample return mission: 1) The lunar surface operation phase requires continuous 48 hours of work, including 2 drilling operations (each consuming 800Wh), 4 spectral analyses (each 150Wh), and a constant temperature system consuming 200W; 2) The power generation curve of the solar panels during the day is P=300*sin(π*t/12), where t is the number of hours during the lunar day (0-12); 3) The initial SOC of the battery is 95% (capacity 2000Wh), and the discharge cut-off SOC is 20%.", + "question": "Formulate a time-based energy distribution plan to ensure the completion of the mission without triggering low battery protection (list the start and stop times of equipment at each time period and the changes in battery SOC).", + "answer": "Key steps: 1) Total demand = 2*800 + 4*150 + 200*48 = 11,800Wh; 2) Daytime power generation ∫[0→12]300sin(πt/12)dt ≈ 2291Wh; 3) Nighttime power supply depends on the battery = (11800-2291)/48 ≈ 198W/h; 4) Safe SOC margin = 2000*(0.95-0.2) = 1500Wh > 198*12 ≈ 2376Wh → not feasible; 5) Adjusted plan: Transfer 50% of the constant temperature load to daytime operation, and maintain only 100W at night → New nighttime demand = (11800-2291-100*36)/12 ≈ 132W/h → 132*12 = 1584Wh < 1500Wh feasible" + }, + { + "id": 823, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin (SPA) on the far side of the Moon, and needs to communicate with the ground station via the Queqiao-2 relay satellite. Given: Queqiao-2 operates in a halo orbit around the Earth-Moon L2 point, with an average altitude of 8000 km above the lunar surface; the lander's transmission power is 10W, and the antenna gain is 5dBi; the relay satellite's receiving antenna gain is 20dBi, and the system noise temperature is 300K; the operating frequency is 2.4GHz (wavelength 0.125m), and the required minimum signal-to-noise ratio (SNR) is 6dB. The free space path loss formula is L = 20 * log10(4 * π * d / λ), where d is the distance.", + "question": "Calculate whether the current link margin meets the communication requirements (considering a receiver sensitivity of -110dBm)? Provide key numerical values (path loss, received power, noise power) and the final conclusion.", + "answer": "1) Path loss L = 20 * log10(4 * π * 8000km / 0.125m) ≈ 191.5dB\n2) Received power Pr = 10dBW + 5dBi + 20dBi - 191.5dB = -156.5dBW = -126.5dBm\n3) Noise power Pn = -228.6 + 10 * log10(300) + 10 * log10(10MHz) ≈ -128.6dBm\n4) SNR = -126.5 - (-128.6) = 2.1dB < 6dB → does not meet requirements" + }, + { + "id": 824, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover experienced an X-band communication interruption during the lunar day, diagnosed as being caused by solar flares damaging the RF front end. Current remaining resources: ① UHF band backup radio (maximum rate 50kbps) ② Relay satellite visibility window of 8 minutes per orbit ③ Remaining DRAM buffer capacity of 2GB. The scientific data generation rate is: panoramic camera 120MB/hour, particle-induced X-ray spectrometer 30MB/hour.", + "question": "To ensure critical data is not lost, please formulate an emergency transmission plan and calculate the minimum number of orbital periods required to transmit the cached data. Explain the basis for the priority order.", + "answer": "1) Priority order: particle data (low bandwidth requirement) > panoramic data (high bandwidth requirement)\n2) Total data volume per hour = 150MB, transmission rate = 50kbps * 3600s ≈ 22MB/h\n3) Data to be transmitted = min(2GB, 150MB * expected repair time)\nIf repair time > 13.3 hours, then 2GB needs to be transmitted: 2000MB / (22MB/h * 8/60) = 34 orbital periods" + }, + { + "id": 825, + "scenario_code": "2.7", + "instruction": " When the Chang'e-7 lander is working at the edge of the Shackleton crater, it suddenly receives a space weather warning: a solar proton event will reach the lunar surface in 25 minutes and last for 4 hours. Currently, the lander is in safe mode (50W power consumption) and needs to urgently move to a permanent shadow area 500 meters away for shelter. Known: 1) Maximum moving speed 0.1m/s; 2) Steering/starting time takes a total of 3 minutes; 3) During sheltering, the life support system (200W) needs to be maintained; 4) Remaining battery capacity is 300Wh.", + "question": "Calculate whether the lander can complete the sheltering before the proton event arrives? And evaluate whether the total energy consumption during the sheltering period exceeds the battery capacity? ", + "answer": "Moving time = 500/0.1 = 5000s ≈ 83.3 minutes, plus steering time totaling 86.3 minutes > 25 minutes → cannot arrive in advance; total sheltering energy consumption = (50W * 25/60h) + (200W * 4h) ≈ 20.8 + 800 = 820.8Wh > 300Wh → insufficient energy" + }, + { + "id": 826, + "scenario_code": "2.10", + "instruction": " The lunar rover needs to conduct centimeter-level precise exploration of a 1-meter diameter ilmenite outcrop. Known: 1) The baseline distance of the stereo vision system is 20cm, focal length is 5mm, pixel size is 4μm; 2) IMU angular velocity measurement error is ±0.01°/s; 3) During the approach phase, the relative position error must be <5cm, and the attitude angle error must be <1°; 4) The last 10 meters use visual servo control, with a movement speed of 0.02m/s.", + "question": "Calculate the theoretical ranging error of the stereo vision system at a distance of 10 meters (formula: ΔZ/Z^2 = Δp/(f*b), Δp is the pixel size), and determine whether it meets the approach accuracy requirements? ", + "answer": "ΔZ = (Z^2 * Δp)/(f * b) = (10^2 * 4e-6)/(0.005 * 0.2) = (100 * 4e-6)/0.001 = 0.4m >>5cm → does not meet the requirement" + }, + { + "id": 827, + "scenario_code": "5.7", + "instruction": " The SSD storage module carried by the Chang'e-7 orbiter uses NAND Flash chips, with a total capacity of 1TB and a block size of 128KB. It is known that: each block has a maximum number of erase/write cycles of 3000; the current wear leveling algorithm adopts a dynamic hot spot adjustment strategy; the average daily write volume is 20GB (including 30% temporary files); the design life of the solid-state storage needs to be ≥5 years.", + "question": "Verify whether the current design meets the life requirement? If not, calculate the daily write volume that needs to be controlled below what level to meet the requirement.", + "answer": "1) Total write volume = 20GB * 365 * 5 = 36.5TB\n2) Total erase/write cycles = 36.5TB / 128KB ≈ 285,000 times\n3) Actual allowed erase/write cycles = 1TB / 128KB * 3000 ≈ 23,400,000 times >> 285,000 times → meets the requirement\nIf insufficient, the upper limit for control calculation: 23,400,000 / (365 * 5) * 128KB ≈ 164GB/day" + }, + { + "id": 828, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing exploration tasks inside the Von Kármán crater, located at point A(10,20). It needs to travel to the scientific target point B(85,60) to collect basalt samples. It is known that: 1) the energy consumption model for the lunar surface is E = 0.12*d + 2.5*h (d is the horizontal distance/km, h is the cumulative ascent height/m); 2) the A→B path consists of three sections: the first section is a 15km flat area (elevation +2m), the second section is a 40km slope (gradient 5°), and the third section is a 30km crater debris area (elevation -3m); 3) the remaining battery capacity is 18kWh, and the motor system efficiency η=92%.", + "question": "Calculate the total energy consumption for Yutu-2 to travel along the shortest straight-line path to point B and determine whether the current power is sufficient to meet the mission requirements? (sin5°≈0.087, cos5°≈0.996).", + "answer": "Total horizontal distance d = sqrt((85-10)^2 + (60-20)^2) = 85km; cumulative ascent h = 15*0 + 40*sin5°*1000 - 30*0.003*1000 ≈ 40*87 - 90 = 3390m; total energy consumption E = 0.12*85 + 2.5*3.39 ≈ 10.2 + 8.475 = 18.675kWh; actual requirement = 18.675/0.92 ≈ 20.3kWh > 18kWh → power is insufficient" + }, + { + "id": 829, + "scenario_code": "5.7", + "instruction": " The 'Queqiao' relay satellite is equipped with 128 GB of NAND flash memory and uses a dynamic wear-leveling algorithm. It is known that the maximum number of erase/write cycles for a flash block is 100,000 times, with the oldest block having been erased/written 82,000 times and the newest block 35,000 times. The onboard file system uses a strategy of separating hot and cold data: the hot data area has an average daily write of 50 GB (evenly distributed), and the cold data area has an average daily write of 5 GB.", + "question": "Calculate the estimated remaining lifespan of the flash memory under the current write load (considering that wear leveling makes the number of erase/write cycles for each block tend to be consistent)?", + "answer": "Average daily total write 55 GB → annual write 20075 GB ≈ 156.8 times/block/year; remaining erase/write cycles = (100000 - ((82000 + 35000) / 2)) / 156.8 ≈ 347 days" + }, + { + "id": 830, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth. The 'Queqiao' relay satellite is deployed in the Earth-Moon L2 point Halo orbit, about 65,000 kilometers from the lunar surface. It is known that the X-band antenna gain of the relay satellite is 42 dBi, the transmission power of the lander is 10 W, and the antenna gain is 6 dBi. The free space path loss formula is: L = 20 * log10(d) + 20 * log10(f) + 92.45, where d is the distance (km), and f is the frequency (8 GHz). The system requires a minimum received power of -120 dBm.", + "question": "Calculate whether the uplink link budget from the lander to the 'Queqiao' relay satellite meets the communication requirements? Provide the final received power (dBm) and compare it with the threshold value.", + "answer": "Calculation steps: 1) Free space loss L = 20*log10(65000) + 20*log10(8) + 92.45 ≈ 20*4.813 + 20*0.903 + 92.45 ≈ 96.26 + 18.06 + 92.45 = 206.77 dB; 2) EIRP = 10*log10(10) + 6 = 10 + 6 = 16 dBm; 3) Received power Pr = EIRP - L + Gr = 16 - 206.77 + 42 = -148.77 dBm < -120 dBm. Conclusion: Does not meet the requirement." + }, + { + "id": 831, + "scenario_code": "4.4", + "instruction": " During the Yutu-2 rover's patrol in the Von Kármán crater, it obtained multispectral data for three candidate sampling points: Point A (KREEP rock probability 68%, distance 1.2km), Point B (volcanic glass probability 85%, distance 2.3km), Point C (breccia probability 92%, distance 0.7km). The rover's movement speed is 0.05km/h, with a maximum operational duration of 8 hours. Scientific priority weights: KREEP rock 3 points, volcanic glass 2 points, breccia 1 point.", + "question": "Based on scientific value and travel time, what is the optimal path planning, which sampling points should be selected, and in what order should they be visited? The total score and time consumption must be explained.", + "answer": "Optimal path: C→A. Sequence logic: 1) Prioritize visiting the nearest C point (time consumption 0.7/0.05=14h exceeds limit, so visiting C alone is not feasible); 2) Change to A+C combination: total travel distance 1.2+0.7+0.5=2.4km (estimated triangular path), time consumption 48h still exceeds limit; 3) Ultimately, only single-point visits can be chosen. Single-point scores: A=68%*3=2.04 points, B=85%*2=1.7 points, C=92%*1=0.92 points. Therefore, choose to visit A point alone, time consumption 1.2/0.05=24h exceeds limit, actually no feasible solution, need to re-plan." + }, + { + "id": 832, + "scenario_code": "5.7", + "instruction": " The 'Queqiao-2' relay satellite uses a 128TB 3D NAND solid-state storage device, with each storage unit capable of withstanding 3000 write-erase cycles. The storage device uses a dynamic wear-leveling algorithm to evenly distribute write operations across all blocks. It is known that the average daily write volume is 500GB, the storage device contains 100 parallel operating NAND dies, and each die contains 2000 blocks (each block is 2MB).", + "question": "Calculate the theoretical lifespan of the storage device (considering all dies writing in parallel and ideal wear leveling).", + "answer": "Calculation steps: 1) Total number of blocks = 100 dies * 2000 blocks/die = 200,000 blocks; 2) Daily number of blocks written = 500GB / (2MB/block) = 256,000 blocks; 3) Actual daily effective number of blocks written = 256,000 / 100 dies = 2560 blocks/die (parallel distribution); 4) Number of writes per block per day = 2560 / 2000 = 1.28 times; 5) Lifespan = 3000 times / (1.28 times/day) / 365 ≈ 6.42 years" + }, + { + "id": 833, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the Moon's South Pole, a shared energy grid needs to be constructed consisting of 3 mobile energy modules (MEMs). Each MEM has a maximum output power of 500W, but due to the extremely low temperatures during the lunar night, 20% of the actual usable power must be reserved as redundancy. In the current mission: MEM 1 is supporting the drilling sampling device at 400W; MEM 2 is supporting the astronomical observation equipment at 350W; MEM 3 is in standby mode (basic power consumption 50W). At this point, a new seismometer with an instantaneous peak demand of 600W is connected, requiring at least 10 minutes of continuous power supply.", + "question": "If a dynamic priority scheduling strategy (scientific instruments > drilling > astronomical observation) is adopted, please calculate whether the current energy grid can meet the peak demand of the seismometer? If not, what is the minimum number of existing devices that need to be shut down to ensure power supply? ", + "answer": "Current total available power = 3 * 500W * 80% = 1200W; Used power = 400W + 350W + 50W = 800W; Remaining power = 1200W - 800W = 400W < 600W. The astronomical observation equipment (350W) with the lowest priority needs to be shut down, after which the remaining power = 400W + 350W = 750W > 600W." + }, + { + "id": 834, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth, and must communicate through the Queqiao relay satellite. The Queqiao satellite operates in the Earth-Moon L2 Halo orbit, about 65,000 kilometers from the Moon. The average distance from Earth to the Moon is 384,400 kilometers, and the Queqiao satellite uses the X band (8 GHz) for communication. At this moment, the Earth station, Queqiao satellite, and the lander on the far side of the Moon are approximately collinear (Earth-Queqiao-Lander). Please calculate the total distance of the communication link between the Earth station and the lander at this time, and estimate the one-way signal transmission delay (speed of light c=3*10^8 m/s).", + "question": "Calculate the total communication link distance and the one-way signal transmission delay between the Earth station and the lander on the far side of the Moon under the current configuration (保留3位小数, i.e., keep 3 decimal places)?", + "answer": "Total link distance = Earth-Moon distance + Queqiao to Moon distance = 384,400 km + 65,000 km = 449,400 km; One-way delay = distance / speed of light = 449,400,000 m / (3*10^8 m/s) ≈ 1.498 s" + }, + { + "id": 835, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover for rock sampling, the ground control center receives a confirmation signal 1.25 seconds after sending a movement command. The maximum speed of the lunar rover is 0.1m/s, and the braking distance formula is d = v^2 / (2 * μ), where the friction coefficient μ = 0.3 (dry lunar soil environment). The control algorithm requires that the real-time position prediction error does not exceed 50% of the braking distance to ensure safety.", + "question": "When the lunar rover is traveling at its maximum speed, calculate the maximum allowable prediction position error threshold (unit: centimeters)?", + "answer": "Braking distance d = (0.1m/s)^2 / (2 * 0.3) ≈ 0.0167m; Maximum allowable error = d * 50% ≈ 0.0083m = 0.83cm" + }, + { + "id": 836, + "scenario_code": "5.7", + "instruction": " The 128GB onboard SSD of the Chang'e-7 orbiter uses NAND flash memory, and the storage controller needs to perform wear leveling. It is known that: 1) Each storage block has a maximum of 100,000 erase/write cycles; 2) The average daily write volume is 20GB; 3) The write amplification factor is 1.5; 4) The storage unit adopts a 200% over-provisioning strategy. The formula for calculating the total physical capacity of the SSD is: Physical capacity = User capacity * (1 + Over-provisioning rate).", + "question": "Calculate the theoretical minimum lifespan of the SSD (in years, rounded to the nearest integer)?", + "answer": "Calculation steps: 1) Physical capacity = 128 * (1 + 2) = 384GB; 2) Daily actual write volume = 20 * 1.5 = 30GB; 3) Annual write volume = 30 * 365 ≈ 10950GB/year; 4) Lifespan in years = (384 * 100000) / 10950 ≈ 3507 years → rounded to 3507 years (Note: This result is abnormally high, the original parameters need adjustment)." + }, + { + "id": 837, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. According to preliminary remote sensing data analysis, the target area contains two typical types of lunar soil: Type A is loose, dry fine-grained lunar soil (hardness 2MPa, viscosity 0.5Pa·s), and Type B is volatile-containing sticky lunar soil (hardness 5MPa, viscosity 8Pa·s). The engineering team has prepared three sampling tools: a rotary impact drill (suitable for hardness >4MPa), an electric grab (suitable for viscosity <5Pa·s), and a screw sampler (suitable for viscosity 3-10Pa·s). The sampling system has a maximum output torque of 15N·m, and each sampling operation must be completed within 20 minutes.", + "question": "If it is necessary to collect samples at a depth of 50cm in Type B lunar soil, which sampling tool should be chosen? Please explain the selection criteria based on the tool's applicable conditions and system constraints.", + "answer": "The screw sampler should be chosen. Because the hardness of Type B lunar soil, 5MPa, meets the hardness range applicable to the screw sampler (no clear lower limit but below the 4MPa threshold for the rotary impact drill), and its viscosity of 8Pa·s is exactly within the viscosity range applicable to the screw sampler (3-10Pa·s). The electric grab is not suitable because its viscosity upper limit is 5Pa·s, and although the rotary impact drill meets the hardness requirement, its viscosity adaptability is not clearly defined." + }, + { + "id": 838, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting scientific investigations within the Von Kármán crater. Based on the interpretation of high-spectral data from the orbiter, three potential sampling sites have been identified: P1 (KREEP rock enrichment area, scientific value weight 0.9, 800 meters from the current position), P2 (volcanic glass belt, scientific value weight 0.7, 400 meters away), and P3 (breccia outcrop, scientific value weight 0.6, 200 meters away). The rover's average daily travel capability is 300 meters, and all sampling sites need to be visited within 3 Earth days. Path planning must take into account both scientific value and mobility energy consumption (energy consumption formula: E=0.12*d, where d is the one-way travel distance, in meters).", + "question": "To achieve the highest overall scientific benefit with the lowest total energy consumption, please provide the optimal visiting order of the three sampling sites and the total energy consumption calculation.", + "answer": "The optimal visiting order is P3→P2→P1. The total energy consumption calculation is as follows: from the starting point to P3 consumes 0.12*200=24; from P3 to P2 consumes 0.12*(400-200)=24; from P2 to P1 consumes 0.12*(800-400)=48; the total energy consumption is 24+24+48=96 units of energy. This order can be completed within 3 days (daily travel distances are 200m, 200m, and 400m, respectively), and it is more energy-efficient than other arrangements." + }, + { + "id": 839, + "scenario_code": "3.6", + "instruction": " When the Chang'e-6 lander enters the lunar night phase, its scientific payload compartment needs to maintain a working temperature range of -20°C to +30°C. The compartment has a surface area of 5㎡, a thermal conductivity of 0.05 W/(m·K), and a designed temperature difference of 150K between the inside and outside (inside -20°C / outside -170°C). The isotope heat source has a rated output power of 25W, and the electric heater has a backup power of 50W.", + "question": "Calculate whether the isotope heat source alone can meet the thermal insulation requirements? If not, how much additional electric heating power is needed to supplement it? ", + "answer": "Heat loss = thermal conductivity * area * ΔT / thickness = 0.05 * 5 * 150 / 0.1 = 375W; Deficit = 375 - 25 = 350W, requiring an additional 350W of electric heating power (exceeding the backup capacity, some equipment needs to be put into hibernation)." + }, + { + "id": 840, + "scenario_code": "3.1", + "instruction": " The Chang'e-7 lander is located near the lunar south pole (latitude 85°S), and its solar panels use a two-dimensional tracking algorithm. According to the lunar ephemeris, the current solar elevation angle is 5°, and the azimuth angle is 45° (with north as 0°). There is a 2-meter-high rock blocking 3 meters to the west of the lander. The single panel area of the solar wings is 2 square meters, with a photovoltaic conversion efficiency of 28%, and the standard solar irradiance is 1367 W/m². The lunar surface albedo is 0.12.", + "question": "Calculate the actual power generation of the solar wings under the current conditions (considering direct sunlight, lunar surface reflection, and shading effects, assuming that two-dimensional tracking always keeps the normal of the panel surface at the minimum angle with the solar incidence direction).", + "answer": "Actual power generation = (direct sunlight power * unshaded ratio + lunar surface reflection power) * conversion efficiency = (1367 * cos(5°) * 2 * (1 - 2/3 * tan(5°)) + 1367 * 0.12 * sin^2(5°/2) * 2) * 0.28 ≈ 532 W" + }, + { + "id": 841, + "scenario_code": "3.4", + "instruction": " During the lunar day, the Yutu-2 rover needs to perform the following tasks simultaneously: ① Continuous operation of the X-ray spectrometer for 20 minutes (peak power consumption 80W) ② Sampling by the robotic arm for 10 minutes (peak power consumption 150W) ③ Data transmission for 15 minutes (peak power consumption 120W). The lithium-ion battery pack has a remaining capacity of 1800Wh, and the current power supply capability of the solar panels is 200W. The system is set to not allow the battery discharge depth to exceed 60%.", + "question": "Determine whether the task sequence needs to be adjusted to avoid over-discharge of the battery (provide the maximum allowable total energy consumption and compare it with the actual demand)?", + "answer": "Maximum allowable energy consumption = 1800Wh * 60% = 1080Wh; Actual demand = (80*20/60 + 150*10/60 + 120*15/60) = 26.67 + 25 + 30 = 81.67Wh <1080Wh, no adjustment needed" + }, + { + "id": 842, + "scenario_code": "3.8", + "instruction": " In the Chang'e-6 sample return mission, the power system needs to complete the following sequence of actions: 1) Drilling sampling (peak power 300W, lasting 2 hours); 2) Sample encapsulation (150W, 1 hour); 3) Data transmission (200W, to be completed in the next 3 communication windows, each window 30 minutes). The current remaining energy of the lithium-ion battery is 800Wh, and the solar array is expected to charge 400Wh in the next 12 hours. The system standby power consumption is 50W.", + "question": "Verify whether the energy budget requirements are met? If not, propose the minimum additional energy reserve (Wh) needed.", + "answer": "Insufficient, need to add 150Wh (Calculation: Total demand = 300 * 2 + 150 * 1 + 200 * 1.5 + 50 * (2 + 1 + 1.5) = 1350Wh; Available energy = 800 + 400 = 1200Wh; Deficit = 150Wh)." + }, + { + "id": 843, + "scenario_code": "5.7", + "instruction": " The SSD storage chip of the Chang'e-7 orbiter has an abnormally high bad block rate, increasing to 0.05%/month (design threshold is 0.01%). Chip specifications: 1) Total capacity 1TB, physical block size 4MB; 2) Supports dynamic bad block mapping and reserves 5% redundant blocks; 3) Current write amplification factor is 1.8, with an average daily write volume of 50GB. The file system uses a log-structured format, and the encryption algorithm is SM4-CTR mode.", + "question": "Calculate the expected safe service life under the current bad block growth rate and propose two on-board operation strategies to mitigate wear.", + "answer": "Safe time = (5% * 1TB) / (50GB * 30 days * 0.05% * 1.8) = approximately 740 days. Mitigation strategies: 1) Enable dynamic wear leveling algorithms to distribute write operations to blocks with low PE cycles; 2) Turn off real-time encrypted writes for non-critical engineering data, and instead store them in batches after encryption." + }, + { + "id": 844, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. The characteristics of the soil in this area are as follows: medium hardness (Mohs hardness 4-5), low viscosity, and a volatile content of about 120 ppm. There are three sampling tools available: A-type rotary impact drill (suitable for rocks with hardness >6), B-type vibratory grab (suitable for loose lunar soil), and C-type adaptive scraper (suitable for hardness 3-6 and volatile-containing materials). It is known that in the tool control parameters, the drill needs to maintain a rotational speed of 200 rpm + axial pressure of 50 N, the grab needs to apply a clamping force of 30 N + vibration frequency of 5 Hz, and the scraper uses a contact force of 20 N + feed speed of 0.1 m/s.", + "question": "Based on the characteristics of the lunar soil and the performance parameters of the tools, which sampling tool should be chosen? What is the corresponding force/position hybrid control parameter combination for the selected tool? ", + "answer": "Choose the C-type adaptive scraper, with control parameters of 20 N contact force + 0.1 m/s feed speed." + }, + { + "id": 845, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container transfer must be verified. The operation process requires:\n1) The success rate of reading the container's RFID tag ≥99%\n2) The pressure in the sealed cabin must be maintained below 10^-4Pa for 30 minutes\n3) The temperature recorder shows the entire process within -50±5℃\n4) The force sensor reading of the robotic arm docking is within 20±2N\nCurrent telemetry data:\n- RFID read success rate 100% in three attempts\n- Sealed cabin pressure 9×10^-5Pa (for 35 minutes)\n- Temperature recorded from -48℃ to -52℃\n- Last docking force reading 25N", + "question": "Based on the verification standards, determine whether the current conditions allow the ascent vehicle to separate? If not, point out the specific non-conformities and the adjustment directions.", + "answer": "Separation is not allowed. The non-conformity is the robotic arm docking force reading of 25N, which exceeds the 20±2N range. The adjustment should reduce the docking force to the 18-22N range, which can be achieved by reducing the clamping force of the robotic arm's end effector or recalibrating the force sensor. The other indicators (RFID, pressure, temperature) all meet the requirements." + }, + { + "id": 846, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the soil in this area are: average hardness of 3.5 on the Mohs scale, viscosity coefficient of 0.8 (moderate viscosity), and volatile content of about 1200 ppm. There are three sampling tools with the following parameters:\n- Rotary Percussion Drill: Suitable for hardness ≤4, viscosity range 0.5-1.2, volatile tolerance threshold 1500 ppm\n- Claw Sampler: Suitable for hardness ≤2.5, no viscosity limit, volatile tolerance threshold 2000 ppm\n- Scraping Sampler: Suitable for hardness ≤3, viscosity range 0.6-1.5, volatile tolerance threshold 800 ppm\nAll tools are equipped with a force/position hybrid control system, with a maximum power consumption limit of 300W.", + "question": "Based on the given soil characteristics and tool parameters, which sampling tool should be chosen? Please explain the specific reasons for excluding the other options.", + "answer": "The rotary percussion drill should be chosen. Reasons: 1) The hardness limit (2.5) of the claw sampler is lower than the actual hardness of the lunar soil (3.5); 2) The volatile tolerance threshold (800 ppm) of the scraping sampler is lower than the volatile content of the lunar soil (1200 ppm); while the rotary percussion drill meets all the parameter requirements (hardness 3.5≤4, viscosity 0.8∈[0.5-1.2], volatile 1200 ppm≤1500 ppm)." + }, + { + "id": 847, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration near the Von Kármán crater. Based on the multispectral data from the orbiter, three candidate sampling points have been interpreted:\nPoint A (45.12°N, 176.34°E): Probability of KREEP rock 68%, terrain slope 8°, 120m from the current position\nPoint B (45.08°N, 176.38°E): Probability of volcanic glass 82%, terrain slope 15°, 80m from the current position\nPoint C (45.15°N, 176.40°E): Probability of breccia 55%, terrain slope 5°, 150m from the current position\nScientific priority weights: KREEP rock > volcanic glass > breccia. The rover's movement energy consumption model is E=0.8*d+5*θ (d is distance in meters, θ is slope in degrees), with remaining power sufficient for 180J of consumption.", + "question": "Please calculate the movement energy consumption for each candidate point, and determine the optimal sampling point based on scientific priority and energy consumption constraints.", + "answer": "Energy consumption at Point A = 0.8*120 + 5*8 = 136J; Energy consumption at Point B = 0.8*80 + 5*15 = 139J; Energy consumption at Point C = 0.8*150 + 5*5 = 145J. The optimal choice is Point B: 1) Although Point A has the highest priority for KREEP rock, the probability is only 68% and the scientific value difference is not significant; 2) Point B has the highest probability of volcanic glass (82%) and the energy consumption is within the limit; 3) Point C has the lowest priority for breccia and the energy consumption is close to the upper limit." + }, + { + "id": 848, + "scenario_code": "4.4", + "instruction": " Yutu-2 is conducting path planning in the Von Kármán crater. Known conditions: Point A (coordinates X12Y34) has a high spectral anomaly area (70% probability of KREEP rock), 3km from the current position; Point B (X15Y30) has a breccia outcrop identified by LiDAR (85% confidence), 2km from the current position; Point C (X10Y40) has a suspected volcanic glass (remote sensing match rate 60%), 4km from the current position. The rover's moving speed is 0.2km/h, and the remaining sunlight time is 8 hours. Scientific priority: KREEP rock > breccia > volcanic glass.", + "question": "Calculate the optimal exploration path and the number of exploration points that can be completed, which must meet both scientific priority and time constraints.", + "answer": "Path: B→A. Time required: B point 2km/0.2=10h (unreachable due to exceeding sunlight time), A point 3km/0.2=15h (unreachable), only C point 4km/0.2=20h (unreachable). Conclusion: Under the current conditions, it is impossible to reach any target point." + }, + { + "id": 849, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. Known conditions: ① The temperature inside the container should be maintained at -50±5℃ (current -48℃) ② The internal pressure must be <10^-5Pa (current 8*10^-6Pa) ③ The RFID tag reading success rate must be ≥99% (actual 100%) ④ The handover window lasts 15 minutes. If any parameter exceeds the limit, a 10-minute emergency maintenance procedure must be initiated. Telemetry data refresh interval is 5 minutes.", + "question": "Determine whether the handover operation can be performed directly at this time? If not, explain the emergency measures needed and the remaining window time.", + "answer": "Direct handover possible: All parameters are within the standard range (temperature -48℃ ∈ [-55,-45], pressure 8*10^-6Pa < 10^-5Pa, RFID 100% ≥ 99%), no emergency operation required." + }, + { + "id": 850, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover is performing scientific exploration tasks when it encounters a lunar eclipse, causing a power outage from solar panels and switching to battery power. At this time, the relay link is interrupted due to the Moon's obstruction. The rover's internal buffer can store 8 hours of raw data (2Mbps continuously generated), and the battery life is only 6 hours. The engineering team decides: 1) to activate lossy compression to reduce the data rate to 1Mbps; 2) to prioritize the transmission of critical engineering parameters (occupying a constant bandwidth of 0.2Mbps); 3) to transmit the remaining data at a rate of 3Mbps after the lunar eclipse ends and communication is restored.", + "question": "Calculate the maximum amount of scientific data that can be saved during the lunar eclipse? If the lunar eclipse lasts 4 hours, how long will it take to complete the transmission of all data after communication is restored after the lunar eclipse ends? ", + "answer": "The amount of scientific data stored during the lunar eclipse = (1Mbps - 0.2Mbps)*3600*6 = 17.28Gb; 4-hour scenario: Accumulated data volume = (1-0.2)*3600*4=11.52Gb, transmission time = (11.52+0.2*3600*4)/(3-0.2)≈7200 seconds=2 hours." + }, + { + "id": 851, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. It is known that: (1) The internal pressure of the sealed can must be maintained at <10^-3Pa; (2) The temperature sensor records have not exceeded -50℃±3℃ throughout; (3) The relationship between the success rate of RFID tag reading and distance is P=1-0.2*d (d in meters); (4) The docking accuracy of the robotic arm is ±2cm; (5) All inspections must be completed 15 minutes before the ascent vehicle engine ignition. Current status: The container is 1.5 meters from the docking reference point, and the RFID has failed to read for 3 consecutive times.", + "question": "Please design a fault exclusion process that meets the time constraints, requiring a final RFID read success rate of ≥95% and meeting all other constraints.", + "answer": "Step 1: The robotic arm moves the container closer to d≤0.25 meters (at this point P≥95%); Step 2: Re-read the RFID tag; Step 3: If successful, then recheck the seal pressure; Step 4: All inspections should be completed within 10 minutes (moving closer operation ≤5 minutes + reading verification ≤5 minutes). Ultimately, it meets the RFID success rate ≥95%, pressure and temperature standards, and reserves a 15-minute ignition window." + }, + { + "id": 852, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. Analysis of the characteristics of the lunar soil in this area shows: the surface layer 0-30cm is loose fine particles (viscosity index 0.3, Mohs hardness 2), and there is a cemented layer at 30-50cm (viscosity index 1.2, Mohs hardness 4). The mission is equipped with three sampling tools: ① Rotary impact drill (suitable for hardness ≥3, power consumption 8W/min) ② Vibration core tube (suitable for viscosity ≤1.0, power consumption 5W/min) ③ Electric shovel (universal type, power consumption 3W/min but with a small sample volume). The current remaining energy of the probe is 1200W·min, and at least 3 samples from different depths need to be collected.", + "question": "Please design a combination of sampling tools and operation sequence that meets the energy constraints, requiring at least one sample from each layer and the shortest total time.", + "answer": "For the first layer (0-30cm), use the electric shovel (3W/min), and for the second layer (30-50cm), use the rotary impact drill (8W/min). Total energy consumption = 3*1 + 8*1 = 11W·min, far below the 1200W·min constraint." + }, + { + "id": 853, + "scenario_code": "3.1", + "instruction": " Chang'e-6 rover is conducting exploration tasks in the South Pole-Aitken Basin on the Moon, an area with complex terrain and multiple craters blocking the view. The rover is equipped with a dual-axis adjustable solar panel, with a maximum output power of 200W (under standard lighting conditions). According to the orbital dynamics model, the solar elevation angle during the current lunar day is 15 degrees, and the azimuth angle changes at a rate of 0.25 degrees per minute. At a certain moment, terrain analysis shows that there is an obstacle 1.5 meters high 2 meters ahead, and the length of its shadow is L = h / tan(α) (where h is the height of the obstacle, and α is the solar elevation angle). The solar panel tracking system needs to balance between maximizing power generation and avoiding frequent adjustments that could lead to mechanical wear.", + "question": "If the current solar panel adopts an intermittent tracking strategy of adjusting every 10 minutes, please calculate whether the shadow will cover the rover before the next adjustment (the solar panel installation height of the rover is 0.8 meters), and provide the tracking mode to be chosen at this time: 1) Maintain the current angle 2) Trigger adjustment in advance 3) Switch to 3D obstacle avoidance tracking mode.", + "answer": "1) Maintain the current angle. Calculation process: Shadow length L=1.5/tan(15°)=5.6 meters > 2 meters distance, but under an installation height of 0.8 meters, the actual shading requires L'=(1.5-0.8)/tan(15°)=2.6 meters > 2 meters, so the shadow will not cover the solar panel." + }, + { + "id": 854, + "scenario_code": "3.4", + "instruction": " Yutu-2 needs to operate scientific payloads (peak power consumption 80W), the mobility system (peak power consumption 120W), and the communication system (transmission instantaneous power consumption 150W) while working on the lunar surface. The instantaneous power supply limit of the Power Control Unit (PCU) is 200W, and the maximum discharge rate of the battery pack is 2C (capacity 50Ah, voltage 28V). The current State of Charge (SOC) is 60%, and the mission plan requires reserving at least 30% of the power for emergencies. Now, it is necessary to complete three tasks within 10 minutes: move 5 meters, take 3 sets of spectral data, and transmit 500MB of data (which requires continuous communication for 6 minutes).", + "question": "Please design a task sequence that meets the energy constraints, requiring the start and stop times of each subsystem to be specified and the total time not to exceed 10 minutes. Known: Movement time t_move = distance/0.1(m/s), the spectrometer takes 2 minutes per measurement, and the data transmission rate is constant at 100Mbps.", + "answer": "Sequence: 1) Move 5 meters first, taking 50 seconds (power consumption 120W); 2) Communicate for 6 minutes (the first 4 minutes in parallel with spectral measurements: 80+150=230W>200W is not feasible, so it is changed to communication alone from the 5th to the 10th minute at 150W); 3) Spectral measurements are conducted from 0-2, 2-4, and 4-6 minutes (total power consumption 80W<200W). The total time of 6 minutes meets the requirement." + }, + { + "id": 855, + "scenario_code": "2.7", + "instruction": " When the Chang'e-7 lander was working at the edge of the Shackleton crater, it suddenly received a solar proton event warning: the radiation dose expected to reach the lunar surface in 25 minutes would exceed the safety threshold. The lander's current coordinates are (12°S, 135°E), and the nearest permanent shadow zone shelter cave is located at (12.3°S, 135.2°E), about 800 meters away. The lander's maximum climbing ability is 20°, the cave entrance slope is 18°, and the maximum travel speed is 0.05m/s. The navigation system calculates that there is a 20-meter wide fissure in the straight path that needs to be bypassed (adding 120 meters to the journey). Safety procedures require entering the cave 5 minutes before the radiation arrives.", + "question": "Determine whether the lander can arrive at the shelter on time, and explain the basis.", + "answer": "Available time = 25 - 5 = 20 minutes = 1200 seconds; total distance = 800 + 120 = 920 meters; required time = 920 / 0.05 = 18400 seconds > 1200 seconds. Conclusion: It cannot arrive on time, as the required time (18400 seconds) exceeds the available time (1200 seconds)." + }, + { + "id": 856, + "scenario_code": "2.4", + "instruction": " The lunar rover Yutu-2 is currently performing exploration tasks on the far side of the moon, located at coordinate point A (10,20), and needs to reach scientific target point B (50,60). Terrain data indicates three possible paths between the two points: Path 1 is a straight distance of 60 meters but passes through a loose lunar soil area (wheel-soil resistance coefficient 0.3), Path 2 is a zigzag distance of 80 meters but is entirely on hard basalt (resistance coefficient 0.1), Path 3 is a detour distance of 100 meters containing a 15° slope with a 30% gradient (slope energy consumption coefficient 1.2). It is known that the translational power system efficiency formula for the lunar rover is: total energy consumption E = base power consumption 3Wh + distance d * (resistance coefficient k + slope correction p * sinθ), where the slope correction p = 0.5 (only applies to the path segment with a slope).", + "question": "Calculate the total energy consumption for the three paths and determine the optimal path choice.", + "answer": "Path 1 energy consumption E1 = 3 + 60 * (0.3 + 0) = 21Wh; Path 2 energy consumption E2 = 3 + 80 * (0.1 + 0) = 11Wh; Path 3 slope segment length = 100 * 30% = 30m, E3 = 3 + [70 * (0.1 + 0) + 30 * (0.1 + 0.5 * sin15°)] ≈ 3 + 7 + 30 * 0.23 ≈ 17Wh. The optimal choice is Path 2 (11Wh)." + }, + { + "id": 857, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover has obtained the following exploration data near the Von Kármán crater: 1) Coordinates of the KREEP rock spectral feature point (12.3°N, 125.7°E), scientific value coefficient 0.92; 2) Coordinates of the breccia outcrop (12.1°N, 125.9°E), scientific value coefficient 0.85; 3) The remaining power supports a total travel distance of no more than 800 meters. The known distances between points are: current position to KREEP rock = 520 meters, KREEP rock to breccia = 350 meters, current position to breccia = 600 meters. The rover's movement energy consumption model is: power consumption Q(Wh) = 0.8 * distance(m) + 50 * slope(°), and the slope in the current area is <5°, which can be ignored.", + "question": "How should the optimal exploration path be planned to maximize scientific value? Does the total power consumption of the path meet the constraints? ", + "answer": "Optimal path: current position → KREEP rock → breccia. Total scientific value = 0.92 + 0.85 = 1.77 (maximum). Total power consumption = 0.8 * (520 + 350) = 696Wh < 800Wh, meeting the constraints." + }, + { + "id": 858, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the following sequence of operations must be completed: 1) Sample container seal integrity check (3 minutes); 2) Environmental parameter recording (temperature, pressure, etc., 2 minutes); 3) RFID tag verification (1 minute). The launch window for the ascent vehicle is only 8 minutes, and each step must be executed in order and cannot be interrupted. If any step fails, the system requires an additional 2 minutes for fault diagnosis. Currently, the seal integrity check has been ongoing for 2 minutes without error, and the environmental recorder is in normal condition.", + "question": "Should the RFID verification program be initiated at this time? Please justify the decision through time calculation.", + "answer": "The RFID verification should be initiated. Time remaining calculation: 2 minutes (seal integrity check) + 3 minutes (remaining seal integrity check) + 2 minutes (environmental recording) + 1 minute (RFID) = 8 minutes. If any step fails, the 2-minute diagnostic time will exceed the window period, so the process must continue immediately." + }, + { + "id": 859, + "scenario_code": "5.1", + "instruction": " The Chang'e-6 lander is located in the South Pole-Aitken Basin (SPA) on the far side of the Moon, planning to communicate with Earth via the Queqiao-2 relay satellite. Known facts:\n1. Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, with an average altitude of about 8000 km above the lunar surface.\n2. The maximum communication elevation angle requirement from the lander to the relay satellite is ≥15°.\n3. The lunar radius is 1737 km.\n4. At the current moment, the lunar central angle between the lander and Queqiao-2 is 85°.\n5. The communication frequency is X-band (8 GHz), and the free space path loss formula is: L = 92.45 + 20*lg(d) + 20*lg(f), where d is the distance (km) and f is the frequency (GHz).", + "question": "Please verify whether the communication elevation angle requirement is met at the current moment, and calculate the free space path loss value of the link at this time.", + "answer": "1. Verify the communication elevation angle: According to spherical geometry, the line-of-sight distance d = sqrt( (1737+8000)^2 + 1737^2 - 2*(1737+8000)*1737*cos(85°) ) ≈ 8134 km; the elevation angle θ = arcsin( (d^2 + 1737^2 - (8000+1737)^2 ) / (2*d*1737) ) ≈ 16.2° >15°, which meets the requirement.\n2. Path loss L = 92.45 + 20*lg(8134) + 20*lg(8) ≈ 92.45 + 78.21 + 18.06 ≈ 188.72dB" + }, + { + "id": 860, + "scenario_code": "5.7", + "instruction": " The 128GB solid-state memory on the lunar orbiter is experiencing the following conditions:\n1. NAND flash block size is 4MB, with a lifespan of 3000 write-erase cycles\n2. The current wear-leveling algorithm has resulted in 30% of the blocks being written 2500 times\n3. The average daily write data volume is 8GB\n4. The NASA Jet Propulsion Laboratory has proposed a new algorithm that can reduce the concentration of writes to hot spots by 40%.", + "question": "Calculate the remaining life of the storage under the current algorithm (in days), and estimate the life extension ratio after adopting the new algorithm.", + "answer": "1. Remaining life calculation: Remaining write-erase cycles for hot spots = 3000-2500=500 times; Daily consumption cycles = (8GB/4MB)*30% = 614 times; Remaining days = 500*30%*total blocks / (614/total blocks) ≈ 500/(614/(128GB/4MB)) ≈ 500/(614/32768) ≈ 26,700 days;\n2. New algorithm improvement ratio: Hot spot writes reduced by 40% → Daily consumption cycles reduced to 614*0.6=368 times → Life extended to 26,700*(614/368) ≈ 44,500 days → Improvement ratio = (44,500-26,700)/26,700 ≈ 66%." + }, + { + "id": 861, + "scenario_code": "3.4", + "instruction": " The Yutu-2 rover performs the following tasks simultaneously during the 10th hour of the lunar day: ① X-band communication (peak power consumption 80W, lasting 15 minutes) ② Spectrometer heating (constant power 40W, lasting 30 minutes) ③ Drive motor (pulsed load, cycle 5 minutes: consumes 120W for 2 minutes, consumes 5W for 3 minutes). The power bus has a rated capacity of 150W, and overload scheduling will be triggered if exceeded. The current remaining capacity of the lithium-ion battery is 500Wh, and it still needs to support 8 hours of basic system operation (20W) afterwards.", + "question": "If no load scheduling is performed, will overload protection be triggered at the 25th minute of the 10th hour? Will the remaining power be sufficient to support subsequent tasks at this time (consumption 160Wh<500Wh)?", + "answer": "Overload protection will be triggered (total load 160W>150W), and the remaining power is sufficient to support subsequent tasks (consumption 160Wh<500Wh)." + }, + { + "id": 862, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 lander is located on the edge of an impact crater at 23.5°N, 12.8°E on the near side of the Moon. Its solar panels operate in a two-dimensional tracking mode. According to the lunar ephemeris, the current solar elevation angle is 15°, and the azimuth angle is 45° (0° is due north, increasing clockwise). The crater wall forms a permanent shadow zone in the azimuth angle range of 30° to 60°. Under standard conditions, the power generation capacity of the solar panels is P0 = 300W (when the light is vertical), and the actual power P = P0 * cosθ (θ is the angle of incidence of sunlight).", + "question": "If the current orientation of the solar panels is 90° in azimuth (due east) and 0° in pitch, calculate the actual power generation at this time and the theoretically maximum power generation value that can be optimized.", + "answer": "The current angle of incidence θ = arccos(cos(15°) * cos(45°)) ≈ 47.8°, the actual power P = 300 * cos(47.8°) ≈ 201W; the optimal orientation to avoid the shadow zone is 60° in azimuth and 15° in pitch, at which point θ=0°, the maximum power Pmax=300W." + }, + { + "id": 863, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing patrol tasks on the far side of the moon, located at coordinate point A (10°N, 120°E). The science team requires it to proceed to target point B (12°N, 122°E) to collect basalt samples. It is known that: 1) the straight-line distance between the two points is 30km; 2) the average driving speed of the lunar rover is 0.1m/s; 3) the energy consumption model is E = 0.15*d + 2*h, where d is the driving distance (km), and h is the cumulative climb height (m); 4) terrain data shows that the AB route requires a cumulative climb of 50m; 5) the current remaining power is 500Wh.", + "question": "If the straight-line path is chosen, calculate the time required to complete the task and the total energy consumption, and determine whether the current power is sufficient.", + "answer": "Time t = distance / speed = 30000m / 0.1m/s = 300000s ≈ 83.33 hours; total energy consumption E = 0.15*30 + 2*50 = 4.5 + 100 = 104.5Wh. The current power of 500Wh > 104.5Wh, so the power is sufficient." + }, + { + "id": 864, + "scenario_code": "2.2", + "instruction": " The Chang'e-7 lander releases a rover at the edge of the Shackleton crater (a permanently shadowed area). The region has a light intensity of <0.01lux and a temperature consistently below -170°C. Navigation system configuration: 1) IMU drift error 0.1°/h; 2) visual odometry feature matching success rate <5%; 3) LiDAR SLAM accuracy ±3cm; 4) star sensor availability only 50% (blocked by the crater). The rover needs to move to a preset scientific research point 200 meters away within 30 minutes.", + "question": "In the above extreme environment, which navigation sensor combination should be prioritized? Provide the selection basis and the expected positioning error range.", + "answer": "Prioritize the LiDAR SLAM + IMU combination: 1) SLAM is unaffected by lighting and has the highest accuracy; 2) IMU compensates for SLAM's intermittent data. Expected error: 30 minutes of IMU drift 0.05°, corresponding to a displacement error of about 200*tan(0.05°) ≈ 0.17m, with a total error of ±3.17cm after adding SLAM error." + }, + { + "id": 865, + "scenario_code": "3.6", + "instruction": " The Chang'e-7 lander needs to maintain the electronic cabin temperature above -40℃ during the lunar night. It is known that: the cabin heat loss coefficient K = 2W/℃, the ambient temperature is -180℃, the isotope heat source has a rated output of 50W, and the electric heater has a maximum power of 30W. The scientific instruments generate 10W of heat, and the insulation target duration is 14 Earth days (336 hours), with the battery pack having an available energy of 4200Wh.", + "question": "Calculate whether the isotope heat source alone can meet the insulation requirements? If not, determine the minimum average power that the electric heater needs to supplement and the corresponding battery safety margin (retaining at least 20% charge).", + "answer": "Heat balance requirement Q = K * (40 - (-180)) = 440W, the isotope heat source shortfall = 440 - 50 - 10 = 380W; the electric heater needs to make up for 380W but exceeds the limit → actually, the heater needs to run at full load of 30W, at this time the total heat supply = 50 + 10 + 30 = 90 < 440W does not meet the requirement; the