Eur. Phys. J. Special Topics 229, 1545–1555 (2020)
https://doi.org/10.1140/epjst/e2020-900128-y

Regular Article

Effects of higher-order multipoles of the lunar disturbing potential on elongated orbits in cislunar space

¹ Aerospace and Mechanical Engineering Dept., University of Arizona, Tucson, USA
² Mechanical Engineering Dept., University of Taubaté, Taubaté, SP, Brazil

^a e-mail: ajrosengren@email.arizona.edu

Received: 2 July 2019
Received in final form: 2 December 2019
Published online: 29 May 2020

Abstract

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.