Sequence search and optimization for transfer trajectory status in Callisto exploration mission
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摘要:
针对使用图形化分析方法设计木卫四环绕任务转移轨道时人工参与度高的问题，提出基于图形化分析的转移轨道状态序列搜索算法。通过对图形性质及共振引力辅助的分析，归纳出轨道状态的变化模式，进而提出迭代求解状态转移序列的搜索算法。对木卫四环绕任务转移轨道进行仿真，结果表明：所提算法可以快速高效获得多个转移序列；对得到的序列求解对应的转移轨道，探测器可以在2.13年内消耗2.108 km/s的速度增量，实现从初始环木大椭圆轨道到木卫四环绕轨道的转移，比对比算法得到的转移序列节省约100～200 m/s的速度增量及约1年的转移时间。
Abstract:A graphical analysis-based search algorithm for the transfer orbit state sequence is presented to address the problem of high manual involvement when designing the transfer orbit for the Callisto orbiting mission using graphical analysis approaches. Through the analysis of graphical properties and resonance gravity assists, the variation pattern of orbit states is summarized, and an iterative search algorithm for solving the state transition sequence is proposed. The algorithm can obtain multiple transfer sequences rapidly and efficiently, as demonstrated by the simulation of the transfer orbit for the Callisto orbiting mission. The solution of the corresponding transfer orbits for the obtained sequences shows that the spacecraft can achieve the transfer from a Jovian highly elliptical orbit to the Callisto orbiting orbit within 2.13 years by consuming a velocity increment of 2.108 km/s, saving approximately 100-200 m/s of velocity increment and about 1 year of transfer time compared to other methods. The method proposed in this paper solves the problem of high manual involvement when using graphical analysis methods.
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图 5 $ {S}_{1} $转移序列 $\left(S_0=\left(3,5\;{\mathrm{km}}/{\mathrm{s}},200\;{\mathrm{d}},10 R_{{\mathrm{J}}}\right)\right) $
Figure 5. Transfer sequence of $ {S}_{1} $ $\left(S_0=\left(3,5\;{\mathrm{km}}/{\mathrm{s}},200\;{\mathrm{d}},10 R_{{\mathrm{J}}}\right)\right) $
图 6 $ {S}_{2} $转移序列 $\left(S_0=\left(4,5\;{\mathrm{km}}/{\mathrm{s}},200\;{\mathrm{d}},10 R_{{\mathrm{J}}}\right)\right) $
Figure 6. Transfer sequence of $ {S}_{2} $ $\left(S_0=\left(4,5\;{\mathrm{km}}/{\mathrm{s}},200\;{\mathrm{d}},10 R_{{\mathrm{J}}}\right)\right) $
图 8 木卫四共振引力辅助轨道及木卫四-木卫三转移轨道
Figure 8. Trajectories with Callisto resonant gravity assist and Callisto-Ganymede transfer trajectory
图 9 木卫三共振引力辅助轨道及木卫三-木卫四转移轨道
Figure 9. Trajectories with Ganymede resonant gravity assist and Ganymede-Callisto transfer trajectory
表 1 S0序列搜索结果
Table 1. Result of sequence search
$ m $ $ \left| {\boldsymbol{v}}_{\mathbf{\infty }}\right| $/(km·s−1) $ T $/d $ {r}_{p} $/RJ $ \Delta {v}_{\text{seq}} $/(km·s−1) 3 5 200 10 1.398 3 6 200 10 1.465 3 7 200 10 1.529 4 5 200 10 1.548 4 6 200 10 1.568 
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表 2 木心J2000系下初始轨道状态
Table 2. The initial orbit state referenced in Jupiter-centered J2000 system
星历时间JD 半长轴/km 偏心率 倾角/
(°)升交点
赤经/(°)近地点
幅角/(°)真近点
角/(°)2464824.508 − 7593520.642 1.094 22.535 350.752 295.361 0
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表 3 木星系内航天器轨道主要数据
Table 3. Main orbital data of spacecraft in Jovian system
事件 UTC时间 速度/(km·s−1) 共振比 JOI 2036-05-11 0.679 PJR 2036-10-28 0.232 C1 2037-04-22 5 C2 2037-07-14 3 C3 2037-09-02 2 C4 2037-10-06 1.5 $ \Delta {v}_{\text{C}2\text{G}} $ 2037-11-26 0.041 G1 2038-01-18 2.5 G2 2038-02-22 1.5 $ \Delta {v}_{\text{G}2\text{C}} $ 2038-06-21 0.043 COI 2038-06-28 1.086(C)/0.670(E) 注：C1、C2、C3、C4为木卫四共振引力辅助；G1、G2为木卫三共振引力辅助。
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