地月L1点低能转移轨道设计与优化

doi:10.12305/j.issn.1001-506X.2024.10.28

摘要/Abstract

摘要：

针对地月空间平动点周期轨道与近地轨道之间的低能转移问题, 提出一种地月L1(Earth-Moon L1, EML1)点Halo轨道到地球静止轨道(geostationary Earth orbit, GEO)的四脉冲低能转移轨道的设计方法。所提方法在扰动流形和Lambert弧段拼接的三脉冲转移轨道设计基础上, 从分析轨道雅可比常数变化与速度增量关系的角度出发设计四脉冲低能转移轨道。数值仿真结果表明, 四脉冲优化模型比三脉冲模型效率更高, 可以得到更优的转移方案, 有效解决了优化过程中由于搜索空间大、极值数量多而导致的优化结果不佳的问题。所提设计方法可以用于EML1其他周期轨道族与各类近地轨道的相互转移问题研究。

关键词: 地月空间, 平动点, 周期轨道, 不变流形, 低能转移轨道

Abstract:

Aiming at the low-energy transfer problem between the periodic orbit of the cislunar space libration point and near-Earth orbit, a design method of 4-impulses low-energy transfer orbit from Earth-Moon L1 (EML1) point Halo orbit to geostationary Earth orbit (GEO) is proposed. Based on the design of 3-impulses transfer orbit which applies disturbed manifold and Lambert arc, the 4-impulses low-energy transfer orbit is designed by analyzing the relationship between the change of Jacobi constant and the velocity increment. Numerical simulation results show that the 4-impulse optimization model is more efficient than 3-impulse model and a better transfer scheme can be obtained, which effectively solves the problem of obtaining poor optimization results due to large search space and numerous extreme values in the optimization process. The proposed design method can be used to study the transfer between other periodic orbit families of EML1 and various near-Earth orbits as well.

Key words: cislunar space, libration point, periodic orbit, invariant manifold, low-energy transfer orbit

中图分类号:

V412.4+1

乔琛远, 杨乐平. 地月L1点低能转移轨道设计与优化[J]. 系统工程与电子技术, 2024, 46(10): 3519-3527.

Chenyuan QIAO, Leping YANG. Design and optimization of Earth-Moon L1 low-energy transfer orbit[J]. Systems Engineering and Electronics, 2024, 46(10): 3519-3527.

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参数	无量纲单位	国际单位制
月球质量	μ=0.012 15	m₂=7.35×10²² kg
地球质量	1－μ	m₁=5.974×10²⁴ kg
距离	r	r×3.844 01×10⁵ km
时间	τ	τ×3.751 9×10⁵ s
速度	v	v×1.024 55 km/s
加速度	a	a×2.731×10^－6 km/s²
一天	0.230 3	86 400 s

参数	速度增量/(km·s^-1)	机动时间/d
Δv₁	0.340 8	20.68
Δv₂	0.285 2	38.47
Δv₃	0.926 2	40.13
总计	1.552 2	40.13

参数	速度增量/(km·s^-1)	机动时间/d
Δv₁	0.320 3	13.84
Δv₂	0.469 7	15.38
Δv₃	0.891 5	16.98
总计	1.681 5	16.98

参数	速度增量/(km·s^-1)	机动时间/d
Δv₁	0.101 9	22.92
Δv₂	0.092 7	27.66
Δv₃	0.335 3	45.75
Δv₄	0.939 6	47.63
总计	1.469 5	47.63

参数	三脉冲转移模型	四脉冲转移模型
迭代次数	100	100
粒子数	100	100
局部最优粒子数目	10	10
计算时间/s	3 567.2	3 389.9