The relative hovering of satellites in highly elliptic orbits (HEO), as one of the most crucial space operations, is modeled and analyzed in this paper. The proposed modeling is based on the new perturbed relative dynamics equations, uses the time-varied parameters depending on the motion of the target satellite. This proposed model considered the dynamic air drag, oblateness of Earth (including all zonal harmonics coefficients) and the Lunar perturbation as an inclined third-body disturbing effect on both follower and target orbits. The non-simplified relative motion model has been obtained by employing the Lagrangian mechanics principals and completed along with the target satellite’s motion characteristic. Then the required thrust for relative hovering mission has been obtained without any simplifications to ensure the accuracy of long-duration flight analyses. To validate the presented model, another model has been built as an ECI based Relative Motion (ERM) model. Then, according to effective parameters on hovering mission design around HEOs such as the eccentricity and inclination of the target obit, the fuel consumption, optimal positioning of the follower, maximum required thrust, and the appropriate time to perform the operation, several examples are provided. Furthermore, the hybrid IWO/PSO algorithm has been used to find the location and the minimum/maximum amounts of thrust force.

中文翻译：

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月球系统中HEO卫星的扰动盘旋研究

本文对高椭圆轨道（HEO）中作为最关键的太空操作之一的卫星的相对悬停进行了建模和分析。所提出的模型基于新的扰动的相对动力学方程，使用时变参数取决于目标卫星的运动。该提议的模型将动态空气阻力，地球扁度（包括所有纬向谐波系数）和月球扰动视为对跟随者和目标轨道的倾斜第三体扰动效应。非简化的相对运动模型是通过采用拉格朗日力学原理获得的，并与目标卫星的运动特性一起完成。然后，无需进行任何简化即可获得相对悬停任务所需的推力，以确保长时间飞行分析的准确性。为了验证提出的模型，已经构建了另一个模型作为基于ECI的相对运动（ERM）模型。然后，根据高空飞行器周围的悬停任务设计的有效参数，例如目标目标的偏心距和倾斜度，燃料消耗，从动件的最佳位置，最大所需推力以及执行操作的适当时间，提供了几个示例。此外，混合IWO / PSO算法已用于查找推力的位置和最小/最大量。根据高空飞行器附近的悬停任务设计的有效参数，例如目标目标的偏心距和倾斜度，燃料消耗，从动件的最佳位置，最大所需推力以及执行操作的适当时间，提供了几个示例。此外，混合IWO / PSO算法已用于查找推力的位置和最小/最大量。根据高空飞行器附近的悬停任务设计的有效参数，例如目标目标的偏心距和倾斜度，燃料消耗，从动件的最佳位置，最大所需推力以及执行操作的适当时间，提供了几个示例。此外，混合IWO / PSO算法已用于查找推力的位置和最小/最大量。