圆型限制性三体问题中双脉冲地月转移轨道设计研究

摘要

基于圆型限制性三体问题模型（ CR3BP ），提出了一种用于设计双脉冲地月转移轨道的微分数值计算方法。通过分析地月转移过程中航天器的初始和末端状态，利用Newton-Raphson迭代法推导转移轨道的微分校正方程，并采用periapsis截面来估计转移轨道的初始状态；然后以估计的初始状态作为迭代初值，经过微分校正方程的迭代得到准确的初始状态，完成双脉冲地月转移轨道的设计，并解决了空间CR3BP多个未知参数的问题。因此，该方法不仅适用于平面CR3BP ，也适用于空间CR3BP的双脉冲转移轨道设计。数值计算结果表明，该方法能有效地进行双脉冲地月转移的数值计算。另外，双脉冲地月轨道和月地返回地球的轨迹是关于x-z平面镜像。%A numerical differential method is developed for calculating the two-impulse trajectories for Earth-Moon transfers in the circular restricted three-body problem ( CR3BP ) .By analyzing the initial and final states of the spacecraft, the Newton-Raphson method is applied to deducing the differential equations of these transfers and the periapsis map is introduced to guess the initial states.With the initial guess, the differential method yields the accu-rate initial state within a few iterations and then the two-impulse Earth-Moon transfer will be accomplished.Espe-cially for the spatial CR3BP , a simple design procedure is developed to deal with the problem that arises from more unknown parameters.Thus, this method is applied not only to the planar CR3BP but also to the spatial CR3BP, and their analysis indicates preliminarily that that this method can effectively enable a large set of two-impulse Earth-Moon transfers to be computed numerically.Moreover, the two-impulse Earth-Moon trajectories and the Moon-Earth return trajectories are mirror images of one another with aspect to the x-z plane or the x-axis.