【摘要】 本文提出了一种新的计算人造卫星二阶摄动的半分析、半数值方法,其基本思想是: i),采用σ^＊作为基本根数系统;这里σ^＊是从密切根数σ中扣去短周期项△σ_s的平根数。 ii),σ^＊的长期、长周期变率（准到三阶）由密切限的变率dσ/dt的数值平均求得。 ii),计算dσ/dt中所用的密切根数σ,由σ^＊加上短周期项△σ_s,而得,其中一阶短周期项△σ_s^（1）用分析公式计算,二阶短周期项△σ_s^（2）用Fourier分析方法求取。由于采用了σ^＊作为根数系统,克服了密切根数σ数值方法的积分步长短、计算时间长、积累误差大等缺点;由于dσ/dt、△σ_s^（2）用数值方法计算,又避免了繁复的公式推导,兼得了计算公式简单,程序编制方便等优点。用本方法计算二阶摄动,计算时间比经典的数值方法要节省十分之九,所占内存的大小可比分析方法节省4/5—5/6。本文还讨论了微分方程的数值积分方法,改进了迭代过程,使得它更适合于卫星动力测地中测轨的要求。本文还给出了用本方法计算的数值结果。数值结果表明:用本方法测轨,向径、垂迹方向误差小于0.1米,沿迹方向误差小于1米。更多还原

【Abstract】 In this paper a new semi-analytical and semi-numerical method for computation of the second order perturbation of artificial earth satellites is presented. Its basie ideas are the following 1. In our analysis, we adopt σ* as the fundamental elements system, where σ*’s are mean elements, obtained after subtracting the short, period terms △σ_s. from the oscula-ting elements. 2. The σ*’s secular and long period rates (up to third order) are derived with the numerical averages of dσ/dt, which are the rates of the osculating elements. 3. The osculating elements in computing dσ/dt are calculated with σ* plus the dt short period terms △σ_s, in which the first order short period terms △σ_s are obtained by analytical method, and the second order ones △σ_s by Fourier analysis. Because of adopting σ~* as the elements system, we have overcome some shortco-mings in the numerical method, such as the shorter step, the longer computing time, the more serious accumulatation of errors, etc. As we compute dσ~*/dt and △σ_s by means of numerical method, we have avoided the development of the complicate for-mulae. In this way, our method also has the advantages of simpler computing for-mulae and more convenient programming. To compute the second order perturbation, the computing time of our method is only 1/10 of the classical numerical method, and the memories is about 1/5 of the pure analytical method. The numerical method of ODE are also discussed. An improved Chebychev itera-tion process is developed to adapt the need of the orbit determination in satellite dynamical geodesy. In this paper we also give detailed formulae for computing the perturbating forces and the numerical results of computation by our method. The numerical results show that the errors in radius and across-track are less than 0.1 m, and that in along-track less than 1 m.更多还原