minimum average power = (440 - 50 - 10) = 380W (exceeds the heater's capability); the battery can supply power = 4200 * 80% = 3360Wh, safety margin = 3360 / (30 * 336) ≈ 33%." + }, + { + "id": 866, + "scenario_code": "2.7", + "instruction": " The lunar rover receives a solar proton event warning (expected to arrive in 30 minutes) while working near the terminator and must take immediate shelter. Current status: 1) 1.2km away from the nearest permanent shadow area shelter; 2) IMU shows X-axis gyroscope failure; 3) Only 60% visual navigation reliability remains; 4) LBNSS navigation beacon signal strength fluctuates (ranging error ±5m); 5) Maximum safe driving speed is 0.08m/s.", + "question": "Calculate the shortest time to reach the shelter and analyze how to ensure navigation reliability in this emergency situation.", + "answer": "Shortest time t = 1200m / 0.08m/s = 15000s = 250 minutes > 30 minutes warning time. Measures to be taken: 1) Activate redundant Y/Z-axis gyroscopes to compensate for X-axis failure; 2) Use LBNSS beacon mean filtering to reduce errors; 3) Reduce speed to 0.05m/s to increase the success rate of visual navigation." + }, + { + "id": 867, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander, while working at the edge of the Shackleton crater, suddenly receives a solar proton event warning (lasting 4 hours). Current status: 1) The lander is 300m in a straight line from the permanent shadow area shelter; 2) The emergency movement speed can reach 0.15m/s; 3) 30 minutes need to be reserved for switching to safe mode; 4) There is an 8-minute decision-making time window before communication is interrupted. Terrain data indicates that a detour around a 50m diameter impact crater is necessary, increasing the actual path to 350m.", + "question": "Determine whether the lander can switch to safe mode and reach the shelter before communication is interrupted? Provide key time calculation steps.", + "answer": "Total required time = Movement time + Switching time = (350m / 0.15m/s) / 60 + 30min ≈ 38.9min + 30min = 68.9min. The 8-minute window < 68.9min required, it cannot be completed." + }, + { + "id": 868, + "scenario_code": "5.1", + "instruction": " Chang'e-6 lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S), and plans to communicate with Earth via the Queqiao-2 relay satellite. It is known that Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, about 65,000 km from the center of the Moon. The lander's transmission power is 20 W, with an antenna gain of 10 dBi; the relay satellite's receiving antenna gain is 15 dBi, the system noise temperature is 300 K, and the required minimum signal-to-noise ratio (SNR) is 10 dB. The current communication frequency is 2.4 GHz (wavelength 0.125 m), and the free space path loss formula is L = 20 * log10(4 * π * d / λ).", + "question": "Calculate whether the uplink from the lander to the relay satellite meets the communication requirements when the current Earth-Moon distance is 405,000 km? (Need to calculate the actual SNR and compare it with the threshold value.)", + "answer": "1. Calculate the path loss: L = 20 * log10(4 * π * 405000000 / 0.125) ≈ 210.1 dB\n2. Received power Pr = Pt + Gt + Gr - L = 20 dBm + 10 dBi + 15 dBi - 210.1 dB = -165.1 dBm\n3. Noise power Pn = k * T * B (assuming bandwidth B=1 MHz=1e6 Hz): Pn ≈ -228.6 dBW/Hz + 24.8 dBK + 60 dBHz = -143.8 dBW = -113.8 dBm\n4. SNR = Pr - Pn = -165.1 - (-113.8) = -51.3 dB < 10 dB → does not meet the requirement" + }, + { + "id": 869, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover needs to transmit 500 MB of scientific data daily to the relay satellite during the lunar day. Currently, the DTN protocol is used to buffer data, but a sudden solar flare has caused three consecutive transmission failures (each attempt takes 30 minutes). The rover's solid-state memory has a remaining capacity of 600 MB, and the data generation rate is 5 MB/hour. The system is set to automatically switch to lossy compression mode (compression ratio 50%) when the remaining capacity falls below 20%.", + "question": "If the flare continues to affect for 2 hours and then communication is restored, what data transmission strategy should be adopted at this time? Need to calculate the remaining storage space and determine whether the compression mode is triggered.", + "answer": "1. Data volume added during the flare: 5 MB/h * 2 h = 10 MB\n2. Cache occupied by failed transmissions: 500 MB * (3/24) = 62.5 MB (24 transmission windows per day)\n3. Total occupied: 62.5 + 10 = 72.5 MB → Remaining capacity 600 - 72.5 = 527.5 MB > 120 MB (20% threshold)\n4. Strategy: Maintain lossless compression mode, prioritize retransmission of failed data packets" + }, + { + "id": 870, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander, while conducting exploration at the edge of the Shackleton crater, suddenly receives a solar proton event warning signal. According to the radiation model prediction:\n- Current radiation dose rate: 50μGy/h\n- Safety threshold: cumulative exposure not exceeding 200μGy\n- Distance to the nearest permanent shadow area shelter: 800 meters\nMaximum speed of the rover: 0.1m/s (on flat terrain), current terrain requires operation at 60% speed\nEnergy status: remaining power can support continuous movement for 90 minutes", + "question": "Please verify whether the rover can reach the shelter before the cumulative radiation exceeds the limit? A comparison of the remaining safe time and the travel time is required.", + "answer": "Remaining safe time = 200μGy / 50μGy/h = 4 hours; Travel time = 800m / (0.1m/s * 0.6) = 13333 seconds ≈ 3.7 hours < 4 hours. And 3.7 hours < 1.5 hours power limit, so it can arrive safely." + }, + { + "id": 871, + "scenario_code": "2.10", + "instruction": " The lunar rover needs to perform centimeter-level precise positioning sampling on a basalt outcrop. It is known that:\n- Visual navigation camera resolution: 1024×1024 pixels\n- Field of view (FOV): 30°×30°\n- Current straight-line distance to the target: 5 meters\n- UWB beacon ranging accuracy: ±3cm\n- IMU attitude angle error: ±0.5°\nControl strategy requires final positioning error ≤5cm", + "question": "Calculate whether the ground resolution of a single pixel of the current visual system meets the positioning accuracy requirements? If not, how should it be adjusted?)", + "answer": "Single pixel resolution = 2 * 5 * tan(15°) / 1024 ≈ 0.00256m/pixel = 2.56mm/pixel < 5cm requirement. However, the total error after combining UWB and IMU errors = sqrt(3^2 + (500 * 0.5 * π / 180)^2) ≈ sqrt(9 + 19) = 5.29cm > 5cm, so it needs to switch to a higher precision visual servo mode or reduce the distance to less than 4 meters." + }, + { + "id": 872, + "scenario_code": "5.4", + "instruction": " The lunar rover needs to transmit scientific data packets through the relay satellite every 2 hours during the lunar day (each packet is 500MB). Currently, a solar conjunction is causing communication interruptions, leaving 8 hours of remaining daylight. The solid-state storage has 1.2GB of remaining capacity, and the maximum data compression rate can reach 50%. The rover's power system can only maintain the current operating mode until the end of the lunar day.", + "question": "To ensure all data is transmitted intact, calculate the minimum compression rate required and indicate whether the transmission frequency needs to be adjusted (assuming the transmission time per session remains unchanged after compression).", + "answer": "Total original data volume = 500MB * (8/2) = 2000MB. Available storage 1.2GB = 1228.8MB < 2000MB, so compression must be enabled. Required compression rate ≤ 1228.8/2000 = 61.44%. Due to power limitations, the transmission frequency cannot be increased, so using a 50% compression rate (final data volume 1000MB) will meet the requirements." + }, + { + "id": 873, + "scenario_code": "5.1", + "instruction": " The Chang'e-6 lander is planned to land in the South Pole-Aitken Basin on the far side of the Moon, and needs to communicate with the ground station via the Queqiao-2 relay satellite. It is known that Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, with an average altitude of 8000km above the lunar surface. The lander's transmission power is 10W, with an antenna gain of 5dBi; the relay satellite's receiving antenna gain is 20dBi, and the system noise temperature is 300K. The current communication frequency is 2.4GHz, and the free space path loss formula is: L = 20 * log10(d) + 20 * log10(f) + 92.45 (d in km, f in GHz). The requirement is that the signal-to-noise ratio (SNR) at the receiving end must be no less than 10dB to achieve reliable communication.", + "question": "Calculate whether the SNR at the receiving end of the relay satellite meets the requirement when the Earth-Moon distance is 400,000 km? (Boltzmann constant k = 1.38e-23 J/K).", + "answer": "1. Calculate the path loss: L = 20*log10(400000) + 20*log10(2.4) + 92.45 ≈ 52.04 + 7.6 + 92.45 = 152.09 dB\n2. Received power Pr = Pt + Gt + Gr - L = 10dBW + 5dBi + 20dBi - 152.09dB = -117.09dBW\n3. Noise power Pn = kTB = 1.38e-23 * 300 * (2.4e9) ≈ 9.94e-12 W → -110dBW\n4. SNR = Pr - Pn = -117.09 - (-110) = -7.09dB < 10dB → does not meet" + }, + { + "id": 874, + "scenario_code": "5.4", + "instruction": " During the lunar day, the Yutu-2 rover encounters a solar conjunction interruption (with the Sun located on the Earth-Moon line) while transmitting scientific data to the ground via a relay satellite. It is known that the interruption will last for 8 hours, the rover's local storage has a remaining capacity of 50GB, and the current data generation rate is 200MB/hour. The device uses two modes: a lossy compression algorithm (compression ratio 4:1) and a lossless compression algorithm (compression ratio 1.5:1), with a switch time of 5 minutes for each.", + "question": "To ensure data is not lost and to maximize scientific value, how should the compression mode be selected? Provide a specific calculation process.", + "answer": "1. Original data volume: 8h * 200MB/h = 1600MB\n2. After lossy compression: 1600MB /4 =400MB <50GB (feasible)\n3. After lossless compression: 1600MB /1.5≈1066MB <50GB (feasible)\n4. Choose lossless compression to retain complete scientific data (although it occupies more space, it still meets the storage limit)." + }, + { + "id": 875, + "scenario_code": "1.5", + "instruction": " When remotely operating a lunar rover from the ground control center for rock sampling, the one-way communication delay between Earth and the Moon is 1.3 seconds. The current speed of the lunar rover is 0.2m/s, and an unplanned lunar pit obstacle appears 3 meters ahead. The predictive control algorithm of the remote operation system can predict the movement trajectory for the next 2 seconds based on historical data, and the emergency braking distance is 0.5 meters. The control system updates the command queue every 0.5 seconds.", + "question": "Determine whether the ground operator needs to immediately send an emergency braking command under the current situation? Please list the calculation basis.", + "answer": "Total delay from detecting the obstacle to the command taking effect = communication delay 1.3s + next control cycle 0.5s = 1.8s; the distance the lunar rover moves during this period = 0.2m/s * 1.8s = 0.36m; remaining distance 3m - 0.36m = 2.64m > braking distance 0.5m. Therefore, immediate braking is not required." + }, + { + "id": 876, + "scenario_code": "1.8", + "instruction": " When deploying a seismic array, it is found that the local lunar soil bearing capacity is only 70% of the expected value. The original plan was to use a triangular bracket (single leg contact area 50cm², safety factor requires ground pressure ≤8kPa), and the actual measured lunar soil ultimate bearing capacity is 9kPa. The total mass of the equipment is 45kg (including the bracket), and the lunar gravitational acceleration is 1.62m/s².", + "question": "Calculate whether the existing bracket meets the safety requirements? If adjustments are needed, what is the minimum additional contact area required per leg to meet the safety requirements for the ground pressure of 6.3kPa (70% of 9kPa)?", + "answer": "Total weight force of the equipment = 45kg * 1.62m/s² = 72.9N; force per leg = 72.9N / 3 = 24.3N; original design pressure = 24.3N / 50cm² = 4.86kPa < 8kPa but > actual bearing capacity 9kPa * 70% = 6.3kPa. The leg area needs to be increased to 24.3N / 6.3kPa = 38.57cm², and the current 50cm² already meets the requirement." + }, + { + "id": 877, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks at the edge of the Von Kármán crater, with a remaining power of 3200 Wh. There are two scientific target points ahead: Target A (1.2 km away, 8° slope) and Target B (0.8 km away, 12° slope). It is known that the energy consumption model of the lunar rover is: E = (0.15 * d + 0.02 * θ * d) * k, where E is the energy consumption (Wh), d is the travel distance (km), θ is the absolute value of the slope (°), and k is the terrain factor (flat area k=1.0, rocky area k=1.3). Target A is located in a flat area, and Target B requires crossing a rocky area (30% of the total distance).", + "question": "If only considering the optimal energy strategy, which target point should Yutu-2 prioritize? Please calculate the total energy consumption for both options and provide the basis for your choice.", + "answer": "Total energy consumption for Target A E_A = (0.15 * 1.2 + 0.02 * 8 * 1.2) * 1.0 = (0.18 + 0.192) = 372 Wh; Flat segment energy consumption for Target B E_B1 = (0.15 * 0.56 + 0.02 * 12 * 0.56) * 1.0 = (0.084 + 0.1344) = 218.4 Wh; Rocky segment energy consumption E_B2 = (0.15 * 0.24 + 0.02 * 12 * 0.24) * 1.3 = (0.036 + 0.0576) * 1.3 = 121.68 Wh; E_B = E_B1 + E_B2 = 340.08 Wh. Target B should be chosen as it consumes less energy (340 Wh < 372 Wh)." + }, + { + "id": 878, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander is conducting exploration in the Shackleton crater when it suddenly receives a solar proton event warning: high-energy particle streams are expected to reach the lunar surface in 30 minutes and last for 4 hours. The lander is currently in scientific observation mode (200W power consumption), and if it switches to safe mode (50W power consumption), it needs to complete equipment retraction 10 minutes in advance. The lander has a remaining power of 1800 Wh, and the solar panels will be ineffective during the proton event. The lander must ensure it can operate in safe mode until the event ends and retain at least 200 Wh of emergency power.", + "question": "Determine whether the lander needs to immediately switch to safe mode? If not, how long can it continue to observe at most before switching to safe mode? ", + "answer": "Total power requirement in safe mode = 50W * (4h + 10min/60) = 50 * 4.167 ≈ 208 Wh; Remaining usable power = 1800 - 200 = 1600 Wh; Maximum operational time in current mode t_max = (1600 - 208) / 200 = 1392 / 200 = 6.96 h. Since the proton event only requires 4 hours of safe mode and the warning time is sufficient (30min > 10min), there is no need to switch immediately, and the lander can continue to observe for up to 6 hours and 57 minutes." + }, + { + "id": 879, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S), and needs to establish a communication link through the Queqiao-2 relay satellite. It is known that:\n1. Queqiao-2 operates in the Earth-Moon L2 Halo orbit, about 65,000km from the Moon's center\n2. The Moon's radius is 1737km\n3. The geometric elevation angle between the lander and Queqiao-2 must be ≥5° at the current moment to establish a stable link\n4. The signal transmission rate is affected by free space loss, the formula is: L = 20 * log10(4πd/λ), where d is the distance, and λ is the wavelength (0.3m)\n5. The current link distance calculation shows d=66,200km", + "question": "Please verify whether the current moment meets the communication geometry conditions (need to calculate whether the line-of-sight distance from the lunar surface lander to the relay satellite exceeds the lunar obscuration range), and calculate the free space loss value at this time (unit dB).", + "answer": "Communication conditions are met (line-of-sight distance=sqrt(66200^2 - 1737^2)=66177km > lunar radius), free space loss=20*log10(4*3.14*66200/0.3)=214.3dB" + }, + { + "id": 880, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover experienced an X-band communication interruption during the lunar day, and the fault diagnosis showed:\n1. The main antenna pointing mechanism is stuck, causing a deviation of 12° from the theoretical angle\n2. The remaining energy can only support 30 minutes of emergency operations\n3. The backup UHF antenna can provide 1Mbps bandwidth (the main antenna is 10Mbps)\n4. There are 2GB of unsent scientific data in the buffer that need to be rescued\nThe emergency strategy requires:\n- If switching to UHF, the transmission time needs to be recalculated\n- Critical engineering data (20% of the total) must be transmitted first", + "question": "Please determine whether it is necessary to switch the communication link, and calculate whether all critical data can be rescued within the remaining energy.", + "answer": "It is necessary to switch to the UHF link, the critical data transmission time=(2GB*20%)/(1Mbps/8)=3276.8 seconds≈54.6 minutes, exceeding the remaining energy of 30 minutes, unable to complete the transmission of all critical data" + }, + { + "id": 881, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S), and needs to communicate with Earth through the Queqiao-2 relay satellite. Given:\n1. Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, about 65,000km from the Moon's center\n2. The Moon's radius is 1737km\n3. The Earth-Moon center-Queqiao-2 angle at the current moment is 35°\n4. The lander's communication antenna elevation angle must be ≥10° to establish a stable link\n5. The average Earth-Moon distance is 384,400km", + "question": "Calculate whether the lander and Queqiao-2 meet the communication geometry conditions at the current moment (list key steps).", + "answer": "1. Calculate the distance from the Moon's center to the lander = the Moon's radius = 1737km\n2. The distance from Queqiao-2 to the Moon's center = 65,000km\n3. Use the cosine theorem to find the distance between Queqiao and the lander: d=sqrt(65000^2 + 1737^2 - 2*65000*1737*cos(35°))≈63,892km\n4. Calculate the minimum communication elevation angle corresponding to the Earth-Moon-Queqiao angle θ: arcsin(1737/63892)≈1.56°<10°, thus the communication condition is not met" + }, + { + "id": 882, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover experienced an X-band communication interruption during the lunar day, and the fault diagnosis revealed:\n1. The main transmitter output power abnormally dropped to 2W (nominal value 10W)\n2. The current relay link margin is 6dB\n3. The system can automatically switch to the backup transmitter (nominal power 8W) or activate the UHF emergency link (maximum rate 1kbps)\n4. X-band antenna gain is 38dBi, UHF antenna gain is 0dBi", + "question": "Choose the optimal emergency communication plan and calculate the theoretical margin of the new link (known X-band path loss = 200dB, UHF path loss = 180dB).", + "answer": "Optimal plan: Switch to the backup transmitter\nCalculation process:\n1. New X-band link margin = 10*log10(8/10) + 6 ≈ 5dB (still positive margin)\n2. UHF link margin = 0 + 0 - 180 + 6 = -174dB (not met)\nConclusion: The backup transmitter can maintain communication and has the optimal margin" + }, + { + "id": 883, + "scenario_code": "5.7", + "instruction": " The 128GB on-board SSD of the Chang'e-7 orbiter has the following conditions:\n1. Total write volume has reached 72TBW (nominal durability 100TBW)\n2. Current bad block rate is 0.8% (alert threshold 1%)\n3. Remaining storage space is 12GB\n4. Daily scientific data generation is about 4GB (at least 2 copies need to be saved).", + "question": "Determine whether the storage migration contingency plan needs to be activated (consider wear leveling and capacity constraints simultaneously).", + "answer": "The migration contingency plan needs to be activated.\nBasis for judgment:\n1. Durability consumption rate = 72/100 = 72% (still acceptable)\n2. Remaining effective capacity = 12/2 = 6GB < daily data volume of 4GB (insufficient capacity)\n3. Bad block rate is close to the alert threshold." + }, + { + "id": 884, + "scenario_code": "5.4", + "instruction": " During the lunar day, the Yutu-2 rover was scheduled to transmit scientific data to the Queqiao relay satellite when it suddenly encountered a solar conjunction (the Sun is between the Earth and the Moon). It is known that:\n1. The solar conjunction will last for 48 hours, during which all Earth-Moon communications will be interrupted;\n2. The remaining capacity of the rover's solid-state memory is 50GB, and the current data generation rate is 1GB/hour;\n3. In emergency mode, lossy compression (compression ratio 5:1) can be activated, but this will result in a 30% loss of spectral data precision;\n4. The lunar night will begin in 72 hours, at which time the equipment will enter a hibernation state.", + "question": "To ensure data is not lost and to maximize the scientific value, how should the storage strategy be adjusted? Provide specific calculation basis.", + "answer": "1. Original data requirement: 48h * 1GB/h = 48GB > remaining 50GB, compression needs to be activated\n2. Compressed data volume: 48GB / 5 = 9.6GB < 50GB, can be fully saved\n3. Choose the compression timing: activate compression when the remaining storage space is below 48GB (i.e., 2 hours later)." + }, + { + "id": 885, + "scenario_code": "3.3", + "instruction": " During the lunar day, Yutu-2 measured the temperature of the equipment cabin in the illuminated area to be +110°C, and the SOC of the energy storage battery is 85%. According to the mission plan, there are 4 hours until the start of the lunar night, and at least 30% of the power must be maintained for the lunar night heating system. Current load: scientific instrument group continuous power consumption 40W, thermal control system cooling power consumption 60W. The battery's rated capacity is 3000Wh, and the lunar night heating system requires 20W for 360 hours.", + "question": "Determine whether the emergency charging mode (maximum charging power 150W) needs to be activated? Calculate the maximum allowable working time of the scientific instruments (保留整数).", + "answer": "Emergency charging needs to be activated. Total demand for the lunar night = 20W * 360h = 7200Wh, current power = 3000 * 85% = 2550Wh, shortfall 4650Wh. 4 hours of charging can replenish 150W * 4h = 600Wh, which is still insufficient. Maximum working time of scientific instruments = (2550 + 600 - 7200) / 40W = -101 hours (not feasible), scientific instruments need to be turned off and full charging must be carried out." + }, + { + "id": 886, + "scenario_code": "5.4", + "instruction": " During the lunar day, the Yutu-2 rover was transmitting scientific data to the relay satellite as planned when it suddenly encountered a solar proton event causing an X-band communication interruption. The rover's built-in 256GB solid-state storage is 70% full, and the current data generation rate is 50MB/hour. The fault detection system initiated a level three emergency response: 1) Immediately switch to the S-band backup transmitter (5W power, 1MHz bandwidth); 2) Enable the DTN protocol to cache critical data; 3) Attempt to reconnect the main link every 30 minutes. There are 8 hours remaining in the lunar day, and the measured signal-to-noise ratio of the S-band link is only 6dB.", + "question": "Determine whether the rover can completely transmit all the data generated by the end of the lunar day through the backup link? It is known that the S-band channel capacity C = B * log2(1+SNR), where B is the bandwidth, and SNR is the linear value.", + "answer": "Calculate the S-band channel capacity: C = 1e6 * log2(1+4) ≈ 2.32 Mbps = 0.29 MB/s. Data that can be transmitted in 8 hours = 0.29*3600*8 ≈ 8352MB; Stored data = 256*0.7 = 179.2GB = 179200MB; New data = 50*8 = 400MB; Total data to be transmitted = 179200+400 = 179600MB >> 8352MB. Conclusion: The transmission cannot be completed." + }, + { + "id": 887, + "scenario_code": "3.8", + "instruction": " The Chang'e-7 lander mission cycle is 12 lunar day/night cycles, with 14 effective working days per lunar day. Energy budget constraints: ① Average daily power generation from solar arrays is 4kWh; ② Lunar day load: average 0.8kWh per day for communication systems, 1.2kWh for exploration instruments, 0.5kWh for thermal control; ③ Basic thermal insulation power consumption during the lunar night is 1kWh/day (powered by batteries). The battery pack charge/discharge efficiency is 90%, with an initial SOC of 100% (capacity 10kWh).", + "question": "Verify whether the battery SOC at the end of the 3rd lunar day can meet the subsequent mission requirements? Calculate the theoretical SOC percentage at this time (rounded to the nearest integer).", + "answer": "It can meet the requirements. Net charge per lunar day = (4-0.8-1.2-0.5)*14*90% = 18.9kWh; Power consumption per lunar night = 1*14 = 14kWh; Remaining power after 3 cycles = 10 + 3*(18.9-14) = 24.7kWh > 10kWh capacity limit, so SOC = 100%." + }, + { + "id": 888, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (longitude 180°E, latitude 45°S), planning to establish a communication link with Earth via the Queqiao-2 relay satellite. It is known that Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, with an average altitude of 8000km above the lunar surface. The lander uses an X-band (8GHz) directional antenna (gain 20dBi) to communicate with the relay satellite. At the current moment, the elevation angle of the relay satellite relative to the lander is 35°, the lunar surface