北京航空航天大学学报 ›› 2014, Vol. 40 ›› Issue (3): 344-349.doi: 10.13700/j.bh.1001-5965.2013.0241

• 论文 • 上一篇    下一篇

月地转移轨道快速设计方法

郑爱武1, 周建平1, 刘 勇2   

  1. 1. 北京航空航天大学 宇航学院, 北京 100191;
    2. 航天飞行动力学技术重点实验室, 北京 100094
  • 收稿日期:2013-05-06 出版日期:2014-03-20 发布日期:2014-03-29
  • 基金资助:
    国家自然科学基金资助项目(11173005,11203003)

Fast design method of moon-to-earth transfer trajectory

Zheng Aiwu1, Zhou Jianping1, Liu Yong2   

  1. 1. School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
    2. Science and Technology on Aerospace Flight Dynamics Laboratory, Beijing 100094, China
  • Received:2013-05-06 Online:2014-03-20 Published:2014-03-29

摘要: 月地转移轨道设计一般分为初步轨道设计和精确轨道设计.其中,初步轨道设计的准确性是确保后续精确轨道设计收敛的关键.提出了一种基于Lambert算法的月地转移轨道快速设计方法.以出月球影响球的时刻、位置和速度为中间变量,将轨道分为地心段和月心段分别进行计算.将探测器飞出月球影响球至指定再入点的地心段轨道简化为一个Lambert问题进行求解,提出了通过牛顿迭代法求解月地转移轨道Lambert问题的方法,避免了Lambert问题求解时大量的超几何函数和级数计算,提高了计算效率.在月心段轨道的快速计算中,提出了根据探测器出影响球速度矢量、月球停泊轨道倾角和近月点高度计算月心双曲线轨道根数的新方法.通过迭代计算,使得两段轨道在月球影响球处的位置和速度连续,从而获得一条完整的满足两端约束的双二体月地转移轨道.该方法计算速度快,精度相对较高.计算结果可以作为后续精确轨道设计的初值.

Abstract: Design of moon-to-earth transfer trajectory is generally divided into two phases, preliminary orbit design and precise orbit design. Among them, the accuracy of preliminary design is the key to the convergence of precise design. A fast design method of moon-to-earth transfer trajectory based on Lambert algorithm was proposed. The time when the probe piercing the lunar sphere of influence, the position and the velocity at that moment were used as intermediate variables. The moon-to-earth transfer trajectory was divided into two segments to calculate separately, geocentric segment and lunar segment. In the rapid calculation of geocentric segment, the geocentric flight from the point where the probe piercing the lunar sphere of influence to the specified reentry point was simplified as a Lambert problem, which was solved by Newton iterative method. It greatly improved the computational efficiency by avoiding a large number of hypergeometric functions or series calculations. In the rapid calculation of lunar segment, a new method was presented to obtain the moon centered hyperbolic orbit elements according to the velocity vector at the sphere of influence, the inclination and perilune altitude of the lunar parking orbit. Making the position and velocity vectors of the two segments continuous at the lunar sphere of influence, a complete moon-to-earth transfer trajectory meeting the constraints at both ends was obtained by iterative calculation. The accuracy of the fast design method is relatively high besides the fast calculation. The results were also used as inputs of the precise orbit design.

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