Satellite relative motion around the Earth has been thoroughly studied during the last two decades. However, considerably less attention has been given to the study of satellite relative motion around Mars. As the cost of space technologies decreases and more space missions are within reach, formation flying missions around Mars have the potential to benefit future exploration missions launched to the Red Planet. A key parameter in such missions will be the frequency at which the spacecraft need to perform formation-keeping maneuvers to compensate for unwanted drifts due to differential perturbations. The Martian \(J_3\) and \(J_4\) gravitational harmonics are significant enough to warrant a dedicated investigation of bounded satellite relative motion configurations. In this study, we derive conditions for bounded satellite relative motion in non-critical inclinations around Mars, while considering its gravitational harmonics up to \(J_4\). We first introduce a family of stable frozen orbits facilitating the implementation of formation flying and then apply differential nodal precession negation and differential periapsis rotation negation methods while considering the gravitational harmonics up to \(J_4\). Using this procedure, we demonstrate how the secular growth of the relative distance can be arrested during long time intervals.

在过去的二十年里，卫星绕地球的相对运动得到了彻底的研究。然而，对围绕火星的卫星相对运动的研究却很少受到关注。随着太空技术成本的降低和更多太空任务的实现，围绕火星的编队飞行任务有可能使未来发射到红色星球的探索任务受益。此类任务中的一个关键参数将是航天器需要执行编队保持机动以补偿由于微分扰动引起的不需要的漂移的频率。火星人\(J_3\)和\(J_4\)引力谐波非常重要，足以保证对有界卫星相对运动配置进行专门研究。在这项研究中，我们推导出了在火星周围非临界倾角下有界卫星相对运动的条件，同时考虑了其高达\(J_4\) 的引力谐波。我们首先介绍了一系列有助于实现编队飞行的稳定冻结轨道，然后应用微分节点进动否定和微分近点旋转否定方法，同时考虑到\(J_4\)的引力谐波。使用这个程序，我们展示了如何在很长的时间间隔内阻止相对距离的长期增长。