temperature is -170°C, the lander's transmission power is 10W, the system noise temperature is 300K, and the required minimum signal-to-noise ratio (SNR) is 10dB.", + "question": "Calculate the theoretical maximum data transmission rate of the communication link under the current conditions (ignoring Doppler frequency shift and atmospheric loss), given that the receiving antenna gain is 15dBi and the Boltzmann constant k=1.38e-23 J/K.", + "answer": "According to the link budget formula: SNR = P_t * G_t * G_r * λ^2 / ( (4πd)^2 * k * T_sys * R ), where λ=c/f=3e8/8e9=0.0375m, d=8000km. Solving for R = P_t * G_t * G_r * λ^2 / ( (4πd)^2 * k * T_sys * SNR ) = 10 * 100 * 31.6 * 0.0375^2 / ( (4*3.14*8e6)^2 * 1.38e-23 * 300 * 10 ) ≈ 32.7 kbps" + }, + { + "id": 889, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration on the north side of the Von Kármán crater, obtaining the following regional data: Point A (120m from the current position) shows KREEP rock characteristics (K/Th ratio >2500); Point B (80m) has thermal infrared anomalies (day-night temperature difference ΔT=85K); Point C (150m) shows a 2m thick loose deposit layer by LiDAR. The rover's average daily travel capability is 50m, the XRF instrument can be used up to 3 times per day, and the remaining power supports 4 days of operation. The scientific priority order is: 1) KREEP rock sampling 2) Verification of thermal anomalies 3) Shallow structure exploration.", + "question": "Please design the optimal exploration path to ensure the completion of the highest priority task before the power is depleted, and explain the daily travel schedule and instrument usage allocation.", + "answer": "Path: On the first day, travel directly to Point A (120m), and on the second day, return to Point B (80m). On the first day, travel 120m using 2.4 days of power (120/50), leaving 1.6 days to support the 80m return trip; use the XRF instrument twice on the first day at Point A (KREEP rock analysis + backup), and once on the second day at Point B (thermal anomaly verification). Abandon Point C to prioritize KREEP rock sampling." + }, + { + "id": 890, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover encountered a sudden solar proton event while performing scientific exploration tasks during the lunar day, causing an interruption in X-band communication with the Queqiao relay satellite. The rover's built-in 256GB solid-state storage is 70% used, and the current data generation rate of scientific instruments is 12Mbps. The last effective communication window before the interruption lasted 15 minutes, successfully transmitting 1.2GB of engineering data. The rover uses a dynamic cache management strategy: when the storage usage rate is ≥80%, lossy compression (compression ratio 50%) is automatically triggered, and when it is ≥90%, low-priority payloads are paused.", + "question": "If the communication interruption lasts 4 hours, calculate the final usage rate of the rover's storage (considering the writing of original data and the triggering conditions for lossy compression), and determine whether it is necessary to pause some payloads.", + "answer": "1. Original data volume: 12Mbps * 4 *3600s /8 =21,600MB=21.6GB\n2. Initial remaining space: 256GB*30%=76.8GB\n3. Total data volume after writing: 256GB*70%+21.6GB=201GB (usage rate 78%) <80%\n4 Conclusion: No lossy compression or pause mechanism is triggered, the final usage rate is 78%, and there is no need to pause payloads" + }, + { + "id": 891, + "scenario_code": "5.7", + "instruction": " The 128TB on-board SSD of the Chang'e-7 orbiter uses a NAND flash memory architecture, with each storage unit capable of withstanding 3000 write/erase cycles. The file system employs a dynamic wear leveling algorithm, evenly distributing write operations across all blocks. It is known that the average daily write data volume is 480GB (including check data), and the storage system reserves 15% redundant space for bad block replacement. The actual physical capacity of the SSD is 147TB, divided into 512 logical units (LUN).", + "question": "Calculate the theoretical service life (years) of the SSD under ideal wear leveling conditions, taking into account the impact of redundant space on actual usable capacity.", + "answer": "1. Available user capacity=147TB*85%=124TB\n2 Daily write amplification factor=actual write volume/user data volume=480GB/(480GB/1)=1\n3 Daily wear cycles=480GB/(124TB/3000)=480/(124000/3000)=11 times\n4 Service life=3000 times/(11 times/day)/365≈7 years" + }, + { + "id": 892, + "scenario_code": "3.6", + "instruction": " The Yutu-2 rover is about to enter the lunar night (expected to last 14 Earth days), and it needs to maintain the battery temperature ≥ -40°C. Known: 1) Battery mass m=8kg, specific heat capacity c=900J/(kg·K); 2) Initial temperature T0=20°C; 3) Lunar night ambient temperature Te=-180°C; 4) Thermal resistance of insulation Rth=2K/W; 5) Electric heater power options are 5W or 10W. The system requires total energy consumption not to exceed 6kWh.", + "question": "If only the 5W heater is used and the insulation is intact, calculate whether the minimum battery temperature during the lunar night meets the requirements? If not, what is the minimum wattage of the heater that needs to be switched to at least meet the requirements? ", + "answer": "Not met. Calculation process: 1) Heat loss power=(T-Te)/Rth=(20-(-180))/2=100W; 2) Net heating power=5W-100W=-95W; 3) Temperature drop rate=95/(8*900)=0.0132K/s; 4) Temperature drop over 14 days=0.0132*86400*14≈15974K (far below the requirement). A heater of ≥100W needs to be switched to, but this exceeds the energy consumption limit, so the insulation layer needs to be optimized or isotopic auxiliary heating should be used." + }, + { + "id": 893, + "scenario_code": "3.8", + "instruction": " In the Chang'e-6 sample return mission, the energy system budget is as follows: 1) Lunar day operation period: 6 Earth days, average daily energy consumption E_day=2.4kWh (including movement, drilling, etc.); 2) Lunar night hibernation period: 14 Earth days, maintenance power consumption E_night=0.6kWh; 3) Solar panel array generates E_gen=3.5kWh on average per lunar day; 4) Battery capacity C=10kWh, initial SOC=80%. The mission requires SOC≥30% before return.", + "question": "Determine whether the current energy budget meets the entire mission requirements? If a fault occurs at the end of the 4th lunar day causing a 50% reduction in power generation, is it necessary to adjust the operation plan? ", + "answer": "Initial plan meets: 1) Total demand=6*2.4+14*0.6=22.8kWh; 2) Total power generation=6*3.5=21kWh; 3) Battery replenishment=(10*0.8)-(10*0.3)+21-22.8=0.2kWh surplus. After the fault, adjustment is needed: Remaining demand after the 4th day=2*2.4+14*0.6=13.2kWh, remaining power generation=2*(3.5*0.5)=3.5kWh, shortfall 9.7kWh > available battery 7kWh (80%-30%), energy consumption must be reduced or the lunar day operation time extended." + }, + { + "id": 894, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover needs to transmit 500MB of scientific data daily through the 'Queqiao' relay satellite during the lunar day. One day, due to a solar flare, the X-band link was interrupted for 3 hours, and the remaining storage capacity of the rover was only 600MB. The original data generation rate is 2Mbps. Using a lossy compression algorithm can reduce the data volume by 50% but will lose 10% of the scientific value, while lossless compression can reduce the data volume by 30%.", + "question": "To ensure all data is transmitted completely and the storage does not overflow, which compression scheme should be chosen? Calculate the minimum transmission rate required after the interruption (in Mbps).", + "answer": "Choose the lossless compression scheme; the amount of data generated during the interruption = 2Mbps * 3600s * 3 = 21600Mb = 2700MB; the compressed data volume = 2700MB * 0.7 + 500MB = 2390MB > 600MB needs to be prioritized for transmission; the minimum rate = (2390-600)MB * 8 / (24-3)h ≈ 91.24Mbps." + }, + { + "id": 895, + "scenario_code": "3.4", + "instruction": " The lunar rover receives three commands simultaneously at the 8th hour of the lunar day: 1) drilling and sampling (peak power consumption 200W, lasting 15 minutes); 2) data transmission (peak power consumption 80W, lasting 30 minutes); 3) moving to a new location (peak power consumption 120W, lasting 20 minutes). The power system has a maximum output power limit of 250W, and a load scheduling strategy needs to be formulated. The priority order is: drilling > data transmission > movement.", + "question": "Design a scheduling plan that meets the power constraints, provide the start times of each task (with the 8th hour of the lunar day as T=0), and calculate the total system time. Assume tasks cannot be interrupted and cannot be executed in parallel.", + "answer": "Scheduling plan: 1) drilling T=0-15min (200W); 2) data transmission T=15-45min (80W); 3) movement T=45-65min (120W). The total system time is 65 minutes." + }, + { + "id": 896, + "scenario_code": "3.6", + "instruction": " Chang'e-6 lander enters the lunar night phase, and its scientific payload cabin needs to maintain a working temperature range of -20°C to +30°C. The cabin has a surface area of 2 square meters, the thermal conductivity of the insulation material is 0.02 W/(m·K), and the thickness is 5cm. The total power of internal heat-generating equipment is 8W, and the external environmental temperature is -180°C. The isotopic heat source can provide a stable 5W heating power. Ignoring the effect of radiative cooling.", + "question": "What is the temperature difference between the inside and outside of the scientific payload cabin when relying only on insulation and internal heat generation? How much additional electrical heating power is required to maintain the minimum operating temperature? ", + "answer": "Heat flow Q = k*A*ΔT/d → ΔT = Q*d/(k*A) = 8*0.05/(0.02*2) = 10K. Initial equilibrium temperature = -180+10=-170°C < -20°C, need to make up for the difference ΔQ = k*A*(20-(-180))/d -13 = (0.02*2*200/0.05)-13=160-13=147W" + }, + { + "id": 897, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks in the South Pole-Aitken Basin, located at coordinate point A(10,20). The science team requires it to travel to coordinate point B(50,60) to collect basalt samples. It is known that: 1) The lunar surface terrain complexity factor is 0.8 (the higher the factor, the greater the energy consumption), the energy consumption model is E = 0.15 * d * k + 2 (d is the travel distance/km, k is the terrain factor); 2) The remaining battery energy is 80Wh; 3) The straight-line path AB passes through a crater with a diameter of 200m requiring a detour, which increases the travel distance by 0.5km.", + "question": "If the shortest detour path is chosen, can Yutu-2 complete the travel from A to B with the remaining power? Please calculate the total energy consumption and provide a judgment conclusion.", + "answer": "Straight-line distance d0 = sqrt((50-10)^2 + (60-20)^2) = 50km; actual travel distance d = 50 + 0.5 = 50.5km; total energy consumption E = 0.15 * 50.5 * 0.8 + 2 = 8.06Wh < 80Wh, it can be completed." + }, + { + "id": 898, + "scenario_code": "2.7", + "instruction": " When the Chang'e-7 lander is working at the edge of the Shackleton crater, it suddenly receives a solar proton event warning (lasting 4 hours). The current lighting conditions allow for solar power, but it needs to enter a permanent shadow area with a radius of 300m within 30 minutes for safety. It is known that: 1) The maximum climbing angle of the lander is 15°, and the height difference between the current position and the entrance of the shadow area is 40m; 2) The IMU shows the current speed is 0.05m/s; 3) The emergency path needs to bypass a dangerous area with a slope of 20°, increasing the path by 60m.", + "question": "Can the lander arrive at the safety zone on time by choosing the shortest safe path? Verify if the travel time is less than 30 minutes.", + "answer": "Minimum horizontal distance L = h / tan(15°) = 40 / 0.268 ≈149.3m; Actual path S = sqrt(149.3^2 +40^2) +60 ≈215m; Time t = S/v =215/0.05=4300s≈71.7min >30min, cannot arrive on time." + }, + { + "id": 899, + "scenario_code": "2.10", + "instruction": " The lunar rover needs to perform a millimeter-level spectral scan on an olivine outcrop with a diameter of 1.2m. It is known that: 1) The stereo camera ranging accuracy is ±3cm@1m; 2) The IMU attitude angle drift error is 0.1°/h; 3) The working distance requirement for scientific instruments is 0.5±0.05m; 4) The current speed limit of the vehicle is 0.02m/s to ensure braking accuracy.", + "question": "To ensure that the final parking position meets the instrument working distance requirements, at what distance from the target should the lunar rover start decelerating? Calculate the most conservative safe distance considering all error sources.", + "answer": "Maximum error source: Ranging error 3cm + (Braking distance v^2/2a=0.02^2/(2*0.01)=0.02m) + Lateral error caused by IMU drift (negligible). Total error δ=5cm, so deceleration should start at D=0.5+0.05+δ=0.6m." + }, + { + "id": 900, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. Analysis of the soil characteristics in this area shows: the surface layer 0-30cm is loose fine particles (shear strength <5kPa), 30-50cm has a cemented layer (shear strength 15-20kPa), and below 50cm is basaltic debris (Mohs hardness 5-6). The probe carries three sampling tools: ① Ultrasonic drill (suitable for hardness >4, maximum power consumption 80W) ② Electric grab (suitable for strength <10kPa, power consumption 40W) ③ Scraper (suitable for strength 5-15kPa, power consumption 20W). The total power limit of the sampling system is 100W, and sampling at a single point must be completed within 10 minutes.", + "question": "If it is necessary to obtain basalt samples below 50cm, which sampling tool combination should be chosen? Please calculate whether the combination meets the power consumption and time constraints.", + "answer": "Choose the ultrasonic drill (80W) for independent operation. Since the basalt hardness >4 requires the use of a drill, its 80W power consumption is below the 100W limit, and the 10-minute operation time meets the requirements." + }, + { + "id": 901, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover experienced an X-band communication interruption during the lunar day. The fault diagnosis shows:\n1. The main transmitter's output power dropped from 5W to 0.5W\n2. Solar proton events caused ionospheric disturbances (TEC value +20%)\n3. Remaining energy can support 10 hours of emergency communication mode (0.5W transmission + relay wake-up)\n4. The next available relay window is provided by Queqiao-2 in 3 hours\nEmergency response options:\nA. Immediately switch to the UHF band to establish a low-rate connection with the relay satellite\nB. Maintain the X-band and attempt repairs, wait for the relay window in 3 hours\nC. Activate the backup radio to directly connect to Earth at 1W power", + "question": "Select the optimal emergency response and explain the reasons, considering: link budget margin, energy constraints, and data rescue priority. Known:\n- X-band free space loss L=20log10(4πd/λ), d=384,400km\n- UHF link margin is 8dB higher than X-band but the rate is only 1/10\n- Direct connection to Earth requires 8dB higher transmission power", + "answer": "Choose option A. Reasons: 1) The UHF link margin is sufficient to ensure connection; 2) It is more energy-efficient than option C; 3) Although the rate is lower, it can immediately transmit critical telemetry data, which is better than the waiting risk of option B" + }, + { + "id": 902, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 45°S, 176°E), and needs to communicate with the ground station via the Queqiao-2 relay satellite. It is known that:\n1. Queqiao-2 operates in a Halo orbit around the Earth-Moon L2 point, approximately 65,000km from the Moon's center\n2. The ground station (40°N, 116°E) must have an elevation angle ≥5° to establish communication with Queqiao-2\n3. The Moon's rotation period is 27.3 days, and at the current UTC time of 2024-06-15T12:00:00, the landing site on the Moon is near the terminator\n4. The half-power beam width of the relay satellite's antenna is 15°, and the communication elevation angle of the lander must be ≥10°", + "question": "Calculate the visibility duration of the ground station to Queqiao-2 at the current moment (unit: minutes), assuming the movement of the ground station due to Earth's rotation can be neglected. The average Earth-Moon distance is 384,400km, the Earth's radius is 6,371km, and arcsin(0.087)≈5°.", + "answer": "Not visible (the elevation angle of the ground station is below 5° at the current moment, as the landing site on the Moon is near the terminator, causing the line of sight between the relay satellite and the ground station to be blocked by the Moon)." + }, + { + "id": 903, + "scenario_code": "1.8", + "instruction": " When deploying a network of seismometers, it was found that the local lunar regolith bearing capacity is only 0.8kPa (design requirement ≥1.5kPa). The total weight of the instruments is 30kg, with a base area of 0.25m². There are three adjustment options: ① Expand the base to 0.4m²; ② Reduce the weight to 22kg; ③ Choose another location 5 meters away with a measured bearing capacity of 1.8kPa. The movement speed is 0.05m/s, and redeployment requires an additional 20 minutes.", + "question": "If time efficiency is prioritized (only 25 minutes remaining in the operation window), which option should be chosen? Provide quantitative evidence.", + "answer": "Choose option ①. Basis: ① Pressure = 30*1.62/(0.4*10000) = 1.215kPa < 1.5kPa, still not up to standard; ② Meets the standard but takes 5/0.05 = 100s < 20 minutes; ③ Total time spent moving (5/0.05) + 1200 = 1300s > 25 minutes. Only ② meets both time and bearing requirements." + }, + { + "id": 904, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration near the Von Kármán crater. There are three candidate sampling points: Point 1 (coordinates [12.34N, 125.67E]) has a spectral feature indicating a 85% probability of KREEP rock; Point 2 [12.31N,125.70E] has a 70% probability of containing breccia; Point 3 [12.36N,125.65E] has volcanic glass characteristics. The rover's remaining power supports a maximum travel distance of 800 meters, and its current position is 600m, 400m, and 500m away from the three points, respectively. The scientific priority order is: KREEP rock > volcanic glass > breccia. The formula for lunar surface movement energy consumption is: E=0.8*d (where d is in meters).", + "question": "Please plan the optimal sampling route to ensure the acquisition of the highest scientific value samples without exceeding the travel limit, and calculate the total energy consumption.", + "answer": "Optimal route: Current position → Point 2 → Point 1. Reason: 1) Prioritize 400m to Point 2 (not the highest priority but on the way); 2) Then move from Point 2 to Point 1 requires sqrt((12.34-12.31)^2+(125.67-125.70)^2)*111km ≈ 335m; total travel distance 735m < 800m. Total energy consumption = 0.8*400 + 0.8*335 = 588Wh" + }, + { + "id": 905, + "scenario_code": "3.4", + "instruction": " The Yutu-2 rover received three mission commands simultaneously at the 3rd hour of the lunar day: ① Transmit 2GB of scientific data to the relay satellite (requires 30 minutes, peak power consumption 80W); ② Use the infrared imaging spectrometer to scan for mineral composition (requires 20 minutes, steady-state power consumption 45W); ③ Operate the robotic arm to collect lunar soil samples (instantaneous start-up current surge reaches 120W, then drops to 60W after 5 seconds). The current available power limit of the energy system is 100W, and the remaining capacity of the lithium-ion battery pack can provide 15Wh of buffer.", + "question": "To avoid triggering the system overload protection, please design a reasonable task execution sequence and time schedule (must meet: data transmission must be completed before scientific exploration; robotic arm operation cannot be interrupted).", + "answer": "Execution sequence: ① Data transmission (0-30 minutes, 80W) → wait for battery recharge for 10 minutes → ③ Robotic arm sampling (40:00-40:05 120W, 40:05-40:20 60W) → ② Spectral scanning (40:20-60:20 45W)." + }, + { + "id": 906, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration within the Von Kármán crater. There are three candidate sampling points: Point A (120m from the current position, spectral characteristics indicate KREEP rock, scientific priority level 5) Point B (80m away, contains breccia outcrop, priority level 4) Point C (200m away, suspected volcanic glass, priority level 3). The rover's movement speed is 0.05m/s, with a daily operational duration of 4 hours, and the remaining power supports a maximum movement distance of 350m. The science team requires the highest priority sample to be obtained first.", + "question": "Please plan the optimal exploration route for the day, calculate the round-trip time required and the remaining mobile distance.", + "answer": "Prioritize going to Point A: round-trip distance 240m, time required 240/0.05=4800 seconds (80 minutes), remaining power supports 350-240=110m of movement distance." + }, + { + "id": 907, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin on the Moon. Analysis of the soil characteristics in this area shows: the surface layer 0-30cm is loose fine particles (shear strength <5kPa), 30-60cm contains cemented breccia (shear strength 15-20kPa), and below 60cm there is a layer of hard basalt (compressive strength >100MPa). The parameters of the existing sampling tools are as follows: Type A scraper (maximum force 50N, suitable for hardness <10MPa), Type B rotary drill (maximum torque 8Nm, suitable for hardness 10-80MPa), and Type C impact drill (impact energy 5J/time, suitable for hardness >80MPa). The sampling depth needs to reach 1 meter to obtain samples from different layers.", + "question": "Please design a stratified sampling tool combination plan based on the characteristics of the lunar soil layers and the performance parameters of the tools, and explain the basis for your selection.", + "answer": "For 0-30cm, use the Type A scraper (loose fine particles are suitable for low-force tools); for 30-60cm, use the Type B rotary drill (cemented breccia requires a medium-hardness tool); and for below 60cm, use the Type C impact drill (hard basalt requires a high-energy impact tool)." + }, + { + "id": 908, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. Known: The container seal pressure must be maintained at 90±5kPa, the temperature recorder shows the current temperature is -50℃ (allowable range -60℃~+40℃), the RFID tag number CE6-S0128 has been verified to match. The maximum tolerance of the ascent vehicle docking mechanism: lateral offset <3cm, angular deviation <1°. Current telemetry data: lateral offset 1.2cm, angle 0.7°.", + "question": "Based on the above parameters, determine whether the sample container meets the handover conditions and list the key indicators that need to be reviewed.", + "answer": "Meets handover conditions. Key indicators review results: 1) Seal pressure 90±5kPa (within range); 2) Temperature -50℃ (within allowable range); 3) RFID match; 4) Lateral offset 1.2cm<3cm; 5) Angle 0.7°<1°. All parameters meet the requirements." + }, + { + "id": 909, + "scenario_code": "1.4", + "instruction": " The lunar base energy grid needs to power three devices simultaneously: 1) Lunar soil analyzer (peak power 200W, priority 3); 2) Communication relay station (peak power 150W, priority 1); 3) Temperature control system (peak power 180W, priority 2). The current available peak power of the grid is 400W. When the total demand exceeds the limit, the system will cut off power to devices in order of priority from low to high. Now, the temperature control system requires an additional 50W of heating power due to the lunar night cooling.", + "question": "Calculate the adjusted total power demand and determine if it is necessary to cut off power to any device? If so, which device should be chosen to cut off power to it? ", + "answer": "Adjusted total demand = 200W + 150W + (180W+50W) = 580W > 400W; it is necessary to cut off power to the lunar soil analyzer (200W) with the lowest priority, leaving a demand of 380W < 400W." + }, + { + "id": 910, + "scenario_code": "1.5", + "instruction": " The Yutu-2 lunar rover needs to be remotely controlled to cross a slope with a communication delay of 1.3 seconds. Given: 1) Slope angle θ=15°; 2) Lunar gravity acceleration g=1.62m/s²; 3) Maximum static friction coefficient of the wheels μ=0.6; 4) Vehicle mass m=140kg. The control system uses a predictive compensation algorithm and needs to pre-calculate the maximum acceleration a_max without slipping (formula: a_max = g*(μ*cosθ - sinθ)).", + "question": "Please calculate the theoretical maximum safe acceleration of Yutu-2 in this slope environment (保留两位小数), and explain whether this value meets the operational precision requirement of 0.1m/s²? ", + "answer": "a_max = 1.62*(0.6*cos15° - sin15°) ≈ 1.62*(0.579 - 0.259) ≈ 0.52m/s²; 0.52m/s² > 0.1m/s², meeting the precision requirement." + }, + { + "id": 911, + "scenario_code": "2.10", + "instruction": " The Chang'e-6 sampling robotic arm needs to perform centimeter-level precise positioning on a 20cm diameter ilmenite outcrop. Given: 1) The visual navigation camera has a resolution of 2048×2048 pixels and a field of view of 60°×60°; 2) The target appears as a 50×50 pixel area in the image; 3) The end-effector positioning error of the robotic arm follows a normal distribution with σ=3mm (99.7% probability of error <9mm under the 3σ rule); 4) The maximum allowable angle between the normal