Calculating Method of Series for the True Anomaly of a Spacecraft Elliptic Orbit
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摘要: 用级数展开方法得到真近点角超越方程，由迭代法求真近点角与时间的关系，讨论迭代收敛的充分条件．对于不满足迭代收敛充分条件情形，列写偏近点角超越方程，用迭代法求偏近点角变化规律，用数值积分方法求出真近点角与时间的关系，指出所有椭圆轨道都满足偏近点角迭代收敛的充分条件．讨论小偏心率椭圆轨道真近点角近似超越方程，由迭代法求真近点角与时间的关系．数值模拟结果表明该方法的有效性．Abstract: The transcendental equation of a true anomaly was written in a power series instead of a differential form.When the sufficient condition of the iterative convergence is satisfied,the relationship between the true anomaly and the time was gotten by the iterative method.And for the others,the transcendental equation of an eccentric anomaly was solved by the iterative method.After the eccentric anomaly had been calculated,the relationship between the true anomaly and the time was gotten with the numerical integral method.The approximate equation,which included the first five terms in general expansion,was written for the spacecraft quasi-circular orbit.And the true anomaly as the function of the time was also gotten by the iterative method.The numerical simulation results show that these methods are efficient.
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Key words:
- spacecraft orbit /
- true anomaly /
- eccentric anomaly /
- iterative method
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