Gravity-assist Earth-to-Jupiter transfer trajectories optimization and midcourse correction design in ephemeris model
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摘要:
木星系探测具有重要的科学意义与战略价值，而地木转移是实现木星系探测的关键基础。基于行星借力飞行技术对地球木星转移轨道进行了优化设计，并在高精度星历模型中针对实际飞行可能存在的轨道误差设计了中途修正策略。基于Tisserand图分析行星借力飞行序列；以进入环木轨道探测器质量最大化为目标，构建考虑行星星历的借力飞行转移轨道优化非线性规划模型；针对实际飞行误差设计多次借力飞行轨道的中途修正策略；以中国木星系探测任务论证为背景，以2034—2036年为发射窗口，在长征5号运载火箭发射能力下，得到了多种借力转移序列的最优与次优转移方案。结果表明：金星-地球-地球借力转移的最优解可以使进入目标环木轨道的探测器质量达到
4340.8 kg，相比霍曼转移提高约1300 kg，而后在星历模型下用蒙特卡罗仿真验证中途修正策略，结果显示，在各种误差情况下终端B平面脱靶量小于50 km，且修正脉冲消耗较小，证明所设计的行星借力转移轨道和中途修正策略能够在高精度力学环境中实现地木转移任务，可为中国木星系探测任务设计提供参考。Abstract:The Jupiter system exploration has important scientific significance and strategic value, and the Earth-to-Jupiter transfer is the key basis for Jupiter system exploration. The optimal design of Earth-to-Jupiter transfer trajectories is carried out using gravity-assist flight technology, and the midcourse correction strategy is designed to reduce orbit errors during actual flight in the high-precision ephemeris model. First, gravity-assist flight sequences were analyzed through the Tisserand graph. Second, in order to maximize the mass of the probe entering the orbit around Jupiter, a nonlinear programming model is established to optimize the planet-assisted transfer trajectories by considering the planetary ephemeris. Then, the midcourse correction strategy is designed to eliminate actual flight errors of the multiple gravity-assist flight trajectories. Finally, with China’s Jupiter system exploration mission as an example, the optimal and suboptimal transfer solutions of various gravity-assist sequences are obtained by considering the capability of the Long March 5 launch vehicle in the launch window between the year 2034 and 2036. The results show that the optimal solution of the Venus-Earth-Earth-assisted transfer can make the mass of the probe entering the target orbit around Jupiter reach
4340.8 kg, which is about1300 kg higher than that of the Hohmann transfer. Monte-Carlo simulations validate the midcourse correction strategy in the ephemeris model. The results show that under various errors, the final B-plane miss distances are less than 50 km, and the correction pulse consumption is small, which proves that the designed gravity-assist transfer trajectories and midcourse correction strategy can realize the Earth-to-Jupiter transfer mission in the high-precision mechanical environment and can provide a reference for the design of China’s Jupiter system exploration mission. -
表 1 变量搜索范围
Table 1. Searching intervals of variables