vector of the rock surface and the axis of the robotic arm is 10°.", + "question": "Calculate whether the current observation distance meets the recognition requirements? If the target image ratio needs to be increased to 100×100 pixels, how should the observation distance be adjusted?)", + "answer": "Single pixel corresponds to angle = 60°/2048 = 0.0293°/px, target angle of view = 50*0.0293 = 1.465°. Distance = 10cm/tan(1.465°/2) = 7.82m meets the requirement; new distance = original distance * (50/100) = 3.91m can achieve 100×100 pixel ratio." + }, + { + "id": 912, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples in the South Pole-Aitken Basin of the Moon. Analysis of the characteristics of the lunar soil in this area shows: the top layer 0-30cm is loose fine particles (viscosity coefficient η=0.8 Pa·s), and 30-50cm contains high-hardness basalt fragments (Mohs hardness 6.5). The probe carries three sampling tools: ① Rotary impact drill (maximum output torque 15N·m, suitable for rocks with hardness >5) ② Electric shovel (maximum digging force 200N, suitable for loose materials) ③ Adaptive gripper (adjustable clamping force 50-300N, with tactile feedback). The sampling system needs to complete three sampling operations at different depths within 10 minutes.", + "question": "If it is necessary to sequentially collect loose lunar soil from the surface layer, mixed materials from the intermediate transition zone, and basalt fragments from the deep layer, please provide the tool selection sequence and corresponding operation parameter settings (torque/digging force/clamping force), and explain the basis for the selection.", + "answer": "Tool sequence: Electric shovel → Adaptive gripper → Rotary impact drill. Parameter settings: ① For the surface layer, use the electric shovel, set the digging force to 150N (below the maximum value to retain a margin); ② For the intermediate layer, use the adaptive gripper, set the clamping force to 180N (balancing fragmentation and maintaining sample integrity); ③ For the deep layer, use the rotary impact drill, set the torque to 12N·m (close to the maximum value to handle high hardness). Basis: The matching of tool characteristics with the hardness of the strata, the electric shovel is suitable for loose layers, the gripper adapts to the uncertainty of the transition zone, and the impact drill specializes in hard rocks." + }, + { + "id": 913, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover conducted exploration in the Von Kármán crater, obtaining the following remote sensing data: ① Hyperspectral images show that at coordinates (12.3°S, 135.7°E), there is a KREEP rock characteristic absorption peak (a 40% drop in reflectivity at a wavelength of 950nm) ② Lidar shows that the terrain undulation within 300 meters around this point is <5° ③ Thermal infrared data indicates that the temperature difference between day and night in this area reaches 280K. The scientific priority ranking rule is: KREEP rock (weight 0.6) + terrain safety (weight 0.2) + temperature stability (weight 0.2), with each indicator normalized to a score range of 0-1. It is known that another candidate point has a KREEP rock confidence of 0.7, a terrain score of 0.9, and a temperature score of 0.4.", + "question": "Calculate the comprehensive scientific priority score for the current target point, and compare it with the candidate point to determine the final exploration direction. List the complete calculation formula and intermediate steps.", + "answer": "Calculation formula: Total score = KREEP rock score * 0.6 + terrain score * 0.2 + temperature score * 0.2. Calculation for the current point: ① KREEP rock score = reflectivity drop ratio 40% / maximum possible value 50% = 0.8; ② Terrain score = 1 - (5° / 15° safety threshold) = 0.67; ③ Temperature score = 1 - (280K / 300K extreme difference) = 0.07; Total score = 0.8 * 0.6 + 0.67 * 0.2 + 0.07 * 0.2 = 0.48 + 0.134 + 0.014 = 0.628. Candidate point total score = 0.7 * 0.6 + 0.9 * 0.2 + 0.4 * 0.2 = 0.42 + 0.18 + 0.08 = 0.68. Decision: Choose the candidate point (0.68 > 0.628)." + }, + { + "id": 914, + "scenario_code": "4.9", + "instruction": " In the Tianwen-5 sample return mission, the ascent vehicle needs to dock with the orbiter in a 100km lunar orbit. The sample container weighs 500g, and the requirements for docking are: axial overload ≤3g, lateral deviation <5cm. It is known that: ① The RFID tag on the container records environmental parameter upper limits of 50°C temperature and an acceleration RMS value of ≤7Grms in the 20-200Hz vibration spectrum; ② Data provided by the ascent vehicle shows that the most recent engine ignition caused the container to experience a peak temperature of 45°C and a 6Grms spike in the vibration spectrum at 80Hz; ③ The docking mechanism has a tolerance compensation capability of ±10cm axially and ±8cm laterally.", + "question": "Determine whether the current sample container meets the handover conditions, and specify at least two parameters that need to be checked and their critical value basis.", + "answer": "Meets handover conditions. Parameters to check and basis: ① Temperature 45°C < 50°C upper limit; ② Vibration 6Grms < 7Grms limit and frequency 80Hz within the 20-200Hz monitoring range; ③ Docking conditions met: axial overload 3g not exceeded (actual value not provided, assumed compliant), lateral deviation 5cm < 8cm compensation capability. Key check items: vibration spectrum peak (≤7Grms), lateral positioning accuracy (<5cm)." + }, + { + "id": 915, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth, and must communicate through the Queqiao relay satellite. Queqiao operates in a Halo orbit at the Earth-Moon L2 point, about 65,000 kilometers from the Moon. Known:\n- Queqiao X-band antenna gain is 42 dBi\n- Lander transmission power is 10 W\n- Free space path loss formula: L = 20 * log10(4 * π * d / λ), where d is the distance, λ is the wavelength (X-band λ=0.03m)\n- Receiver sensitivity is -110 dBm\n- System margin requirement ≥ 3 dB", + "question": "Calculate whether the maximum theoretical communication distance from the lander to Queqiao meets the actual needs (need to verify if the link budget meets the receiver sensitivity + system margin)?", + "answer": "Calculation steps:\n1. Free space loss L = 20 * log10(4 * π * 65000 * 1000 / 0.03) ≈ 214.3 dB\n2. Transmission power 10 W = 40 dBm\n3. Received power Pr = Pt + Gt - L = 40 + 42 - 214.3 = -132.3 dBm\n4. Required threshold = -110 + 3 = -107 dBm\nConclusion: -132.3 dBm < -107 dBm, does not meet the requirement (need to increase transmission power or antenna gain)." + }, + { + "id": 916, + "scenario_code": "5.4", + "instruction": " During the lunar day, the Yutu-2 rover was transmitting scientific data to Queqiao via the relay link when it suddenly encountered a solar outage causing a communication interruption. Known:\n- 85% of the data (total 2GB) had been transmitted before the interruption\n- 1.5GB of SSD cache space remaining\n- 4 hours of lunar day remaining\n- 2 MHz available bandwidth in the X-band\n- QPSK modulation efficiency 2 bit/s/Hz\n- Protocol overhead ratio 20%.", + "question": "Please evaluate whether it is necessary to activate the emergency transmission mode (need to calculate if the time required to transmit the remaining data is within the lunar day window)?", + "answer": "Calculation steps:\n1. Remaining data volume = 2GB * 15% = 300MB\n2. Available SSD space 1.5GB > 300MB, can cache\n3. Effective rate = 2MHz * 2bit/s/Hz * 80% = 3.2Mbps\n4. Transmission time = (300*8)/3.2 ≈ 750 seconds ≈ 12.5 minutes < 4 hours\nConclusion: No need to activate emergency mode, can complete within the normal window." + }, + { + "id": 917, + "scenario_code": "5.7", + "instruction": " The Chang'e-5 orbiter's onboard SSD uses NAND Flash storage chips, with the following characteristics:\n- Total capacity 512GB, operating in parallel across 8 channels\n- Each channel contains 4 dies, each die can be erased and written up to 3000 times\n- Wear leveling algorithm uses a dynamic + static hybrid strategy\nThe current average erase/write cycles for each channel are as follows:\nChannel 0: 1421 times | Channel 1: 1538 times | Channel 2: 2976 times | Channel 3: 1255 times | Channel 4: 2899 times | Channel 5: 1120 times | Channel 6: 3021 times | Channel 7: 1566 times", + "question": "Based on the current wear status, which channel's die is most likely to reach its lifespan limit first? What emergency measures should be taken immediately after identifying the critical channel(s)?", + "answer": "Analysis steps:\n1. Channel 6 with 3021 cycles has exceeded the limit (immediate shutdown required)\n2. Channel 2 (2976 cycles) and Channel 4 (2899 cycles) are approaching the limit\nEmergency measures:\n- Immediately mark Channel 6 as read-only\n- Activate backup blocks to replace Channel 6\n- Adjust the wear leveling algorithm to prioritize writing to low-wear channels (such as 5/7)." + }, + { + "id": 918, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin. The characteristics of the lunar soil in this area are: the top layer 0-30cm consists of loose fine particles (viscosity coefficient k=0.8 Pa·s), and 30-50cm contains high-hardness basalt fragments (Mohs hardness 6.5). The probe is equipped with three sampling tools: ① Rotary impact drill (suitable for hardness >5, power consumption 300W) ② Vibratory coring tube (suitable for viscosity <1Pa·s, power consumption 200W) ③ Electric shovel (only suitable for the top 20cm, power consumption 150W). The probe currently has 800Wh of remaining energy and needs to complete sampling within 2 hours.", + "question": "If it is required to obtain deep (>30cm) samples without exceeding the energy consumption limit, which tool combination should be chosen? Please calculate the maximum allowable continuous working time.", + "answer": "Choose the rotary impact drill. Maximum working time = remaining energy / power = 800Wh / 300W ≈ 2.67 hours > mission duration of 2 hours." + }, + { + "id": 919, + "scenario_code": "4.9", + "instruction": " Before the ascent vehicle separates from the lander, the sample container handover inspection must be completed. It is known that: ① The internal temperature of the container must be maintained between -50°C and +20°C (current reading -35°C) ② The sealing pressure should be >0.8atm (current 0.92atm) ③ The integrity of the RFID tags must be 100% (currently 3/5 tags responding) ④ The handover window is only 8 minutes. Reactivating each tag requires 90 seconds, and the temperature control system adjusts at a rate of 5°C per minute.", + "question": "List the emergency procedures that must be immediately executed, and calculate whether all operations can be completed before the window closes.", + "answer": "Steps: 1) Reactivate missing tags (2*90 seconds = 3 minutes) 2) Increase temperature to -20°C (requires (20-35)/5 = 3 minutes). Total time required is 6 minutes < 8-minute window." + }, + { + "id": 920, + "scenario_code": "2.7", + "instruction": " While the Chang'e-7 lander is working at the edge of the Shackleton crater, it suddenly receives a solar proton event warning (expected to arrive in 30 minutes). Current status:\n- Remaining safe evacuation time: 25 minutes\n- Distance to the nearest permanent shadow area shelter: 120 meters\n- Flat terrain normal speed: 8 meters/minute\n- Current area terrain complexity factor η=1.5 (actual speed=normal speed/η)\n- In emergency mode, the motor power can be increased to reduce η to 1.2, but the energy consumption increases by 50%.", + "question": "Can the lander safely reach the shelter without activating the emergency mode? If it must be activated, what is the minimum number of minutes in advance it needs to be triggered to ensure safety before the solar proton event arrives in 30 minutes from now? ", + "answer": "In normal mode, the actual speed=8/1.5≈5.33 meters/minute, required time=120/5.33≈22.5 minutes<25 minutes, so the emergency mode does not need to be activated. If the emergency mode is activated: speed=8/1.2≈6.67 meters/minute, required time=120/6.67≈18 minutes, it needs to be triggered at least 18 minutes in advance." + }, + { + "id": 921, + "scenario_code": "2.4", + "instruction": " Yutu-2, the lunar rover, is currently performing exploration tasks on the far side of the Moon, located at point A (177.6°E, 45.5°S), and needs to travel to point B (177.8°E, 45.3°S) for rock sampling. Given: 1) The straight-line distance between the two points is 800 meters, but the actual path requires detouring around 3 craters, increasing the total travel distance to 1200 meters; 2) The energy consumption model of the lunar rover is E = 0.15*d + 2*h, where d is the travel distance (meters), and h is the climb height (meters); 3) Path elevation analysis shows a cumulative climb of 8 meters; 4) The current remaining battery energy is 200Wh.", + "question": "If the motor efficiency of the lunar rover is 90%, determine whether the remaining power can support this travel task? If not, by how much at least should the climb height be reduced to meet the requirement? ", + "answer": "Calculate the total energy consumption E = 0.15*1200 + 2*8 = 180 + 16 = 196Wh; considering the motor efficiency, the actual requirement is 196/0.9≈217.78Wh > 200Wh. The power is insufficient, and the energy consumption needs to be reduced to 200*0.9=180Wh. Let the new climb height be h', then 180=0.15*1200+2*h' → h'=(180-180)/2=0 meters. Therefore, the climb must be completely eliminated." + }, + { + "id": 922, + "scenario_code": "3.4", + "instruction": " Yutu-2 rover needs to perform the following tasks simultaneously during the lunar day: 1) X-ray spectrometer (peak power consumption 50W, lasting 10 minutes); 2) Laser rangefinder (instantaneous pulse power consumption 200W, once per second, each time 10ms); 3) Data transmission (stable power consumption 30W, lasting 15 minutes). The energy system uses a supercapacitor to buffer instantaneous loads, with a maximum discharge current of 20A and operating voltage of 28V. It is known that: 1) the maximum continuous output power of the lithium-ion battery pack is 100W; 2) the efficiency of the supercapacitor η=95%.", + "question": "Determine whether the current energy configuration can meet the needs of all equipment operating simultaneously, and explain the key calculation steps.", + "answer": "It can meet the needs. Calculation steps: 1) The battery needs to bear the stable load=50+30=80W<100W; 2) The average power of the laser pulse=200*0.01*1=2W; 3) The instantaneous power of the supercapacitor=200W corresponding current=200/28=7.14A<20A" + }, + { + "id": 923, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover needs to transmit 500 MB of scientific data daily via the 'Queqiao' relay satellite during the lunar day. During a communication session, a solar conjunction interruption (with the Sun located on the Earth-Moon line) is expected to last for 48 hours. The rover has 300 MB of remaining storage capacity, and the data generation rate is 20 MB per hour. The equipment uses a dynamic compression algorithm: normal mode has a 50% compression rate (lossy), and emergency mode has a 70% compression rate (lossy + prioritizing key data).", + "question": "To ensure no scientific data is lost, please plan the storage and transmission strategy during the interruption period (including when to switch compression modes and the theoretical remaining capacity).", + "answer": "1) Use normal mode for the first 15 hours: 20*15=300 MB generated → 150 MB after compression, just filling the remaining storage; 2) Switch to emergency mode from the 16th hour: 20*33=660 MB generated → 198 MB after compression; total demand=150+198=348 MB < 500 MB original data limit. Final remaining capacity=500-348=152 MB" + }, + { + "id": 924, + "scenario_code": "5.7", + "instruction": " The 'Chang'e-5' orbiter's SSD storage uses NAND Flash chips, with a total capacity of 1 TB and a block size of 128 KB. The wear-leveling algorithm requires that the difference in the number of erase/write cycles between any two blocks does not exceed 10%. The oldest block has been written 5000 times, and the newest block has been written 4200 times. The storage writes 80 GB of data daily (evenly distributed), and each data packet write requires a full block.", + "question": "Calculate the minimum number of days required to reach the balancing threshold (the newest block written 4500 times) and the total average number of erase/write cycles at that time.", + "answer": "1) Need to make up the difference: 4500-4200=300 times; 2) Daily additional erase/write cycles: (80GB/128KB)=625000 times/1M blocks≈625 times/block; 3) Minimum number of days=300/(625/1M*10%)=48 days; 4) Total average erase/write cycles=(5000+4500)/2=4750 times" + }, + { + "id": 925, + "scenario_code": "1.5", + "instruction": " In the Chang'e-7 mission, the ground control center needs to remotely control the lunar rover to complete rock sampling within a 10-meter distance. Given: the one-way communication delay between Earth and the Moon is 1.3 seconds, the maximum movement speed of the lunar rover is 0.1 m/s, and the positioning error of the robotic arm is ±2 cm. The control system uses a predictive algorithm to compensate for the delay: it sends a sequence of command packets in advance containing speed v and direction θ (each packet is valid for 4 seconds), and if a new command packet does not arrive in time, the previous command is continued. Currently, the lunar rover is 8.2 meters away from the target rock and has just received the command packet [v=0.08 m/s, θ=5°].", + "question": "If the next command packet is lost due to a communication failure, calculate the theoretical deviation distance between the final stopping position of the lunar rover and the target rock (assuming the lunar rover moves strictly in a straight line).", + "answer": "Deviation distance = 8.2m - (0.08m/s * 4s) = 8.2 - 0.32 = 7.88m; Angular offset = tan(5°) * 7.88 ≈ 0.689m. Total deviation = sqrt(0.689^2 + (8.2 - 7.88)^2) ≈ 0.76m (after adding the positioning error, it may reach ±2.76m)." + }, + { + "id": 926, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, energy supply becomes a key constraint. In the current mission, a mobile power module (output power 200W) needs to power three devices: a seismometer (peak power consumption 80W, priority 1), a magnetometer (peak power consumption 60W, priority 2), and a thermal drill (peak power consumption 120W, priority 3). The power module uses a dynamic allocation strategy: when the total demand exceeds 200W, power to lower-priority devices is cut off in order of priority, and devices of the same priority are allocated power according to the ratio of their remaining power (current remaining power: seismometer 40%, magnetometer 70%, thermal drill 30%).", + "question": "If all three devices enter peak operating mode simultaneously, how will the power module allocate power? Please list the actual power values received by each device.", + "answer": "Seismometer 80W (met), magnetometer 60W (met), thermal drill 0W (cut off). Total demand 260W>200W, retain seismometer and magnetometer with a total of 140W, remaining 60W allocated according to power ratio: magnetometer receives 60*(70/(70+40))=38.18W, seismometer receives 21.82W. However, the original demands of both are already met, so no re-allocation is needed." + }, + { + "id": 927, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is conducting patrol exploration on the far side of the moon, currently located at point A (177.6°E, 45.5°S), and needs to travel to point B (177.8°E, 45.3°S) to carry out scientific exploration tasks. According to the digital elevation model (DEM) data of the lunar surface transmitted by the orbiter, there are three optional paths between the two points:\n1. Path 1: straight-line distance 2.1km, average slope 8°, passing through a soft lunar soil area (rolling resistance coefficient 0.25)\n2. Path 2: detour distance 2.8km, average slope 3°, passing through a basaltic plain (rolling resistance coefficient 0.15)\n3. Path 3: zigzag distance 2.4km, including one short steep slope of 10° (200m long), the rest of the sections have a slope of 5°, the terrain is mixed lunar dust (rolling resistance coefficient 0.20).\nIt is known that the motor efficiency of the lunar rover η=85%, the total battery capacity is 400Wh, the current remaining power is 300Wh, the base power consumption for driving is 50W (excluding slope climbing power consumption), and the additional power consumption formula for climbing slopes is P_slope = 120 * sinθ * v (θ is the slope angle, v is the speed 0.1m/s).", + "question": "If it is required to retain at least 100Wh of emergency power, which path should Yutu-2 choose to ensure it reaches the target point? Please make a decision by calculating the total energy consumption of each path.", + "answer": "Path 2\nCalculation process:\n1) Maximum allowable energy consumption = 300Wh - 100Wh = 200Wh\n2) Total energy consumption calculation for each path:\n - Path 1: travel time = 2100m / (0.1m/s) = 21000s ≈ 5.83h\n Base consumption = 50W * 5.83h = 291.5Wh\n Slope climbing consumption = 120 * sin(8°) * 0.1 * 21000/3600 ≈ 9.7Wh\n Rolling consumption = 0.25 * 2100 * 0.1 ≈ 52.5Wh\n Total consumption = 291.5 + 9.7 + 52.5 = 353.7Wh > 200Wh\n - Path 2: travel time = 2800m / (0.1m/s) = 28000s ≈ 7.78h\n Base consumption = 50W * 7.78h = 389Wh\n Slope climbing consumption = 120 * sin(3°) * 0.1 * 28000/3600 ≈ 4.9Wh\n Rolling consumption = 0.15 * 2800 * 0.1 ≈ 42Wh\n Total consumption = 389 + 4.9 + 42 = 435.9Wh > 200Wh\n - Path 3: travel time = 2400m / (0.1m/s) = 24000s ≈ 6.67h\n Base consumption = 50W * 6.67h = 333.5Wh\n Slope climbing consumption = [120 * sin(10°) * 0.1 * 200/3600] + [120 * sin(5°) * 0.1 * (2400-200)/3600] ≈ 11 + 27 = 38Wh\n Rolling consumption = 0.20 * 2400 * 0.1 ≈ 48Wh\n Total consumption = 333 + 38 + 48 = 419Wh > 200Wh\nConclusion: All three paths exceed the energy consumption budget, and a new plan or recharging is required." + }, + { + "id": 928, + "scenario_code": "2.6", + "instruction": " When the Chang'e-7 lander conducts exploration in the permanently shadowed area, its inertial navigation system (INS) accumulates errors due to long-term operation. It is known that:\n- The INS position drift model is δx = 0.t + 12t^2 (unit cm, t is hours)\n- Astronomical correction can be performed every 4 hours using a star sensor, with a correction accuracy of ±3cm\n- The last correction was 38 hours ago\n- The current laser rangefinder detects a scientific target 50 meters ahead", + "question": "Calculate whether the current INS positioning error will affect the safe approach to the target (requirement: final positioning error <1% of the exploration distance), and explain whether the correction procedure needs to be initiated immediately.", + "answer": "Immediate correction is required\nCalculation process:\n1) Current INS error δx = 12 * (38)^2 = 12 * 1444 = 17328cm ≈ 173m\n2) Maximum allowable error threshold = 50m * 1% = 0.5m\n3) 173m >> 0.5m and far exceeds the rangefinder range (50m)\nConclusion: The error has reached 346 times the allowable value, and the star sensor correction must be initiated immediately." + }, + { + "id": 929, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to sample in an area on the far side of the Moon rich in KREEP (potassium, rare earth elements, and phosphorus) rocks. The hardness of the lunar regolith in this area is 3.5 on the Mohs scale, with moderate viscosity and a high content of volatiles. There are three sampling tools available: Type A drill (suitable for rocks with hardness > 4, high power consumption), Type B scoop (suitable for loose lunar regolith with moderate viscosity, moderate power consumption), and Type C scraper (suitable for low-hardness lunar regolith, low power consumption). The mission requires that the total power consumption during the sampling process does not exceed 150W·h, and the integrity of the samples must be guaranteed.", + "question": "Based on the above conditions, which sampling tool(s) should be selected to meet the mission requirements? Please explain your reasoning.", + "answer": "Select the Type B scoop. Reasons: 1) The hardness of the lunar regolith (3.5) is below the standard suitable for the Type A drill; 2) The Type B scoop is suitable for lunar regolith with moderate viscosity and its power consumption meets the requirement; 3) Although the Type C scraper has low power consumption, it is not suitable for lunar regolith with moderate viscosity." + }, + { + "id": 930, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover obtained the following remote sensing data while patrolling the Von Kármán crater: Point 1 (coordinates X12,Y34) shows a 68% probability of KREEP rock and a 22% probability of breccia; Point 2 (X15,Y38) shows a 55% probability of volcanic glass, and moving to it requires 80W·h of energy; Point 3 (X18,Y35) shows a 73% probability of breccia, and moving to it requires 120W·h of energy. The current remaining energy is 300W·h, and at least 100W·h must be reserved for emergencies. The scientific priority order is: KREEP rock > volcanic glass > breccia.", + "question": "Please calculate the optimal exploration path and the combination of points that can be safely visited.", + "answer": "Optimal path: Point 1 → Point 2. Possible combinations: 1) Visit Point 1 alone (0 energy consumption); 2) Point 1 + Point 2 (total energy consumption 80W·h < 200W·h); 3) Visit Point 3 alone (energy consumption 120W·h < 200W·h). Due to the highest scientific priority, the preferred combination is Point 1 + Point 2." + }, + { + "id": 931, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (longitude 180°E, latitude 45°S). The ground station is located in Kashgar, China (longitude 76°E, latitude 39°N). It is known that the Queqiao-2 relay satellite is in a Halo orbit around the Earth-Moon L2 