二体问题状态转移矩阵的分析解和数值解的比较

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。

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

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.