月地转移轨道精确轨道设计

以基于Lambert算法的快速轨道设计结果为初值,开展精确轨道设计研究.通过对月地返回飞行阶段的摄动项和量级分析,建立了月地转移轨道的动力学方程,提出了一种双向嵌套循环搜索算法,采用该算法求解同时满足两端约束条件的精确月地转移轨道.该算法以出月球影响球的时刻和位置、速度为中间变量,一方面采用前向数值积分和微分改正法搜索满足地球再入端的轨道,另一方面采用后向数值积分并进行倾角和近月距修正得到满足月球端的轨道,通过这种双向嵌套循环,使得两段轨道在月球影响球边界处的位置和速度连续,从而获得一条完整的满足两端约束条件的月地转移精确轨道.最后以2017年1月26日出月球影响球作为返回窗口,给出了具体的设计算例,并通过STK软件仿真验证了程序的设计结果.

Accurate Design of Moon-to-Earth Transfer Orbit

An accurate design of moon-to-earth transfer orbit is presented,using the results of rapid orbit design based on Lambert algorithm as initial inputs.Orbit dynamics equations are established for the moon-to-earth transfer orbit through analysis of the perturbations and corresponding orders of magnitude in the lunar return flight,and a bidirectional nested loop search algorithm is proposed to get the accurate moon-to-earth transfer orbit satisfying the constraints at both ends.The time when the lunar probe pierces the lunar sphere of influence and the position and the velocity at that moment are used as intermediate variables in the algorithm.On one hand,forward integration and differential correction method are used to find the geocentric orbit phase which meets the reentry conditions.On the other hand,backward integration is used to find the lunar orbit phase satisfying the moon-side constraints with amendment of the inclination and the height of periselenium.Through the bidirectional nested loop search,a complete moon-to-earth transfer orbit satisfying the constraints at both ends is obtained by making the position and the velocity of the two orbit phases continuous at the lunar sphere of influence.Finally,an exit point from the lunar sphere of influence in the return window of January 26,2017 is presented as an example and the design results of the program are simulated and validated with STK.