变量 搜索范围下界 搜索范围上界 ${t_0}$ ${t_{\text{i}}}$ ${t_{\text{f}}}$ ${t_1}$ $ {t_0} + \gamma _{0,1}^{\text{L}}t_{0,1}^{{\text{hoh}}} $ $ {t_0} + \gamma _{0,1}^{\text{U}}t_{0,1}^{{\text{hoh}}} $ ${t_2}$ $ {t_1} + \gamma _{1,2}^{\text{L}}t_{1,2}^{{\text{hoh}}} $ $ {t_1} + \gamma _{1,2}^{\text{U}}t_{1,2}^{{\text{hoh}}} $ ${t_{k + 1}}$ $ {t_k} + \gamma _{k,k + 1}^{\text{L}}t_{k,k + 1}^{{\text{hoh}}} $ $ {t_k} + \gamma _{k,k + 1}^{\text{U}}t_{k,k + 1}^{{\text{hoh}}} $ 
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表 2 优化设计中约束的参数设置
Table 2. Parameters of constraints in optimization design
$C_3^{\lim } $/（km2·s−2） ${h_{\lim }} $/km $\Delta {v_{\lim }} $/（km·s−1） ${t_{\lim }} $/a 90 200 0.6 8
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表 3 转移轨道优化结果
Table 3. Results of transfer orbit optimization
转移
序列发射
时刻
(年/月/日)到达
木星
时刻
(年/月/日)总飞行
时长/d发射
能量/
(km2·s−2)到达
能量/
(km2·s−2)近木
制动
脉冲/
(km·s−1)借力
飞行时
施加
脉冲/
(km·s−1)发射
质量/kg到达
质量/kg借力
天体借力
时刻
(年/月/日)飞掠
近拱点
半径/km近拱点
脉冲/
(km·s−1)借力
等效脉冲/
(km·s−1)EMJ 2035/12/5 2042/8/16 2445.63 59.34 28.14 0.514 0.294 4023.82 3110.84 火星 2039/6/25 3589.5 0.294 1.5734 EMEJ 2035/11/9 2042/7/3 2427.95 32.64 34.58 0.569 1.6×10−6 4654.28 3882.57 火星 2038/6/27 3744.1 2.7×10−8 2.0452 地球 2039/12/28 8485.77 1.6×10−6 5.9198 EVEJ 2035/12/26 2041/4/14 1935.54 27.45 37.46 0.594 0.215 4776.82 3691.60 金星 2037/3/30 6296.17 0.212 7.0512 地球 2038/12/8 6658.19 0.00297 6.5130 EMEEJ 2036/2/4 2044/1/24 2910.76 44.61 34.00 0.564 0.610 4371.77 3008.24 火星 2037/11/18 8816.91 2.6×10−9 0.7571 地球 2038/4/28 38462.14 0.153 2.0983 地球 2040/12/15 6571.61 0.457 7.7237 EVEEJ 2036/3/31 2042/10/6 2380.65 10.83 32.16 0.548 2.8×10−6 5169.26 4340.80 金星 2036/9/26 7841.4 2.8×10−9 6.4299 地球 2038/3/2 20793.51 5.9×10−7 2.9778 地球 2039/10/30 9032.28 2.2×10−6 5.8380 EVEMJ 2036/4/2 2044/3/23 2912.05 12.12 36.73 0.588 0.570 5138.89 3554.23 金星 2036/10/2 9033.38 2.3×10−7 5.9063 地球 2038/3/4 7401.51 8.0×10−10 6.7006 火星 2041/7/16 3589.5 0.570 1.4368
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表 4 2种优化模型的结果对比
Table 4. Comparison of results between two different optimization models
借力序列 速度增量为优化目标的
到达质量/kg本文模型优化的
到达质量/kgEMJ 3029.02 3110.84 EMEJ 3831.82 3882.57 EVEJ 3626.27 3691.60 EMEEJ 2842.30 3008.24 EVEEJ 4199.13 4340.80 EVEMJ 3501.46 3554.23
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表 5 初始停泊轨道和目标环木轨道参数
Table 5. Parameters of initial parking orbit and target orbit around Jupiter
地球停泊
圆轨道
高度/ km地球停泊
圆轨道
倾角/（°）目标环木
轨道近木点
半径/ km目标环木
轨道远木点
半径/ km目标环木
轨道倾角/（°）400 40 75492 8×106 10
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表 6 各类误差取值
Table 6. Values of different errors
位置误差/km 速度误差/(m·s−1) 大小误差/% 方向误差/(°) 入轨 导航测量 入轨 导航测量 30 15 15 0.03 1.5 0.15
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表 7 各段修正次数与修正时刻
Table 7. Times and periods of corrections in different intervals
修改时刻 修正次数 各次修正时刻/d 1次 2次 3次 4次 5次 6次 E-V段 4 7 116 158 172 V-E段 5 3 333 459 501 515 E-E段 5 4 229 481 565 593 E-J段 6 1 478 856 982 1024 1038
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