双三体系统不变流形拼接成的低成本探月轨道

传统的探月轨道设计原理为二体模型框架下的Hohmann变轨理论,但1991年日本的Hiten探月器利用太阳的摄动,用比传统的方法更少的燃料完成了探月任务。利用三体问题非线性系统的不变流形设计了节省燃料的探月轨道。沿用JPL研究组的思路,将太阳-地球-月亮-航天器四体问题分解成太阳-地球-航天器和地球-月亮-航天器两个共面的圆形限制性三体问题,对Hiten类的探月轨道给出了更深刻的数学、力学解释;给出了流形的结构以及更合理的拼接方式;找到了发射位置、发射速度和拼接点;设计出了类似Hiten探月器的探月轨道,可比传统方法节省速度增量12%左右。结果证明了三体系统不变流形在登月轨道设计研究中的可行性和优越性。

Low Energy Transfer to the Moon Using the Patching of Invariant Manifolds of Two There-Body Systems

Traditional method is Hohmonn transfer following the two-body model,but the Japanese Hiten mission succeeded in exploring the Moon with lower energy in 1991 utilizing perturbation of the Sun.In this paper,using the invariant manifolds of non-linear 3-body systems,we constructed low energy transfer trajectories to the Moon.Along the method used by JPL research group,we approximated the Sun-Earth-Moon-spacecraft four-body system as two plane circular restricted there-body systems,and then presented more profound explanation for Hiten's trajectory in mathematics and dynamics.Considering the direction of the rotation of Earth-Moon L2 stable manifolds,we presented their structures and a more reasonable patching method,and obtained the position and velocity of the spacecraft at the launch point,and finally designed a trajectory which requires 12% less velocity increment than traditional method.The results prove the feasibility and advantage of invariant manifolds of 3-body systems in designing and constructing trajectories from the Earth to the Moon.