The present work proposes a closed-form solution for circular repeat ground track (RGT) orbit designs and constellations and its application strategy. The proposed solution is an equation of motion proving that the characteristic of a circular RGT orbit is similar to that of the parametric curve of Ptolemy's model and provides a low computational cost for the RGT orbit design and related numerical analysis. The application strategy is to coincide with the self-intersection point of an RGT orbit over a specific target of interest on Earth and make it the starting point of the first satellite orbit in the satellite group. The remaining satellites are designed to have the same RGT orbit as the first satellite; therefore, the entire group has twice the repeat cycle over a specific target. To this end, this study represents an algorithm to match the specific target and the intersection point through an iterative numerical analysis method centering on the RGT equation. A set of orbital elements for a satellite group is also derived herein. The satellite group with a repeat cycle that doubles for a specific target shows a significantly shorter revisit time compared with the conventional Walker constellation.

本工作提出了一种用于圆形重复地面轨道（RGT）轨道设计和星座的封闭形式解决方案及其应用策略。所提出的解决方案是一个运动方程，证明圆形RGT轨道的特性与托勒密模型的参数曲线相似，并且为RGT轨道设计和相关数值分析提供了低计算成本。应用策略是使RGT轨道的自交点与地球上特定目标的交点重合，并使其成为卫星组中第一个卫星轨道的起点。其余卫星的设计与第一颗卫星具有相同的RGT轨道；因此，整个小组在特定目标上的重复周期是原来的两倍。为此，这项研究代表了一种通过以RGT方程为中心的迭代数值分析方法来匹配特定目标和交点的算法。这里还导出了卫星群的一组轨道元素。与常规沃克星群相比，针对特定目标的重复周期翻倍的卫星群显示出明显更短的重访时间。