Application of Fourier series to the dynamics of a test particle in the CR3BP with an oblate primary

This study delves into periodic orbits within the circular restricted three-body problem (CR3BP), where a negligible mass orbits under the gravitational pull of two primary bodies. Specifically, we examine the dynamics of the third body in the CR3BP with an oblate larger primary. We determine periodic orbits around the libration points, accounting for the oblate spheroidal shape of the larger primary, using the Fourier series method. We analyze both short and long periodic orbits, presenting variational graphs to depict changes in the period $T$ of the orbits. Furthermore, we investigate how oblateness and mass parameters affect the dimensions and periods of the periodic orbits.