point, with an average altitude of 8000km above the lunar surface. At the current moment, the Moon's rotation causes the line connecting the lander and Queqiao-2 to form a 35° angle with the lunar surface tangent, and a 60° angle with the Earth-Queqiao line. The X-band antenna gain of the relay satellite is 42dB, the lander's transmission power is 10W, the antenna gain is 38dB, and the system loss is 3dB.", + "question": "Calculate the free space loss (FSL) of the Earth-Moon communication link under the current conditions, and determine if it meets the minimum receiving power requirement (-120dBm)? Given the X-band frequency f=8GHz, and the speed of light c=3*10^8 m/s.", + "answer": "FSL = 20 * log10(4 * π * d / λ) = 20 * log10(4 * π * 8000 * 1000 / (3*10^8 / 8*10^9)) ≈ 20 * log10(268082573106.4) ≈ 208.6dB; receiving power = EIRP + G_r - FSL - L_s = (10*log10(10) + 38) + 42 - 208.6 - 3 = 10 + 38 + 42 - 208.6 - 3 = -121.6dBm < -120dBm, does not meet the requirement." + }, + { + "id": 932, + "scenario_code": "5.3", + "instruction": " Yutu-2 rover needs to transmit high-resolution lunar soil spectral data during the lunar day, with an original data rate of 2Mbps. Due to the relay satellite's overhead time of 15 minutes, the following adaptive strategy is adopted: 1) When the remaining power > 30%, lossless compression (compression ratio 1:1.5) is used; 2) When power ≤ 30%, lossy compression (compression ratio 1:4) is activated. The current battery has 25% remaining, and the solid-state storage has 500MB of available space, with a telemetry link bandwidth of 256kbps.", + "question": "Determine whether all data can be transmitted within the communication window under the current conditions. Key calculation steps must be explained.", + "answer": "1) Lossy compression is currently enabled, effective data rate = 2Mbps/4 = 512kbps > 256kbps; 2) Data to be transmitted = 512kbps * 900s = 460800kb ≈ 56.25MB < 500MB; 3) However, the transmission requirement of 512kbps exceeds the link bandwidth of 256kbps, making real-time transmission impossible, and batch transmission using a buffer is required." + }, + { + "id": 933, + "scenario_code": "5.6", + "instruction": " The ground station sends attitude adjustment commands to the Chang'e-7 lander, using CRC-16 checksum and command echo mechanism. Known: 1) Command frame structure: [header identifier 0xAA55][2-byte length][command code][parameters][CRC]; 2) After receiving a complete frame, the lander must return [original command code][execution status][new CRC] within 200ms; 3) The one-way communication link delay is 120ms. During a certain operation, the ground station did not receive an echo 450ms after sending the command.", + "question": "Analyze the possible fault points and explain the basis for the judgment.", + "answer": "The fault point is that the lander did not respond correctly: 1) Total allowed response time = transmission delay 120ms + processing 200ms + return delay 120ms = 440ms < 450ms; 2) No timeout but no echo received, excluding transmission delay issues, it is determined that the lander did not generate a response (command parsing failed or execution timeout)." + }, + { + "id": 934, + "scenario_code": "3.4", + "instruction": " The Yutu-2 rover executes three tasks simultaneously during the 8th hour of the lunar day: 1) The X-band communication transmitter continuously transmits data at 8W power; 2) The infrared imaging spectrometer operates at 15W power for 20 minutes; 3) The drilling and sampling system needs to complete 3 impact drillings within 10 minutes (each impact consumes 120W of power instantaneously for 5 seconds, with a 30-second interval). The power bus has a rated output power limit of 40W, and the battery has a maximum instantaneous discharge capacity of 50W.", + "question": "To ensure the system does not overload and to prioritize the drilling task, design a load scheduling plan and calculate the maximum instantaneous power the battery needs to provide.", + "answer": "Scheduling plan: Suspend the spectrometer during drilling. The maximum instantaneous power occurs during drilling: 8W (communication) + 120W (drilling) = 128W, the battery needs to provide 128W - 40W = 88W (exceeding the 50W limit), so the drilling sequence needs to be adjusted to ensure the peak does not exceed 90W." + }, + { + "id": 935, + "scenario_code": "3.6", + "instruction": " The Queqiao relay satellite of Chang'e-4 is about to enter the lunar night phase, and its critical electronic cabin needs to maintain a working temperature range of -20°C to +40°C. Given: 1) The lunar night environment temperature is -180°C; 2) The cabin surface area is 1.8m², with a thermal resistance R=5 m²·K/W for the multi-layer insulation material; 3) The radioisotope heat source (RHU) can provide a continuous 6W of thermal power; 4) The electric heater has a maximum power of 10W but consumes precious battery energy.", + "question": "Calculate whether the equilibrium temperature of the electronic cabin relying solely on the RHU for heating meets the requirements? If not, determine the minimum additional power required from the electric heater (ignoring the heat generated by internal equipment).", + "answer": "Thermal balance formula: Q=ΔT/R → ΔT=Q*R=6*5=30K. When the environment is -180°C, the cabin temperature is -150°C < -20°C lower limit. Additional heating power needed ΔQ=(20-(-180))/5 -6=40-6=34W (exceeding the electric heater's capability, requiring entry into sleep mode)." + }, + { + "id": 936, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed areas of the lunar south pole, it is necessary to provide power to 3 devices (seismometer, spectrometer, heat flow probe) simultaneously. The current system uses a distributed power grid, with a total available peak power of 120W. It is known that: the seismometer has a basic power consumption of 15W, and an instantaneous peak of +8W during sampling; the spectrometer has a basic power consumption of 20W, and an additional +12W when the excitation light source is working; the heat flow probe has a constant power consumption of 10W. All devices have synchronized sampling cycles (starting once every 10 minutes), with a sampling window lasting 30 seconds. The excitation light source works for no more than 5 seconds each time, and the probability of overlapping with the seismometer's sampling time must be less than 20%.", + "question": "If the current scheduling strategy is 'spectrometer excitation priority' (i.e., allowing it to use the excitation light source every time it samples), calculate whether the system will experience instantaneous overload? If so, what is the maximum overload amount? ", + "answer": "There will be an instantaneous overload, with a maximum overload of 5W. Calculation process: Maximum total power consumption = Seismometer (15+8) + Spectrometer (20+12) + Heat flow probe (10) = 65W, exceeding the system's peak power of 120W - 65W = 55W redundancy. The actual overload occurs when the spectrometer excitation overlaps with the seismometer sampling: (15+8) + (20+12) + 10 = 65W > 55W, 65-55=10W overload. However, according to the constraint that the overlap probability <20%, the actual maximum overload is calculated as 5W (since the excitation lasts only 5 seconds/30 seconds sampling window)." + }, + { + "id": 937, + "scenario_code": "1.8", + "instruction": " When deploying a lunar-based telescope, it is necessary to avoid areas with strong local magnetic fields. Given: the measured magnetic field strength at the current coordinate point is 52nT, the safety threshold is ≤50nT; the magnetic field strength decays with distance according to the formula B = 80 * e^(-0.2*d) (d is the distance in kilometers from the interference source). The deployment platform can move north at a speed of 0.1km/min, and the energy consumption cost for movement is E = 2 * d^1.3 (d is the distance in kilometers moved).", + "question": "Find the minimum energy consumption movement plan that meets the magnetic field safety conditions, and calculate the required time and energy consumption.", + "answer": "The minimum energy consumption plan is to move 0.104km north, taking 1.04 minutes, with an energy consumption of 0.27 units. Derivation process: Solving the equation 50=80*e^(-0.2*d) gives d=-ln(50/80)/0.2≈0.104km; time t=d/v=0.104/0.1=1.04 minutes; energy consumption E=2*0.104^1.3≈2*0.133≈0.266≈0.27 (rounded to two decimal places)." + }, + { + "id": 938, + "scenario_code": "3.4", + "instruction": " Yutu-2 needs to perform three tasks simultaneously during the lunar day: ① Continuous sampling by the X-ray spectrometer (power consumption 25W, high priority); ② Rock drilling by the robotic arm (instantaneous peak power consumption 120W, lasting 5 minutes, medium priority); ③ Data transmission (power consumption 45W, to be completed within the next 30 minutes, low priority). The current remaining power is 180Wh, and the solar input is stable at 80W. The battery discharge efficiency is 95%.", + "question": "Please design a load scheduling plan that meets all task requirements and calculate the remaining power after execution.", + "answer": "Execution order: ① Always on (25W) + ② First 5 minutes on (120W) + ③ Last 10 minutes on (45W). Total energy consumption = [25*30 + (120-25)*5 + (45-25)*10]*0.95 = (750+475+200)*0.95 = 1353.75Wh; Power generation = 80*0.5h=40Wh; Remaining power = 180 +40 -1353.75/60 ≈ 180 +40 -22.56 ≈ 197.44Wh" + }, + { + "id": 939, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander detected a solar proton event warning at the edge of the Shackleton crater, predicting that high-energy particles will reach the lunar surface in 20 minutes. The lander needs to urgently shut down scientific payloads and enter safe mode (which takes 15 minutes). The current GNC system has detected: 1) The azimuth of the nearest permanent shadow refuge is 45°, and the distance is 800m; 2) The maximum climbing ability of the lunar rover is 15°, with an average slope of 12° on the path; 3) The movement speed limit on the lunar surface is 0.1m/s.", + "question": "Can the lander complete the risk avoidance before the proton event arrives? If not, what emergency measures should be taken?)", + "answer": "It cannot be completed. Time required for risk avoidance = 800/(0.1*3600) ≈ 22.2 minutes > 20-15 = 5 minutes remaining time. Emergency measures: Immediately enter safe mode on-site, prioritizing power supply to the core system." + }, + { + "id": 940, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing a detection mission on the far side of the moon, located at coordinate point A (10°N, 120°E). The mission planning system requires it to go to target point B (12°N, 122°E) to collect basalt samples. It is known that: 1) the lunar surface terrain is a gentle slope with an average gradient of 5°; 2) the motor efficiency of the lunar rover η = 85%, the battery capacity Q = 5000Wh; 3) the driving energy consumption model is E = 0.15*d + 5 (d is the horizontal distance, unit km); 4) the communication window is only 4 hours, and 30 minutes need to be reserved to establish scientific instruments. The circumference of the lunar equator is 10921km.", + "question": "Calculate whether Yutu-2 can complete this task under the constraints of remaining power and time? If not, what is the maximum allowable one-way driving distance? (Retain 1 decimal place.)", + "answer": "It can be completed. The horizontal distance d between A and B = 10921 * 2 / 360 * sqrt((12-10)^2 + (122-120)^2) = 10921 / 90 * sqrt(8) ≈ 172.3km; Total energy consumption E = 0.15 * 172.3 + 5 ≈ 30.8Wh; Required time t = 172.3 / (200m/h) / 1000 ≈ 0.86h < 4 - 0.5 = 3.5h; 30.8Wh < 5000Wh * 85% = 4250Wh." + }, + { + "id": 941, + "scenario_code": "3.1", + "instruction": " Chang'e-6 rover is conducting exploration tasks in the lunar south pole region, which has complex terrain with many craters blocking the view. The rover is equipped with a two-dimensional adjustable solar panel, with a maximum tracking angle of ±45°. According to the lunar calendar, the current solar elevation angle is 15°, and the azimuth angle is 30°. There is a 20-meter-high crater 50 meters ahead of the rover, with an azimuth angle of 45°. The theoretical power generation capacity of the solar panel without obstruction is 200W. It is known that the relationship between the angle of incidence of sunlight and power generation efficiency is: efficiency = cos(incidence angle) * 100%.", + "question": "Considering the terrain obstruction and the position of the sun, calculate the optimal adjustment angle of the solar panel and the actual power generation capacity.", + "answer": "The optimal adjustment angle is an azimuth of 30° (aligned with the solar azimuth) and an elevation angle of 15° (aligned with the solar elevation angle). Since the crater is located at an azimuth of 45°, with a height of 20 meters and a distance of 50 meters, its obstruction angle is arctan(20/50) = 21.8°, which is greater than the solar elevation angle of 15°, so the solar panel is completely obstructed, and the actual power generation capacity is 0W." + }, + { + "id": 942, + "scenario_code": "3.3", + "instruction": " The Yutu-2 lunar rover is about to enter the lunar night phase. The current battery pack has 40% remaining charge, and the lunar night lasts for 14 Earth days. The lunar rover needs 5W to maintain the minimum survival power consumption, and 10W to keep the scientific instruments warm. The total capacity of the battery pack is 2000Wh, with a discharge depth limit of 80%. The isotope heat source can provide a continuous heat output of 8W. The temperature during the lunar night will drop to -180°C.", + "question": "Please calculate and determine whether the battery pack alone can support the lunar rover to safely survive the entire lunar night? If not, how should the energy distribution strategy be adjusted to ensure survival during the lunar night phase? ", + "answer": "Usable battery capacity = 2000Wh * 40% * 80% = 640Wh. Total energy consumption during the lunar night = (5W + 10W - 8W) * 24h * 14 = 2352Wh. 640Wh < 2352Wh, which is insufficient. Adjustment strategies are needed: 1) Turn off the heating for scientific instruments and only maintain the minimum survival power consumption + isotope heat source: energy consumption = (5W - 8W) * 24h * 14 = -1008Wh (feasible); 2) or further reduce the survival power consumption to below 3W." + }, + { + "id": 943, + "scenario_code": "3.6", + "instruction": " The lithium-ion battery carried by the Chang'e-7 lander needs to maintain a working temperature range of -20°C to +10°C during the lunar night. The battery weighs 5kg with a specific heat capacity of 900J/(kg·K). The external environmental temperature is -180°C, and the multi-layer thermal insulation material reduces the heat flux density to 0.5W/m², with a battery surface area of 0.2m². The electric heater has an efficiency of 95%, and the power supply voltage is 28V.", + "question": "Calculate the minimum heating current required to raise the battery temperature from -180°C to -20°C and the continuous heating power needed to maintain -20°C. (Ignore latent heat of phase change.)", + "answer": "The heat required for temperature increase Q=5kg*900J/(kg·K)*[ -20 - (-180) ]=720kJ. Heat loss power=0.5W/m²*0.2m²=0.1W. Let the heating time be t seconds: Heating power P=(720000/t +0.1)/0.95; The minimum current occurs when t→∞: I_min=0.1/(0.95*28)=3.76mA. Maintenance power P_maintain=0.1/0.95=105mW." + }, + { + "id": 944, + "scenario_code": "2.7", + "instruction": " The Chang'e-7 lander, while working at the edge of the Shackleton crater, suddenly receives a solar proton event warning (lasting 8 hours). Current status: 1) The IMU shows that the lander's attitude angle deviation has reached the safety threshold of ±3°; 2) The emergency shelter mode requires 20% of the remaining power to activate the temperature control system; 3) Remaining power is 40Wh; 4) Under normal mode, it consumes 1.5Wh per hour, and under shelter mode, it consumes 3Wh per hour.", + "question": "If choosing to immediately enter shelter mode and maintain it until the event ends, calculate whether the remaining power after the event is higher than the minimum safety value of 15Wh.", + "answer": "Power consumption for shelter activation = 40 * 20% = 8Wh; Remaining power = 40 - 8 = 32Wh; Power consumption during shelter = 3 * 8 = 24Wh; Final power = 32 - 24 = 8Wh < 15Wh, does not meet the safety value." + }, + { + "id": 945, + "scenario_code": "2.10", + "instruction": " The lunar rover needs to perform a millimeter-level spectral scan on an olivine outcrop with a diameter of 30cm. Known: 1) Navigation camera resolution 0.1mm/pixel @ 1m distance; 2) End-effector positioning accuracy of the robotic arm ±5mm; 3) Scientific payload working distance requirement 0.3-0.5m; 4) The inclinometer on the lunar surface shows that the current area's slope is 8°.", + "question": "Calculate the range of distances that the lunar rover's final parking position should be controlled within to ensure the validity of the spectral data? What key sources of error need to be considered.", + "answer": "Effective distance range: Maximum 0.5m (payload limit), minimum take MAX(0.3m, 30cm / (2 * tan(8°)) = 0.3m); Key sources of error: Robotic arm positioning error ±5mm, slip error caused by slope ≈ 42mm (0.5 * sin8°)." + }, + { + "id": 946, + "scenario_code": "2.7", + "instruction": " The lunar rover has received a solar proton event warning and needs to reach a safe haven with a radius of 500m within 20 minutes. Current status: 1) Remaining battery power 15kWh; 2) The safe haven path includes an 8° uphill segment (corresponding climb height = distance * sin8°); 3) Base power consumption 2kW, the driving energy consumption model is E=0.12*d + 5*h (d:km, h:km). Maximum speed 0.08km/min.", + "question": "Calculate the maximum safe haven distance that can be planned under the power constraint, and verify whether it meets the time requirement.", + "answer": "Let the maximum distance d: 0.12d +5*(d*sin8°) +2*(d/0.08)/60 ≤15 → d≤3.27km; Time t=3.27/0.08=40.9min>20min, cannot meet both constraints simultaneously." + }, + { + "id": 947, + "scenario_code": "5.7", + "instruction": " The relay satellite uses 128 GB NAND flash memory to store scientific data and employs wear-leveling algorithms to extend its lifespan. The maximum number of erase/write cycles for the flash memory blocks is 3000, and the daily write volume fluctuates between 2-8 GB. The storage has been in operation for 200 days, with an average daily write volume of 5 GB (write amplification factor of 1.2).", + "question": "Calculate the total amount of data written so far (considering write amplification) and estimate the remaining lifespan in days (assuming the worst-case scenario of 8 GB per day). If a dynamic reserved space strategy is adopted to reduce the write amplification to 1.1, how many more days can the lifespan be extended by this optimization measure.", + "answer": "Current write volume = 200*5*1.2 = 1200GB; remaining erase/write cycles = 3000 - (1200/128*3000/3000) = 3000 - 9.375 ≈ 2991 times; worst-case lifespan = 2991/(8*1.2/128*365) ≈ 1095 days; after optimization, daily wear = 8*1.1/128 ≈ 0.06875 times/day, can be extended to 2991/0.06875 ≈ 43505 days." + }, + { + "id": 948, + "scenario_code": "1.5", + "instruction": " The Yutu-2 rover needs to complete lunar rock sampling through Earth remote operation. Given: the end-effector positioning accuracy requirement is ±3mm, the one-way communication delay between Earth and Moon is 1.28 seconds, and the robotic arm movement speed v=5mm/s. After the operator issues the 'advance 10mm' command, they immediately notice a target position deviation of +4mm (requiring reverse adjustment).", + "question": "Calculate the latest time in seconds within which the operator must send a correction command to avoid exceeding the positioning accuracy tolerance? Assume no additional delay in command transmission and execution.", + "answer": "Allowable deviation accumulation time = (3mm tolerance) / (5mm/s) = 0.6 seconds; remaining adjustment time = (4mm - 3mm) / (5mm/s) = 0.2 seconds; total response time = 0.6 + 0.2 = 0.8 seconds" + }, + { + "id": 949, + "scenario_code": "4.9", + "instruction": " Lunar sample return capsule design parameters: 1) The inner diameter of the sealed container is 20cm, height is 30cm; 2) The size limit for the sample bag is 15×15×25cm; 3) The read/write distance of the RFID tag must be ≥5cm; 4) The positioning accuracy of the ascent vehicle's robotic arm during handover is ±3cm. The inner wall of the container is equipped with 6 RFID readers, arranged in two circles (3 each), with each circle spaced 10cm apart.", + "question": "To ensure that the sample bag can be identified by at least 2 readers in any placement orientation, what is the minimum installation angle interval for the readers.", + "answer": "The minimum installation angle interval is 120 degrees. Calculation basis: 1) Spherical coverage problem; 2) The read/write range radius of 5cm corresponds to a solid angle of approximately 0.13 steradians; 3) When 6 readers are evenly distributed, each circle with 3 readers at 120-degree intervals can ensure double coverage; 4) The maximum diagonal size of the sample bag ≈ 30cm < the minimum inner diameter of the container 20cm ensures that it is within the coverage range in any orientation." + }, + { + "id": 950, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, a temporary energy sharing network needs to be established. There are currently 3 devices: A (seismometer, peak power requirement 50W), B (magnetometer, peak power 30W), C (heat flow probe, peak power 20W). The shared power module has a maximum output power of 80W and uses dynamic priority scheduling: scientific data acquisition priority A>B>C. When the total demand exceeds 80W, devices are shut down in descending order of priority. Now A and B start the sampling program simultaneously, and C is in standby mode (basic power consumption 5W). 10 minutes later, C is remotely activated to start working.", + "question": "Calculate the actual power distribution scheme of the power system and the operating status (operating/shutdown) of each device after C is activated.", + "answer": "A operating (50W), B shutdown (0W), C operating (20W). Total power consumption = 50 + 0 + 20 = 70W < 80W." + }, + { + "id": 951, + "scenario_code": "4.1", + "instruction": " The Chang'e-6 mission plans to collect lunar soil samples from the South Pole-Aitken Basin of the Moon. The characteristics of the soil in this area are: medium hardness (Mohs hardness 4-5), low viscosity, and a higher content of volatile components (about 3%). There are three sampling tools available: 1) a diamond-coated rotary drill bit (suitable for rocks with hardness >6); 2) a titanium alloy scoop (suitable for loose lunar soil); 3) a tungsten carbide scraper (suitable for medium-hardness, sticky substances). The sampling process must maintain the volatiles in the samples without loss, and the tool's power consumption must not exceed 200W.", + "question": "Based on the above characteristics of the lunar soil and the constraints, which sampling tool should be chosen? Please explain your reasoning.", + "answer": "The tungsten carbide scraper should be chosen. Reasons: 1) The lunar soil has a medium hardness (4-5), making the tungsten carbide scraper suitable; 2) The scraper is better than the scoop for maintaining volatiles; 3) Although the rotary drill can adjust its power, it is not suitable for the hardness level and poses a high risk of power consumption." + }, + { + "id": 952, + "scenario_code": "4.5", + "instruction": " A 2.5-meter deep drilling task is to be performed in the Oceanus Procellarum region on the near side of the Moon. It is known that: 1) the energy consumption for drilling and core sampling in the loose soil layer (0-1.5 meters) is 15W·h/cm; 2) the energy consumption increases to 25W·h/cm in the dense layer (1.5-2.5 meters); 3) the base power consumption of the drill is 50W; 4) the mission time window is 2 hours, and the maximum power supply from the solar panels is 300W. The maximum length of a single advance of the drill rod is 30cm, and a 10-minute stabilization time is required after each advance.", + "question": "Calculate the maximum drilling depth that can be achieved within this time window, and explain whether it meets the scientific objectives.", + "answer": "The maximum drilling depth is 180cm. Calculation process: 1) Total available energy = 300W * 2h = 600W·h; 2) Energy consumption per advance = 50W * (10/60)h + (15W·h/cm * 30cm) = 8.33 + 450 = 458.33W·h; 3) Number of advances possible = 600 / 458.33 ≈ 1.3 → 1 time; 4) Depth = 30cm * 6 layers = 180cm (the first 6 layers are all loose). This does not meet the 2.5-meter target." + }, + { + "id": 953, + "scenario_code": "1.8", + "instruction": " When deploying a seismometer array, it was found that the local lunar soil bearing capacity is only 150kPa, while the grounding pressure of a standard three-legged bracket's single leg is 180kPa (contact area 20cm^2). Given that the total mass of the bracket is 12kg and the lunar surface gravitational acceleration is 1.62m/s^2. The engineer proposes two solutions: A) Increase the contact area to 30cm^2; B) Reduce the ballast mass to lower the total weight to 10kg.", + "question": "Verify through calculation which solution can ensure the stable deployment of the bracket? If the actual measured maximum pressure per foot after adopting the qualified solution is 145kPa, determine the possible reasons.", + "answer": "Original single-foot pressure=(12*1.62/3)/(20*10^-4)=32.4kPa < 150kPa, already qualified. New pressure of solution A=32.4*(20/30)=21.6kPa; New pressure of solution B=(10*1.62/3)/(20*10^-4)=27kPa. The actual measurement anomaly may be due to uneven lunar soil or the bracket tilting causing uneven load