For an Earth satellite in cislunar space, the effects of the third or higher-order harmonics in the solar disturbing function are negligible. For lunar perturbations, however, these terms become increasingly important as the semimajor axis increases. We investigate the effects of these higher-order multipole moments on circular, moderate, and highly elliptical orbits, where the semimajor axis is a relatively large fraction (~20%) of the Moon’s one. We specifically characterize the regions of cislunar space where the octupole-order approximation, often used in celestial and astrophysical dynamics for studying the stability and fates of hierarchical planetary systems, is actually a valid truncation of the gravitational interactions.

中文翻译：

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月球扰动势的高阶多极对顺月空间中拉长轨道的影响

对于在月球空间中的地球卫星，太阳干扰功能中三次或更高级次谐波的影响可以忽略不计。但是，对于月球摄动，这些术语随着半长轴的增加而变得越来越重要。我们研究了这些高阶多极矩对圆形，中度和高度椭圆形轨道的影响，其中半长轴是月球轨道的相对较大部分（约20％）。我们专门描述了在月球和天体动力学中用于研究分级行星系统的稳定性和命运的八极级逼近实际上是重力相互作用的有效截断的顺月空间区域。