Multiple families of synodic resonant periodic orbits in the bicircular restricted four-body problem

Periodic orbits in gravitational many-body problems have been fundamental special solutions for analyzing phase-space flows not only in autonomous systems but also in time-dependent non-autonomous systems. The growing interest in cislunar space may require deeper understandings of periodic orbits in the Earth-Moon system beyond the simplified dynamics in the circular restricted three-body problem. The present paper deals with two mechanisms of the generation of multiple families of synodic resonant periodic orbits in the bicircular restricted four-body problem through numerical examples adopting planar and three-dimensional retrograde periodic orbits around the Earth. The first part of the paper reveals complex interplays between a synodic resonant periodic orbit and multi-revolutional orbits originated from period-multiplying bifurcations. Extensions of continuation curves beyond the usual limit find another 12 : 11 synodic resonant planar retrograde periodic orbit around the Earth in addition to the one already found in the previous work. The sec-ond part shows that a doubly symmetric periodic orbit in the circular restricted three-body problem can generate four families of synodic resonant periodic orbits in the bicircular restricted four-body problem. This work identifies linearly stable, 1 : 1 synodic resonant, three- dimensional retrograde periodic orbits around the Earth and indicates their substantially large stability regions under solar gravitational perturbations. (C) 2022 COSPAR. Published by Elsevier B.V. All rights reserved.