二体问题状态转移矩阵的分析解和数值解的比较

Comparison Between Analytic and Numerical Solutions of State Transition Matrices of Two Body Problem

对二体问题的状态传播问题， 以Ａｊｉｓａｉ 卫星某历元的初轨为例，考虑５ｄ （ 天） 、１０ｄ （ 天） 和１００ｄ （ 天） 间隔的弧长， 本文分别给出了它们的分析解和数值解。结果表明： 对应于５ｄ、１０ｄ、１００ｄ 间隔的弧长， 二体问题状态转移的分析解与数值解在１０－１０ 、１０ －８ 和１０－７ 以内的相对偏差下能够保持其一致性。

The analytic and numerical solutions of state transition matrices of Two Body problem are presented in this paper. During the computation, a specific initial state vector of the satellite Ajisai is adopted and the time spans are 5 days, 10 days and 100days, respectively. The results indicate, at least, that analytic and numerical solutions agree with each other as long as the tolerances of their relative deviation of 10 -10 , 10 -8 and 10 -7 are acceptable,corresponding to the cases of 5 day, 10 day and 100 day intervals respectively.