distribution." + }, + { + "id": 954, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the moon, located at point A(10,20), and needs to reach the scientific target point B(50,60). It is known from terrain data that there are two feasible paths between the two points: Path 1 is a straight-line distance of 55 meters but passes through a soft lunar soil area (wheel-soil resistance coefficient 0.15), Path 2 is a zigzag distance of 70 meters but is entirely on hard basalt (wheel-soil resistance coefficient 0.05). The motor efficiency of the lunar rover is 85%, the total battery energy is 5000J, and the driving power consumption model is: energy consumption E = (base power consumption 3W + resistance coefficient * vehicle weight 100kg * 9.8m/s^2 * speed 0.1m/s) * time. The mission requires reserving at least 1000J of emergency energy.", + "question": "Please calculate the total energy consumption of the two paths and determine which path meets the energy constraint.", + "answer": "Path 1 time=55/0.1=550s, energy consumption=(3+0.15*100*9.8*0.1)*550=4125J; Path 2 time=70/0.1=700s, energy consumption=(3+0.05*100*9.8*0.1)*700=3430J. Only Path 2 meets the 5000-3430=1570J>1000J constraint." + }, + { + "id": 955, + "scenario_code": "1.5", + "instruction": " The Chang'e-7 lander needs to control the lunar rover to perform rock sampling through Earth-based remote operation. The one-way communication delay between Earth and the Moon is 1.3 seconds, the movement control command cycle of the lunar rover is 100ms, and the maximum travel speed is 0.1m/s. Currently, a target rock has been found 3 meters ahead, but there is a crater with a diameter of 0.8 meters on the path. The braking distance formula for the lunar rover is d=0.05*v^2 (v is the speed, in units of m/s).", + "question": "To avoid the risk of falling into the crater and minimize sampling time, calculate the maximum allowable approach speed and the corresponding shortest safe stopping distance that should be set in the remote control command.", + "answer": "The maximum speed must satisfy the braking distance ≤ (3-0.8/2) = 2.6m. From d=0.05*v^2 ≤ 2.6, we get v ≤ √(2.6/0.05) = 7.21m/s, but limited by the maximum speed of 0.1m/s, so v = 0.1m/s, at this time d = 0.05*0.1^2 = 0.0005m" + }, + { + "id": 956, + "scenario_code": "2.10", + "instruction": " Chang'e-7 lander needs to perform centimeter-level precise close-up observations of a titanium-iron ore outcrop 0.5 meters in diameter. The visual navigation system has a positioning accuracy of ±2cm (3σ), and the end-effector of the robotic arm has a repeat positioning accuracy of ±1mm. The current relative position of the lander to the target is: 1.2m ±3cm east, elevation difference -0.3m ±1cm (coordinate system: East-North-Sky). To avoid collision risks, the final parking position must maintain a distance of 15±5cm from the target and the robotic arm's working range is limited to a ±80° cone.", + "question": "Calculate the optimal parking point coordinates (East, North, Sky components) that satisfy all constraints, and verify the reachability of the robotic arm. Assume the target is at the origin of the coordinate system.", + "answer": "Optimal parking point: 1.05m east (1.2-0.15), elevation -0.3m (maintain level); the north distance must satisfy √(x^2+y^2)=15cm→y=√(0.15^2-0^2)=±15cm. Verify the robotic arm cone angle: arctan(√(1.05^2+0.15^2)/0.3)=74°<80°, constraints are met." + }, + { + "id": 957, + "scenario_code": "1.4", + "instruction": " The lunar surface power grid supplies power to 3 scientific devices: a seismometer (continuous power consumption 20W), a spectrometer (peak power consumption 50W, duty cycle 40%), and a drill (120W when operating). The power bus has a maximum output power of 100W and uses a priority scheduling strategy: seismometer > spectrometer > drill. When the total demand exceeds 100W, lower-priority devices will be throttled or paused.", + "question": "If the drill starts working for 10 minutes, during which the spectrometer is in its peak cycle, what is the actual power distribution at that time? ", + "answer": "Seismometer 20W + Spectrometer 50W + Drill 30W" + }, + { + "id": 958, + "scenario_code": "1.4", + "instruction": " The lunar base energy grid powers three devices: a mobile rover (peak power 200W), life support systems (constant 150W), and scientific payloads (peak 300W). The grid's total output is capped at 500W, with the life support system having the highest priority. Currently, the rover is performing a hill-climbing task (requiring 180W), and the scientific payload has started calibration mode (requiring 250W). A sudden lunar dust storm has caused a decrease in solar input.", + "question": "Based on priority and current load, how should the grid dynamically adjust power distribution to avoid overload? ", + "answer": "First, ensure 150W for the life support system; in the remaining 350W capacity, reduce the rover's frequency to 170W (180-10), and reduce the scientific payload to 180W (250-70), making the total load = 150+170+180=500W without exceeding the limit." + }, + { + "id": 959, + "scenario_code": "1.8", + "instruction": " The Yutu-2 rover plans to deploy a seismometer at the edge of a 5-meter diameter circular crater. The measured bearing capacity of the lunar soil in this area is 8kPa, the instrument weighs 3kg with a base contact area of 0.005m². The safety factor must be ≥2, and the lunar surface gravitational acceleration is 1.62m/s². Before deployment, it is also necessary to check whether the local magnetic field strength is less than 50nT to avoid interfering with the sensors. The current magnetic field reading is 42nT.", + "question": "Determine if this location meets the deployment requirements and calculate the actual bearing capacity safety factor (formula: safety factor = lunar soil bearing capacity / instrument pressure on the lunar soil).", + "answer": "This location meets the deployment requirements. The instrument's pressure on the lunar soil P=(3*1.62)/0.005=972Pa=0.972kPa; safety factor=8/0.972≈8.23＞2; and the magnetic field 42nT＜50nT meets the conditions." + }, + { + "id": 960, + "scenario_code": "1.8", + "instruction": " Before deploying the lunar rover's magnetometer, it is necessary to detect the local magnetic field strength. It is known that the background magnetic field in this area is 200nT, and the magnetometer's range is ±500nT. When the detected magnetic field absolute value exceeds 300nT, the interference resistance mode (increased energy consumption by 15%) needs to be activated. The current five consecutive measurement values are: -180nT, 220nT, -310nT, 190nT, -290nT. There is a 30-second delay for switching the interference resistance mode.", + "question": "According to the 3/5 majority voting principle, determine whether the interference resistance mode needs to be activated, and how much energy is wasted from the first time the threshold is exceeded to the mode taking effect? (Base power consumption 40W).", + "answer": "30 seconds * (40W * 0.15) = 180 joules" + }, + { + "id": 961, + "scenario_code": "1.2", + "instruction": " In the Chang'e-7 mission, a drill-sampling integrated device (Drill-Sampler Unit, DSU) and a lunar-based telescope array unit (Lunar-based Telescope Array, LTA) need to be deployed at the lunar south pole. The DSU must complete drilling and sampling of the lunar soil before the LTA can begin calibration. The installation of the DSU takes 2 hours, and the sampling operation takes 1.5 hours; the installation of the LTA takes 3 hours, and the calibration takes 2 hours. Due to the extremely low temperature environment on the lunar surface, all operations must be completed within a continuous 8 hours. The DSU and LTA installation teams share the same power supply, and each operation can only support one device's installation or operation at a time.", + "question": "If the mission starts with the installation of the DSU, calculate the shortest completion time for the entire deployment process and explain the critical path.", + "answer": "The shortest completion time is 8 hours. Critical path: DSU installation (2h) → DSU sampling (1.5h) → LTA installation (3h) → LTA calibration (2h). Total time = 2 + 1.5 + 3 + 2 = 8.5h, but constrained by the 8-hour limit, adjustments through parallelization are required (such as overlapping the LTA installation with the DSU sampling by 0.5h)." + }, + { + "id": 962, + "scenario_code": "5.7", + "instruction": " The onboard SSD of the Chang'e-5 orbiter uses NAND flash chips with a total capacity of 1 TB and a block size of 128 KB. The wear-leveling algorithm requires that the difference in the number of erase/write cycles for each block does not exceed 5%. Current monitoring shows: 90% of the blocks have been erased and written 3000-3200 times, while 10% of the blocks have reached 3400 erase/write cycles. The chip's rated lifespan is 5000 erase/write cycles.", + "question": "Calculate whether the current maximum wear difference percentage exceeds the standard, and determine the amount of data that needs to be migrated (assuming all blocks that exceed the standard need to be reallocated).", + "answer": "1. Wear difference percentage = (3400 - 3000) / 3000 ≈ 13.3% > 5% → Exceeds standard\n2. Number of blocks that need to be migrated = Total number of blocks * 10% = (1 TB / 128 KB) * 10% = (1024 * 1024 KB / 128 KB) * 0.1 ≈ 819 blocks\n3. Data volume that needs to be migrated = 819 * 128 KB ≈ 104 MB" + }, + { + "id": 963, + "scenario_code": "1.8", + "instruction": " Before deploying the lunar surface magnetometer, it is necessary to detect local magnetic field interference. It is known that the residual magnetic field of the lander's thrusters is 20nT at 5 meters, and the attenuation rule is B(r) = B0 * (r0/r)^3, where r0=5m. The magnetometer's background noise is 3nT, and the requirement is that the interference magnetic field at the measurement point does not exceed 150% of the background noise.", + "question": "Find the minimum safe distance for deploying the magnetometer (in whole meters).", + "answer": "7m" + }, + { + "id": 964, + "scenario_code": "5.1", + "instruction": " In the Chang'e-4 mission, the lander and rover are located on the far side of the Moon, unable to communicate directly with Earth, and must communicate through the Queqiao relay satellite. The Queqiao satellite operates in a Halo orbit around the Earth-Moon L2 point, about 65,000 km from the Moon. It is known that the lander's transmission power is 10 W, the antenna gain is 12 dBi; the Queqiao receiving antenna gain is 15 dBi, the system noise temperature is 200 K, and the bandwidth is 1 MHz. The free space path loss formula is: L = 20 * log10(4 * π * d / λ), where d is the distance, and λ is the wavelength (assuming the communication frequency is 2.4 GHz).", + "question": "Calculate the uplink signal-to-noise ratio (SNR) from the lander to the Queqiao satellite, and determine whether it meets the minimum communication requirement (SNR ≥ 10 dB). Boltzmann constant k = 1.38e-23 J/K.", + "answer": "1. Calculate the wavelength λ = c / f = 3e8 / 2.4e9 = 0.125 m\n2. Path loss L = 20 * log10(4 * π * 6.5e7 / 0.125) ≈ 191.6 dB\n3. Received power Pr = Pt + Gt + Gr - L = 10 dBW + 12 dBi + 15 dBi - 191.6 dB = -154.6 dBW\n4. Noise power Pn = k * T * B = 1.38e-23 * 200 * 1e6 ≈ -168.6 dBW\n5. SNR = Pr - Pn = -154.6 - (-168.6) = 14 dB ≥ 10 dB → meets the requirement" + }, + { + "id": 965, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the moon, located at coordinate point A (10°N, 120°E). The mission center has planned two scientific target points: Point B (12°N, 122°E) has a basalt outcrop that needs sampling, and Point C (11°N, 121.5°E) has a suspected lava tube entrance that needs to be surveyed. It is known that: 1) The AB path has flat terrain, with a distance d_AB=30km; the BC path has a slope, with a distance d_BC=15km. 2) The energy consumption model is E=0.08*d_flat + 0.15*d_slope + 2*N_turn (unit: Wh, d_flat/d_slope are the distances of flat/slope roads, N_turn is the number of turns). 3) The remaining energy E_remain=50Wh, and each 90-degree turn consumes an additional 2Wh. If choosing the A→B→C path, a turn is required once at point B.", + "question": "Please calculate the total energy consumption of Yutu-2 choosing the A→B→C path, and determine whether the current energy level meets the requirements for this path.", + "answer": "Total energy consumption E = 0.08*30 + 0.15*15 + 2*1 = 2.4 + 2.25 + 2 = 6.65 Wh. Remaining energy 50Wh > 6.65Wh, meeting the requirement." + }, + { + "id": 966, + "scenario_code": "5.1", + "instruction": " In the Chang'e-6 mission, the lander is located in the South Pole-Aitken Basin on the far side of the Moon (SEL: 177.6°E, 45.5°S). The ground station is located in Kashgar, China (longitude 76°E), using the X-band (8GHz) to establish a communication link with the Queqiao-2 relay satellite. It is known that:\n1. Queqiao-2 operates in the Earth-Moon L2 Halo orbit, with an average altitude of about 8000km above the lunar surface;\n2. The Moon's rotational period is synchronized with its orbital period;\n3. The X-band free space loss formula: L = 20 * log10(d) + 20 * log10(f) + 92.45 (d: km, f: GHz);\n4. The current elevation angle of Queqiao-2 from Kashgar is 35°, and the elevation angle of the lander from Queqiao is 15°.", + "question": "Calculate the total free space loss (to two decimal places) for the current state of the Kashgar station → Queqiao-2 → lander communication link, and determine whether the minimum receiving power threshold of -110dBm is met (given the transmission power is 20W and the total antenna gain is 60dB).", + "answer": "Total free space loss = L1 (Kashgar-Queqiao) + L2 (Queqiao-lander)\n= [20*log10(384400*cos35°) + 20*log10(8) + 92.45] + [20*log10(8000/sin15°) + 20*log10(8) + 92.45]\n≈ (181.17 + 18.06 + 92.45) + (77.72 + 18.06 + 92.45)\n= 291.68 + 188.23 = 479.91 dB\nReceiving power = Transmission power (43dBm) + Antenna gain (60dB) - Total loss (479.91dB) = -376.91dBm < -110dBm → Not met" + }, + { + "id": 967, + "scenario_code": "3.1", + "instruction": " The Chang'e-5 lander landed in the Mons Rümker region at 43.06 degrees north latitude and 51.92 degrees east longitude on the near side of the Moon. The solar altitude angle in this area varies between 5° and 35° during the lunar day, and the solar panels use a two-dimensional tracking mode (azimuth + elevation). It is known that: 1) Each solar panel has an area of 2 square meters, with a photovoltaic conversion efficiency of 28%; 2) Under standard test conditions (AM0, 25°C), the solar radiation intensity is 1367 W/m²; 3) Terrain blocking reduces the effective power generation time by 30% daily; 4) The azimuth tracking error is ±3°, and the elevation tracking error is ±5°.", + "question": "If the current solar altitude angle is 20°, calculate the percentage loss of actual power generation compared to the ideal maximum value (considering the combined effect of tracking errors and terrain blocking)?", + "answer": "The percentage loss of actual power generation = Terrain blocking loss 30% + (1-30%)*(1-cos(azimuth error 3°)*cos(elevation error 5°)) = 30% + 70%*(1-0.9986*0.9962) ≈ 30% + 0.41% = 30.41%." + }, + { + "id": 968, + "scenario_code": "3.6", + "instruction": " The Yutu-2 rover needs to maintain a cabin temperature above -40°C during the lunar night. Given: 1) the cabin surface area is 5m², thermal conductivity is 0.05 W/(m·K); 2) the external environmental temperature is -180°C; 3) the isotope heat source provides a constant power of 8W; 4) the electric heater has a maximum power of 15W with 95% efficiency; 5) the lunar night lasts 14 Earth days.", + "question": "To ensure the temperature remains within the required range throughout and to minimize total energy consumption, calculate the minimum duration the electric heater needs to operate (ignoring heat generation from internal equipment)?", + "answer": "Heat loss Q = thermal conductivity * area * ΔT = 0.05 * 5 * (40 - (-180)) = 55W; required additional power = 55W - 8W = 47W; the electric heater actually needs to output 47W / 0.95 ≈ 49.47W; operating time = (49.47W * 14 * 24h) / 15W ≈ 1106 hours" + }, + { + "id": 969, + "scenario_code": "3.1", + "instruction": " The Chang'e-5 rover is conducting exploration tasks in the area at 43.06°N, 51.92°E on the lunar near side, where the lunar day lasts about 14 Earth days. The solar wings use two-dimensional tracking (azimuth + elevation), with a nominal power of 180W (AM0 condition) per wing. The current solar elevation angle is 30°, azimuth angle is 120°, and terrain obstruction reduces the actual effective illumination time to 70% of the nominal value. Known parameters: 1) The solar constant on the lunar surface is 1368W/m²; 2) The solar cell conversion efficiency is 28%; 3) The two-dimensional tracking algorithm has a pointing error of ±5°.", + "question": "Calculate the actual output power of a single wing (considering light attenuation, cosine loss due to pointing error, and conversion efficiency), and round the result to the nearest integer.", + "answer": "85W" + }, + { + "id": 970, + "scenario_code": "2.6", + "instruction": " The Chang'e-4 lander is conducting a navigation calibration experiment in the Von Kármán crater. Its Inertial Navigation System (INS) accumulates a drift error of 0.5° per hour, and it has been continuously operating for 8 hours without correction. The lander measures its actual azimuth angle to be 45° (true value) through astronomical navigation, while the INS displays the current azimuth angle as 48.5°. It is known that landmark matching correction can reduce the error to ±0.1°, but it requires a 20-minute communication window.", + "question": "If the mission requires the azimuth angle error to be <0.3°, should landmark matching correction be initiated immediately? Please explain the basis for your judgment.", + "answer": "1) Current INS error = 48.5°-45°=3.5°; 2) If not corrected, the maximum allowable operating time for subsequent tasks = (0.3-(-0.1))/0.5=0.8 hours < 1 hour; 3) The current error of 3.5° far exceeds the 0.3° threshold, so immediate correction is necessary." + }, + { + "id": 971, + "scenario_code": "3.6", + "instruction": " The Chang'e-4 lander enters the lunar night phase and needs to maintain the temperature of the core electronic equipment box at ≥-40°C. The thermal control system uses: 1) multi-layer thermal insulation material (overall thermal resistance 8K/W); 2) plutonium-238 isotope heat source (steady heat output 12W); 3) electric heating backup (maximum power 10W). The thermal capacity of the equipment box is 200J/K, the current temperature is -20°C, and the temperature difference with the environment is ΔT=160K. It is known that the lunar night lasts 14 Earth days, and the remaining energy in the battery is 800Wh.", + "question": "Calculate whether the isotope heat source alone can maintain the temperature requirement? If not, determine the minimum power that the electric heating system needs to supplement and the corresponding total energy consumption ratio (保留1位小数).", + "answer": "Cannot maintain; need to supplement 4.0W, total energy consumption ratio 33.6% " + }, + { + "id": 972, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, power must be supplied simultaneously to three devices (seismometer, spectrometer, heat flow probe). The current power grid has a total output of 120W, with the basic power consumption of each device being: seismometer 15W (requires continuous operation), spectrometer peak 80W (works for 10 minutes every 2 hours), heat flow probe 30W (works periodically, duty cycle 50%). The power management system adopts a dynamic priority allocation strategy: ① highest priority for life support related equipment; ② second for data acquisition equipment; ③ lowest for other equipment.", + "question": "If a priority ① emergency communication device (constant power consumption 40W) is suddenly connected, how should the system adjust the power supply to each device to ensure the operation of key tasks? Please list the specific power distribution plan.", + "answer": "Emergency communication device 40W (highest priority) + seismometer 15W (second priority) = 55W; the remaining 65W is allocated to the spectrometer and heat flow probe: the spectrometer is downgraded to a peak of 65W (original 80W * 81.25%), the heat flow probe remains at 30W but reduces the duty cycle to 43.3% (30 * 0.433 ≈ 13W, 65 - 13 = 52W available for the spectrometer)." + }, + { + "id": 973, + "scenario_code": "1.5", + "instruction": " When remotely controlling a lunar rover to perform rock sampling, the one-way communication delay between Earth and the Moon is 1.28 seconds. The current speed of the lunar rover is 0.2m/s, and the positioning accuracy of the end of the robotic arm needs to be maintained at ±5cm. The transmission of control commands uses a predictive control algorithm, with the position compensation formula being: compensation distance = delay time * current speed * friction coefficient μ (lunar soil μ=0.6). The control system updates the trajectory prediction every 2 seconds.", + "question": "When the lunar rover suddenly detects an obstacle 30cm ahead and needs to brake urgently, if the time for uploading new commands is not considered, can the existing predictive control avoid a collision? Please explain through calculations.", + "answer": "No. The braking distance required = 0.2m/s * 1.28s * 0.6 = 15.36cm compensation, the remaining distance 30 - 15.36 = 14.64cm > 5cm positioning tolerance, and before the next control update, the vehicle will move 0.2m/s * 2s = 40cm > 14.64cm." + }, + { + "id": 974, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, energy sharing issues must be considered. The current mission has three devices: A (seismometer, continuous power consumption 50W), B (spectrometer, peak power consumption 120W, average 80W), and C (drilling sampler, instantaneous start-up current demand 200W/10 seconds). The total output power of the energy grid is limited to 200W, and the instantaneous overload capacity does not exceed 250W (duration <15 seconds). The priority of the devices is B>A>C. A dynamic power distribution plan needs to be designed.", + "question": "When all three devices request power simultaneously, how should the system allocate power according to the given priorities and power limits? Please explain the actual power supply and duration for each device.", + "answer": "First, meet the peak power demand of 120W for device B, then allocate the remaining 80W to supply 50W to device A, and temporarily do not supply power to device C. When device B's power consumption drops to the average of 80W, the remaining 120W can be allocated as 50W to device A + 70W to device C (the drilling start-up current must be limited to below 150W to meet the total power limit of 200W)." + }, + { + "id": 975, + "scenario_code": "1.8", + "instruction": " When deploying the lunar-based telescope, it was found that the local lunar soil bearing capacity is only 3kPa (lower than the expected 5kPa). The single-foot contact area of the triangular bracket of the telescope is 0.02m², with a total mass of 60kg (including the shock absorption mechanism). The bracket angle adjustment range is ±5°, and the maximum offset of the center of gravity is 0.3m. It is known that the safety factor needs to be ≥1.5, and the lunar surface gravitational acceleration is 1.62m/s².", + "question": "Determine whether the current deployment plan meets the load-bearing requirements? If not, calculate how much the contact area needs to be increased or to what range the bracket angle needs to be adjusted at least.", + "answer": "Actual pressure per foot = (60*1.62/3)/0.02 = 1620Pa = 1.62kPa < 3kPa/1.5=2kPa → Not met. The area needs to be increased to (60*1.62/3)/2000 = 0.0162m² (an increase of 81% from the original area), or adjust the center of gravity offset to make the load per foot ≤40kg (i.e., the offset ≤(40*3/60)*0.3=0.6m corresponding to an angle of approximately ±3°)." + }, + { + "id": 976, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is conducting a scientific exploration mission from point A (coordinates X=100m, Y=50m) to point B (X=300m, Y=250m). It is known that: 1) The lunar surface slope is less than 15°, and the wheel-soil mechanics model shows energy consumption coefficients of 0.12Wh/m (flat) and 0.18Wh/m (uphill); 2) The current path planning shows a total distance of 200m, with 30m being an uphill section; 3) The solar panel's current output power is 20W, and the remaining battery capacity is 150Wh; 4) 30Wh needs to be reserved for scientific instrument operation.", + "question": "Calculate the total energy consumption under the current path planning and determine whether the remaining battery capacity meets the mission requirements.", + "answer": "Total energy consumption = (200-30)*0.12 + 30*0.18 = 26.4Wh; Available power = 150-30 = 120Wh > 26.4Wh, meeting the requirements." + }, + { + "id": 977, + "scenario_code": "2.2", + "instruction": " When the Chang'e-7 lander conducts exploration in the permanently shadowed area, the navigation system adopts a multi-sensor fusion solution: 1) The IMU position error accumulates over time at 0.1m/s; 2) The visual odometry (VO) relative positioning error is ±2%; 3) The LiDAR SLAM absolute positioning error is ±0.5m. It is known that the detector moves at a speed of 0.1m/s, and VO updates every 5 seconds, while IMU data updates every second.", + "question": "If no SLAM correction is received for 10 minutes of continuous operation, calculate the maximum possible position error range at this time.", + "answer": "IMU drift error = 0.1*600 = 60m; VO cumulative error = (0.1*600)*2% = 1.2m; Total error = ±(60+1.2+0.5) = ±61.7m" + }, + { + "id": 978, + "scenario_code": "2.2", + "instruction": " Chang'e-7 lander conducts exploration in the permanently shadowed area of the Shackleton crater, with its navigation system adopting a multi-sensor fusion solution: 1) Visual odometry positioning error ±3m/100m; 2) IMU drift error 1m/min; 3) LiDAR SLAM absolute accuracy ±0.5m. It is known that the distance from the starting point to the scientific target point is 80m in a straight line, with a movement speed of 0.1m/s, and it experiences 2 ten-minute communication interruptions during which the IMU cannot be corrected.", + "question": "Calculate the maximum possible positioning error when the probe reaches the target point (do not consider the cancellation of system error superposition), and explain the main source of error.", + "answer": "Maximum error calculation: 1) Visual error = 80/100*3 = 2.4m; 2) IMU error = 20min*1m/min = 20m (10 minutes each for two interruptions); 3) SLAM error = 0.5m; Total = 2.4 + 20 + 0.5 = 22.9m. Main source of error: Uncompensated IMU drift during communication interruptions (contributes 87% of the error)." + }, + { + "id": 979, + "scenario_code": "2.7", + "instruction": " When the lunar rover is patrolling near the terminator and receives a solar proton event warning, it needs to reach an emergency shelter pit 3 kilometers away within 30 minutes. Terrain constraints are as follows: 1) The shortest path involves a slope with a gradient of 25°, with a climbing energy consumption coefficient k=1.8; 2) The flat detour path is 5 kilometers long, with an energy consumption coefficient k=1.0. The basic energy consumption formula is E=k*d (d is in kilometers), and the current remaining energy is 12Wh.", + "question": "Determine whether the lunar rover can safely reach the shelter point via the shortest path? If not, provide a solution that meets the energy and time constraints (movement speed ≤0.2m/s).", + "answer": "Energy consumption for the shortest path E=1.8*3=5.4Wh<12Wh, but the time required t=3000/(0.2*60)=250 minutes>30 minutes, which is not feasible. Solution: Choose the flat path, energy consumption E=1.0*5=5Wh<12Wh, time t=5000/(0.2*60)=417 seconds≈7 minutes<30 minutes, meeting all constraints." + }, + { + "id": 980, + "scenario_code": "5.7", + "instruction": " The 'Chang'e-5' orbiter's SSD storage module uses NAND flash chips with a total capacity of 512 GB and a block size of 128 KB. The wear-leveling algorithm must ensure that the difference in the number of erase/write cycles between blocks does not exceed 10%. The oldest block has already reached 3,000 erase/write cycles, while the newest block has 2,700 cycles. The storage controller needs to dynamically adjust the data writing strategy to avoid exceeding the chip's rated erase/write life (5,000 cycles).", + "question": "Calculate whether the current wear-leveling status is compliant and determine which type of block (oldest/newest/random) the next group of data (160 MB) should be prioritized to write to.", + "answer": "The difference rate (3000-2700)/3000=10% equals the upper limit of the threshold but is still compliant. 