With high-precision DEM (Digital Elevation Model) and GMTI (Ground Moving Target Indicator) as the demand background, the influence of zonal harmonic term perturbation on the relative motion of the millimeter-level short-range leader-follower satellites in near-circular orbit is studied through the relative perturbation method. An equation of motion that can describe the motion of the leader-follower satellites under the influence of perturbation in near-circular orbit is derived, and the characteristics of the trajectory of in-plane periodic motion are analyzed. A study shows that under the influence of the relative perturbation of the term, the in-plane periodic motion of the leader-follower satellites in near-circular orbit is a symmetrical closed “drop-shaped” trajectory with a period of . By comparing with the results of numerical simulations, the correctness of the conclusions obtained in this paper is verified. According to the research results, it can be known that only using a thruster as the actuator to maintain the relative position can no longer meet the requirements of the long-term mm-level relative position maintenance. In the future, a new technical approach needs to be explored to achieve the long-term relative position maintenance with millimeter-level control accuracy.

中文翻译：

---

毫米级精度的相对位置维持要求下卫星编队的相对摄动分析

以高精度DEM（数字高程模型）和GMTI（地面移动目标指示器）为需求背景，区域谐波项摄动对毫米级近距离前导跟随者卫星在近圆形中的相对运动的影响通过相对摄动法研究轨道。推导了可以描述前跟随卫星在近圆形轨道上受扰动影响的运动的运动方程，并分析了面内周期性运动的轨迹特征。研究表明，在该术语的相对摄动的影响下，跟随者卫星在近圆形轨道上的面内周期性运动是周期为的对称闭合“滴状”轨迹。。通过与数值模拟结果的比较，验证了本文结论的正确性。根据研究结果可以知道，仅使用推进器作为致动器来保持相对位置已不能满足长期毫米级相对位置保持的要求。未来，需要探索一种新的技术方法，以实现毫米级控制精度的长期相对位置维护。