Fourier Series Methodology for Exploring the Periodic Orbits in the CR3BP with Spherical Primaries

Abstract

In this paper, we have scrutinized the circular restricted three-body problem (CR3BP) while considering both primaries as spherical. We have determined the positions of the libration points and their stability using the dynamics of the third body. Furthermore, we have drawn the periodic orbits by retaining the terms up to third order in the Fourier series expansion. Consecutively, the variation in time period of the periodic orbits impacts the networks of long- and short-period orbits in terms of its shape, size and time period. After that, two models of our solar system are examined using the procedures outlined in this manuscript.