On the effects of Sun's gravity and solar radiation pressure to the Earth-Moon distant retrograde orbits

太阳引力和太阳光压力对地月远距离逆行轨道的影响特性研究

¹ Xi'an Institute of Electromechanical Information Technology, Xi'an 710076, China
² School of Mechanics and Transportation Engineering, Northwestern Polytechnical University, Xi'an 710072, China
³ Beijing Aerospace Control Center, Beijing 100048, China

Received: 24 March 2025

Abstract

The distant retrograde orbits(DROs) form a family of planar periodic orbits that are retrograde around the Moon in the Earth-Moon circular restricted three-body problem(CR3BP). Known for their "low-energy insertion, long-term stability, and global accessibility", DROs are regarded as ideal candidates for future cis-lunar exploration. Sun's gravity and solar radiation pressure(SRP), as primary perturbations in the Earth-Moon system, could significantly alter the orbit dynamics of spacecraft. Based on the above considerations, the effect of the Sun's gravity and SRP on the dynamics and geometry of Sun-resonant DROs within a quasi-bicircular problem(QBCP) is investigated. Each resonant DRO in the CR3BP bifurcates into at least two branches in the QBCP. Furthermore, the Sun's gravity can qualitatively alter the phase-space structure of most resonant DROs, transforming them from stable to unstable, which opens the possibility of low-energy transfer. Regarding SRP, it induces more complex changes in the phase-space structures and leads to more bifurcation types, such as tangent bifurcation, period-doubling bifurcation and second-class Hopf bifurcation, thus deriving richer families of orbits. It is worthily noted that SRP may help stabilize orbits, making it beneficial for station-keeping. Additionally, SRP can significantly alter the geometry of DROs. Especially when the spacecraft which has a relatively large lightness number, is pitched at certain angles, the planar DROs evolve into spacial orbits to make them more suitable for cis-lunar space missions.

摘要

远距离逆行轨道(distant retrograde orbit, DRO)是地月圆型限制性三体问题中围绕月球逆行的平面周期轨道, 具有"低能入轨、长期稳定、全域可达"的性质, 是未来地月空间探测的重要任务轨道之一。太阳引力和太阳光压力作为地月系统的主要摄动力, 会显著改变航天器的轨道运动特性。因此, 立足于拟双圆问题, 探讨太阳引力和太阳光压力对地月共振DRO的动力学和几何结构的影响。在太阳引力的作用下, 圆型限制性三体问题中的每条共振DRO至少会分出2条拟双圆问题中的轨道。并且, 太阳引力可以定性地改变共振DRO的相空间结构, 使其由稳定轨道变为不稳定轨道, 为低能转移轨道设计提供了可能性。太阳光压力则会使轨道的相空间结构发生更加复杂的变化, 并出现更多的分岔类型, 如正切分岔、倍周期分岔和类第二Hopf分岔等, 进而衍生出更加丰富的新轨道族。在太阳光压力作用下, 部分DRO由不稳定变为稳定, 因此太阳光压力可以起到稳定轨道的作用。另外, 太阳光压力会使轨道形状发生显著变化, 特别是当航天器具有较大光压因子和一定俯仰角时, DRO由平面轨道变化为三维轨道, 在地月任务中具有更广阔的应用前景。