Abstract The objective of the present paper is to show a method to find orbits near artificial equilibrium points for a satellite equipped with a continuous thrust that allows it to stay near the poles of a celestial body. The physical system includes the presence of a moon of the celestial body under observation, and the perturbation caused by this moon is counteracted by an algorithm to help the satellite to stay close to its original position, instead of escape from it. The equations of motion are changed under some approximations, and analytical solutions for these equations are obtained and analyzed. Initial conditions are used such that their secular terms are nullified. These solutions are restricted to a short period of time, but we propose a method in which there are periodic updates in the thrust. Thus, the solutions can be extended for the duration of the mission. A numerical simulation is obtained, whose results are required to be in agreement with the analytical solution using these periodic adjustments of the thrust. This agreement means that the motion of the spacecraft remains bounded close to its initial position for longer times. Several systems with different sizes and mass parameters are used to show the results of the research, like Sun-Earth-Moon, Sun-Ida-Dactyl, Sun-Saturn-Titan and Sun-Mars-Phobos systems. The results also indicate the locations of points that require minimum magnitude of the thrust.

中文翻译：

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寻找轨道以观察天体的两极

摘要 本文的目的是展示一种方法，为配备了连续推力的卫星寻找人工平衡点附近的轨道，使其能够停留在天体的两极附近。物理系统包括被观测天体的卫星的存在，并且由该卫星引起的扰动通过算法来抵消，以帮助卫星靠近其原始位置，而不是逃离它。在某些近似下改变运动方程，并获得并分析这些方程的解析解。使用初始条件使得它们的长期条款无效。这些解决方案仅限于短时间内，但我们提出了一种在推力中有周期性更新的方法。因此，可以在任务期间延长解决方案。获得数值模拟，其结果需要与使用推力的这些周期性调整的解析解一致。该协议意味着航天器的运动在更长时间内保持在接近其初始位置的范围内。几个不同大小和质量参数的系统被用来展示研究结果，如太阳-地球-月亮、太阳-艾达-Dactyl、太阳-土星-泰坦和太阳-火星-火卫一系统。结果还表明需要最小推力大小的点的位置。该协议意味着航天器的运动在更长时间内保持在接近其初始位置的范围内。几个不同大小和质量参数的系统被用来展示研究结果，如太阳-地球-月亮、太阳-艾达-Dactyl、太阳-土星-泰坦和太阳-火星-火卫一系统。结果还表明需要最小推力大小的点的位置。该协议意味着航天器的运动在更长时间内保持在接近其初始位置的范围内。几个不同大小和质量参数的系统被用来展示研究结果，如太阳-地球-月亮、太阳-艾达-Dactyl、太阳-土星-泰坦和太阳-火星-火卫一系统。结果还表明需要最小推力大小的点的位置。