A method for the determination of accurate analytical expressions for the time dependence of the relative motion of two noninteracting masses under the gravitational influence of a spherical primary mass is presented and discussed. The case of the elliptic reference orbit is considered and the case of a circular reference orbit is analyzed as a special case. The approach also leads to accurate initial conditions for the elimination of drift away from periodic relative motion. The solution for the relative motion is in closed-form in terms of the eccentric anomalies of the target and chaser orbits, while the eccentric anomalies themselves are expressed in terms of the orbits’ respective eccentricities, using an iterative method.

中文翻译：

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椭圆参考轨道相对运动的解析解

提出并讨论了一种确定精确解析表达式的方法，该解析表达式用于确定两个非相互作用质量在球形初级质量的重力影响下的时间相关性。考虑椭圆参考轨道的情况，并分析圆形参考轨道的情况作为特例。该方法还导致了精确的初始条件，以消除偏离周期性相对运动的漂移。相对运动的解以目标轨道和追赶者轨道的偏心异常为封闭形式，而偏心异常本身则使用迭代方法以轨道各自的偏心率表示。