160 MB requires 160*1024/128=1280 blocks, and should be prioritized to write to the newest block (2700 times) to reduce the difference rate to (3000-(2700+1280/512))/(3000+1280/512)≈9.8%." + }, + { + "id": 981, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing a patrol mission on the far side of the Moon, located at coordinate point A(10,20). The mission center has planned three scientific target points: B(30,40), C(50,60), and D(70,80). According to the wheel-soil mechanics model, the energy consumption formula for the lunar rover traveling on the lunar surface is: E = 0.15 * d + 2.5, where d is the travel distance (meters), and E is the energy consumption (watt-hours). The lunar rover currently has 45 watt-hours of remaining power. It is known that traveling from A to B requires passing through a steep slope area, where the actual travel distance will be 20% longer than the straight-line distance.", + "question": "If Yutu-2 needs to visit at least two scientific target points before the power is depleted, which two points should be prioritized? Please calculate the total energy consumption for each combination and provide the optimal choice.", + "answer": "The straight-line distance AB = sqrt((30-10)^2+(40-20)^2)=28.28 meters, the actual AB distance = 28.28*1.2=33.94 meters; AC=56.57 meters; AD=84.85 meters; BC=28.28 meters; BD=56.57 meters; CD=28.28 meters. The energy consumption for the combination AB+BC = (0.15*33.94+2.5)+(0.15*28.28+2.5)=14.08 watt-hours; AB+BD=14.08+(0.15*56.57+2.5)=25.56 watt-hours; AC+CD=(0.15*56.57+2.5)+(0.15*28.28+2.5)=19.08 watt-hours. The optimal choice is the AB+BC combination (total energy consumption 14.08 watt-hours < 45 watt-hours)." + }, + { + "id": 982, + "scenario_code": "5.7", + "instruction": " The 128 TB solid-state storage device carried by the Chang'e-7 orbiter adopts the following management strategies:\n1. Uses NAND flash chips, with each block capable of 10,000 write-erase cycles\n2. Average write amplification factor of 1.5\n3. Average daily write volume of 40 GB (including scientific data and system logs)\n4. Uses dynamic wear leveling algorithm to ensure the difference in write-erase cycles among blocks does not exceed ±5%.", + "question": "Calculate the theoretical minimum service life of the storage device before all blocks reach their maximum write-erase cycle limit (unit: years).", + "answer": "14.0 years" + }, + { + "id": 983, + "scenario_code": "1.4", + "instruction": " When deploying scientific equipment in the permanently shadowed regions of the lunar south pole, it is necessary to power a drilling sampling device (peak power 120W), a seismometer (continuous power 15W), and a thermal control system (intermittent operation, peak power 80W). The power module uses a hybrid solar-battery power supply, with solar panels providing 200W of continuous power during the day and relying on batteries (total capacity 2000Wh) at night. All equipment must operate continuously for 30 Earth days (approximately 708 hours), with lunar day and lunar night each occupying half of the time.", + "question": "If the battery is required to have a remaining charge of no less than 20% at the end of the lunar night, and the thermal control system only needs to operate for 4 hours per day-night cycle, calculate the minimum initial charge of the battery that should be satisfied in Wh.", + "answer": "Initial charge ≥ (15W * 354h + 80W * 4h * 15 days) / (1 - 0.2) = (5310 + 4800) / 0.8 = 12637.5Wh" + }, + { + "id": 984, + "scenario_code": "2.9", + "instruction": " The Lunar Orbit Navigation Satellite System (LBNSS) provides positioning services for Chang'e-6, given: 1) The real-time coordinates of orbiting satellites S1, S2, S3 are (100,200,300), (400,500,600), (700,800,900) respectively; 2) The signal transmission delays received by Chang'e-6 are 1ms, 3ms, 4ms (including clock bias); 3) The speed of light is 299792458m/ms. The lander's own UWB beacon measures the distance to the rover as 50±0.m.", + "question": "If clock bias is ignored and there is no refraction error in the signal, please calculate the coordinates (x,y,z) of Chang'e-6 based on the principle of trilateration. Hint: Distance formula d=c*Δt, the system of equations needs to solve (x-100)^2+(y-200)^2+(z-300)^2=(299792458*1)^2 and two other similar equations.", + "answer": "d1=299792458*1=299792458m; d2=299792458*3=899377374m; d3=299792458*4=1199169832m. Solve: (x-100)^2+(y-200)^2+(z-300)^2=(299792458*1)^2; (x-400)^2+(y-500)^2+(z-600)^2=(299792458*3)^2; (x-700)^2+(y-800)^2+(z-900)^2=(299792458*4)^2 → x=y=z=(d1^2-d2^2+d3^2)/(2*(-600))= (specific numerical solution omitted)." + }, + { + "id": 985, + "scenario_code": "1.8", + "instruction": " When deploying a magnetometer network on the lunar surface, an abnormal magnetic field fluctuation of 10-50nT was found in a local area. The measurement error of a single magnetometer is ±2nT, and the spacing between adjacent nodes is 20 meters. To distinguish between real magnetic field changes and instrument noise, it is required that at least 3 adjacent nodes simultaneously detect a change exceeding 6nT to trigger data marking. In a certain measurement, nodes A, B, and C recorded changes of +7nT, +9nT, and +4nT, respectively.", + "question": "According to the above judgment rules, should the system mark the measurement results as valid abnormal signals? Please explain the judgment basis step by step.", + "answer": "Not marked. Because the change at node C is 4nT < 6nT, it does not meet the condition that 'at least 3 adjacent nodes all exceed 6nT' (only A/B meet the standard)." + }, + { + "id": 986, + "scenario_code": "3.1", + "instruction": " The Chang'e-6 lander is located on the edge of an impact crater at 23.5°N, 12.8°E on the lunar near side. Its solar panels use a two-dimensional tracking algorithm (azimuth + elevation). According to the lunar ephemeris, the current solar elevation angle is 15°, and the azimuth angle is 45° (0° is due north, increasing clockwise). The crater wall forms an obstruction in the azimuth range of 30° to 60°, with a shadow length of 2 meters. The horizontal distance from the center of the lander's solar panels to the crater wall is 5 meters, and the wingspan is 3 meters. It is known that the power generation per unit area without obstruction is P0=300W/m², and the power generation of the obstructed part drops to 0.", + "question": "Calculate the actual total power generation of the solar panels under the current conditions (consider the shading effect, assuming the wingspan is fully extended and the efficiency is uniform).", + "answer": "450W" + }, + { + "id": 987, + "scenario_code": "3.1", + "instruction": " Chang'e-6 lander is located in the lunar near side at 45° North latitude, and its solar panels use a two-dimensional tracking algorithm (azimuth + elevation). According to the lunar ephemeris, the current solar elevation angle is 15°, and the azimuth angle is 30° (0° is due north, increasing clockwise). There is a 1.5-meter-high rock 3 meters west of the landing site that obstructs the view. The single panel of the solar wing measures 0.5m×0.8m, with a standard light power generation of P0=120W/m², and the power in the shaded area decreases to 10%.", + "question": "If the theoretical output power of the solar wing when fully aligned with the sun is 48W, what is the actual maximum output power considering the terrain obstruction? ", + "answer": "Actual maximum output power = 48W * (1 - 0.5m*0.8m / (0.5m*0.8m) * 0.9 + 48W * (0.5m*0.8m / (0.5m*0.8m)) * 0.1 = 43.2W * unobstructed ratio + 4.8W * obstructed ratio. Since the shadow angle formed by the 1.5m high rock at a distance of 3 meters is arctan(1.5/3)=26.565°, which is greater than the solar elevation angle of 15°, the entire area is obstructed, so the actual power = 48W*10% = 4.8W." + }, + { + "id": 988, + "scenario_code": "3.4", + "instruction": " Yutu-2 rover needs to perform three tasks simultaneously during the lunar day: ① Rock debris detector (peak power consumption 80W, lasting 20 minutes); ② Panoramic camera shooting (peak power consumption 50W, lasting 10 minutes); ③ X-ray spectrometer preheating (constant power consumption 30W, needs to be started 5 minutes in advance). The energy management system sets the instantaneous power consumption limit to 100W, and the rock debris detection has the highest priority. The current available battery capacity is 120Wh, and 40Wh needs to be reserved before the next lunar night.", + "question": "Design the task start sequence that meets all constraints (provide the start time of each device), and verify whether the total energy consumption is safe.", + "answer": "Sequence: X-ray spectrometer starts at t=0, rock debris detector starts at t=5min, panoramic camera starts at t=25min; total energy consumption=(30*35 + 80*20 + 50*10)/60 ≈ 78.3Wh < 80Wh safety margin" + }, + { + "id": 989, + "scenario_code": "3.6", + "instruction": " Before the Chang'e-7 lander enters the lunar night phase, it needs to maintain the battery temperature ≥ -20℃. Given: ① Battery mass 10kg, specific heat capacity 900J/(kg·℃); ② Equivalent thermal resistance of multi-layer insulation material R=2K/W; ③ Isotope heat source rated heat output Q_h=8W; ④ Lunar night environmental temperature T_env=-180℃; ⑤ Initial temperature T_init=10℃. Ignore other heat exchange paths.", + "question": "Verify whether the isotope heat source alone can meet the insulation requirement for 14 days of lunar night (need to calculate the final temperature), if not, then find the minimum additional electric heating power required.", + "answer": "Final temperature T_final = -164.8℃ (not met), additional electric heating power required ≥ 6.4W" + }, + { + "id": 990, + "scenario_code": "2.7", + "instruction": " When the lunar rover patrols near the terminator and receives a solar proton event warning, it needs to reach an emergency shelter pit within a 500-meter radius within 30 minutes. Current status: position P(25°N,30°E), speed 0.08 km/h, maximum turning angle 15°/s; terrain data shows that there is a deep pit C1 (safety level 90%) 300 meters due north, and a rock shelter area C2 (safety level 70%) 400 meters northeast. Energy consumption model: turning energy consumption E_turn = 5 * (Δθ)^1.3 J, straight-line energy consumption E_straight = 0.2 * d J.", + "question": "Calculate the theoretical minimum energy consumption (J) for traveling to C1 and C2, and select the optimal risk avoidance path (must meet the 30-minute reachability constraint).", + "answer": "1) C1 path: straight 300m, E = 0.2 * 300 = 60 J, time t = 0.3 / 0.08 = 3.75 h > 0.5 h not feasible; 2) C2 path: need to turn 45°, E_turn = 5 * (45)^1.3 ≈ 680 J, E_straight = 0.2 * 400 = 80 J, total E = 760 J, time t_turn = 45 / 15 = 3 s, t_move = 0.4 / 0.08 = 5 h still exceeds time. Conclusion: neither option meets the time constraint, need to activate the on-site emergency mode." + }, + { + "id": 991, + "scenario_code": "2.9", + "instruction": " The lunar orbit navigation satellite LBNSS-1 has three sources of error in its distance measurement to the rover: 1) Ephemeris error ±5m; 2) Ionospheric delay ±2m; 3) UWB beacon clock desynchronization ±1m. Currently, four independent distance measurement data points have been obtained: [1847m, 1853m, 1849m, 1855m], with the known true distance being 1850m.", + "question": "Calculate the actual distance measurement accuracy (standard deviation) of the current system, and determine whether it meets the requirement of ≤3m.", + "answer": "Mean distance = (1847 + 1853 + 1849 + 1855) / 4 = 1851m; Variance = [(1847 - 1851)^2 + (1853 - 1851)^2 + (1849 - 1851)^2 + (1855 - 1851)^2] / 4 = (16 + 4 + 4 + 16) / 4 = 10; Standard deviation = sqrt(10) = 3.16m > 3m, does not meet the requirement." + }, + { + "id": 992, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing exploration tasks on the far side of the Moon, located at coordinate point A (10°N, 120°E). The mission planning system requires it to reach scientific target point B (12°N, 122°E) within the lunar day (about 14 Earth days) and complete at least 48 hours of scientific observations. It is known that: 1) The average driving speed of the lunar rover is 0.05 km/h; 2) The energy consumption model is E = 0.15 * d + 5 (Wh/km), where d is the driving distance; 3) The current remaining battery energy is 2000 Wh; 4) The solar power generation power during the lunar day is constant at 50 W. The formula for calculating the great circle arc distance between two points is: Distance = R * arccos(sinφ1*sinφ2 + cosφ1*cosφ2*cosΔλ), where R = 1737 km, φ is the latitude, and λ is the longitude.", + "question": "Calculate the theoretical shortest path distance (km) from point A to point B for Yutu-2, and determine whether it can complete 48 hours of scientific observations after reaching point B under the current energy constraints (assuming the energy consumption during the scientific observation period is 20 W).", + "answer": "1) Calculate the distance: d = 1737 * arccos(sin10°*sin12° + cos10°*cos12°*cos2°) ≈ 1737 * 0.0349 ≈ 60.6 km; 2) Driving energy consumption: E_move = 0.15 * 60.6 + 5 ≈ 14.1 Wh; 3) Driving time: t_move = 60.6 / 0.05 = 1212 h ≈ 50.5 days, exceeding the duration of the lunar day, thus the task cannot be completed." + }, + { + "id": 993, + "scenario_code": "1.4", + "instruction": " The lunar base energy grid needs to allocate peak power to three devices: life support system (priority 1, requires 10kW), mobile power module (priority 2, requires 8kW), and scientific payload (priority 3, requires 6kW). The grid currently has a peak power availability of 18kW and must fully meet the power demand of priority 1 devices. When power is insufficient, lower priority devices are allocated the remaining power proportionally.", + "question": "Calculate the actual power allocation for each device and explain the allocation logic.", + "answer": "Life support system: 10kW (fully met); Mobile power module: 8kW * (18-10)/(8+6) ≈4.57kW; Scientific payload: 6kW * (18-10)/(8+6) ≈3.43kW. Allocation logic: After fully meeting the demand of priority 1, the remaining 8kW is allocated according to the demand ratio of priorities 2 and 3." + }, + { + "id": 994, + "scenario_code": "1.5", + "instruction": " The Yutu-2 lunar rover needs to be remotely controlled to cross obstacles with a communication delay of 1.3 seconds. The vehicle's current speed is 0.15m/s, and a crack appears 3 meters ahead requiring emergency braking. The braking acceleration is 0.1m/s^2, and the control system's predictive algorithm compensates for 60% of the delay time.", + "question": "Determine if it can safely stop before the crack (calculate the stopping distance) and explain how the predictive compensation affects the result.", + "answer": "Stopping distance d = v^2/(2*a) = (0.15)^2/(2*0.1) =0.1125m <3m; Effective reaction time=1.3s*60%=0.78s, during which the travel distance=0.15*0.78=0.117m. Total stopping distance=0.1125+0.117=0.2295m <3m, can stop safely. Predictive compensation reduces the impact of actual reaction delay." + }, + { + "id": 995, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently executing a patrol mission on the far side of the moon, located at coordinate point A (0,0), and needs to reach the scientific target point B (100,50) (unit: meters). Terrain data indicates that there are two optional paths between the two points: Path 1 is a gentle slope with an average gradient of 5° and a straight-line distance of 120 meters, and Path 2 is a flat area with a zigzag distance of 110 meters but requires detouring around an impact crater. It is known that the energy consumption coefficient of the lunar rover when driving on a 5° slope is 0.15 Wh/m, and the energy consumption coefficient on a flat area is 0.1 Wh/m. The current remaining battery energy is 18 Wh, and it must reach the target point within 10 minutes to ensure the communication window. The maximum speed of the lunar rover is 0.2 m/s.", + "question": "To ensure that both the energy constraint and the time constraint are met, which path should Yutu-2 choose? Please calculate the total energy consumption and required time for both paths.", + "answer": "Choose Path 2. Calculation process: Total energy consumption of Path 1 = 120m * 0.15Wh/m = 18Wh (equal to the remaining power without margin), required time = 120m / 0.2m/s = 600s = 10 minutes; Total energy consumption of Path 2 = 110m * 0.1Wh/m = 11Wh, required time = 110m / 0.2m/s = 550s ≈ 9.17 minutes. Path 2 meets both the energy consumption ≤ 18Wh and the time ≤ 10 minutes." + }, + { + "id": 996, + "scenario_code": "4.9", + "instruction": " When the ascent vehicle transfers the sample container to the return capsule, the following conditions must be met:\n- Temperature records must be maintained at -50±5°C throughout the process\n- The success rate of RFID tag reading must be ≥99%\n- The sealing pressure must be maintained between 10^-4Pa and 10^-6Pa\nFault records show:\nContainer No.1 pressure sensor malfunction (continuously showing 10^-3Pa)\nContainer No.2 had 1 RFID read failure during transfer\nContainer No.3 temperature record showed a peak of -62°C", + "question": "According to the transfer standards, which numbered sample containers can be accepted? Specify the exact values of non-conforming items and the standard ranges.", + "answer": "Only Container No.2 can be accepted. Non-conforming items are as follows:\nContainer No.1 pressure 10^-3Pa (exceeds the upper limit of 10^-4Pa)\nContainer No.3 temperature -62°C (exceeds the lower limit of -55°C)\nContainer No.2 RFID read success rate 99% (meets the standard of ≥99%)" + }, + { + "id": 997, + "scenario_code": "2.4", + "instruction": " The Yutu-2 lunar rover is currently performing exploration tasks on the far side of the moon, located at coordinate point A(10,20), and needs to reach the scientific target point B(50,60). Terrain data indicates that there are two optional paths between the two points: Path 1 is a straight-line distance of 70 meters but requires crossing a 15° slope, Path 2 is a zigzag distance of 85 meters but all slopes are less than 5°. It is known that the motor efficiency of the lunar rover is 85% on a 5° slope, which drops to 60% on a 15° slope, the base power consumption on flat ground is 5W, and the travel speed is constant at 0.05m/s. The battery currently has 8000J of remaining energy, and at least 2000J must be reserved for emergencies.", + "question": "Calculate the total energy consumption for both paths and determine which path meets the energy constraints? Hint: The energy consumption formula is E = (base power consumption / motor efficiency + slope compensation term) * travel time, where the slope compensation term = 0.1 * slope angle (°).", + "answer": "Path 1 energy consumption: E1 = (5/0.6 + 0.1*15) * (70/0.05) = (8.33+1.5)*1400 = 13762J; Path 2 energy consumption: E2 = (5/0.85 + 0.1*5) * (85/0.05) = (5.88+0.5)*1700 = 10846J. Only Path 2 meets the energy constraint of 8000-2000=6000J." + }, + { + "id": 998, + "scenario_code": "2.7", + "instruction": " The lunar rover is conducting exploration in a permanently shadowed area when it suddenly receives a solar proton event warning, requiring it to reach a 3-kilometer distant emergency shelter within 30 minutes. The current area has complex terrain: there is a deep pit to the exact north that cannot be crossed, and 300 meters to the northeast, there is a known lava tube passage that can shorten the route but poses a risk of lunar dust accumulation. The maximum safe speed of the lunar rover is 0.1m/s, and the detour via the regular route is 4000 meters. The lava tube passage can reduce the total distance to 3200 meters, but the speed must be reduced to 0.05m/s, and it takes 10 minutes to clear the lunar dust.", + "question": "Analyze whether the two plans can meet the safety time limit? Which path should be chosen? ", + "answer": "Regular route time: 4000/0.1 = 40000 seconds (about 666 minutes) exceeds the limit; Lava tube plan: 300/0.1 + 10*60 + (3200-300)/0.05 = 3000+600+58000 = 67000 seconds (about 1117 minutes) still exceeds the limit. Conclusion: Neither plan can meet the 30-minute (1800 seconds) time limit, and a higher priority emergency protocol must be initiated." + }, + { + "id": 999, + "scenario_code": "4.4", + "instruction": " The Yutu-2 rover is conducting exploration in the Von Kármán crater, obtaining the following remote sensing data:\n- Hyperspectral imaging shows that the coordinates (12.3°S, 135.7°E) have a KREEP rock characteristic peak (absorption depth >15%)\n- LiDAR terrain data indicates that the slope at this point is 8°, and the distance from the current location is 320 meters\n- The solar elevation angle will drop below 5° in 2 hours\nEnergy constraint: travel power consumption = 0.8Wh/m + 3Wh (base), remaining power 82Wh\nScientific priority: KREEP rock (weight 3) > volcanic glass (weight 2) > ordinary lunar soil (weight 1).", + "question": "Determine whether to proceed to the sampling point and calculate the maximum allowable exploration time (assuming sampling consumes 5Wh)? List the path energy consumption formula and time calculation formula.", + "answer": "Should proceed to the point. Calculation process:\n1. Path energy consumption E_path = 320 * (0.8 + 3/320) = 262.4Wh > 82Wh → actually unreachable\n2. Due to slope > 5°, activate slope climbing mode, energy consumption corrected to E_path * 1.5 = 393.6Wh > 82Wh → still unreachable\nConclusion: due to power limitations, should not proceed (Note: the original problem setting has a contradiction, this is the verification process)." + }, + { + "id": 1000, + "scenario_code": "5.4", + "instruction": " The Yutu-2 rover needs to transmit scientific data to Earth via the relay satellite during the lunar day. The following situation is currently encountered:\n1. A solar proton event has caused the current communication link's bit error rate to rise sharply to 10^-2 (threshold is 10^-5);\n2. The remaining operational time window is only 30 minutes;\n3. The remaining capacity of the SSD cache is 50GB, and the data generation rate is 200MB/minute;\n4. Alternative plan: Switching to a lower frequency band (S-band) can reduce the bit error rate to 10^-6, but the bandwidth will decrease by 60%.", + "question": "Please decide whether to switch the communication frequency band and calculate the total amount of data that can be safely transmitted (considering a 2-minute switching time).", + "answer": "Decision analysis:\n1. Remaining transmission volume on X-band: 200MB/min * (30min-2min) = 5600MB\n Transmission volume on S-band: 200MB/min*(30min-2min)*40% = 2240MB\n2. Effective data volume on X-band: 5600*(1-0.01)=5544MB (error loss 56MB)\n Effective data volume on S-band: 2240*(1-0)=2240MB\n3. SSD overflow risk: 200*30=6000MB <50GB (safe)\nConclusion: Maintaining X-band transmission can achieve more effective data (5544MB>2240MB), no need to switch frequency bands." + } +] \ No newline at end of file