The analysis of periodic orbits generated by Lagrangian solutions of the restricted three-body problem with non-spherical primaries

TL;DR

This paper investigates how the oblateness of primaries affects the periodic orbits in the restricted three-body problem, using numerical methods to analyze different parameter configurations.

Contribution

It introduces a detailed numerical analysis of periodic orbits considering oblateness, extending previous models to more realistic celestial body shapes.

Findings

Oblateness significantly influences the shape and stability of periodic orbits.

Numerical methods effectively reveal the impact of oblateness on orbital dynamics.

The study provides a framework for future research on non-spherical celestial bodies.

Abstract

The present paper deals with the periodic orbits generated by Lagrangian solutions of the restricted three-body problem when both the primaries are oblate bodies. We have illustrated the periodic orbits for different values of $\mu, h,\sigma_1$ and $\sigma_2$ ($h$ is energy constant, $\mu$ mass ratio of the two primaries, $\sigma_1$ and $\sigma_2$ are oblateness factors). These orbits have been determined by giving displacements along the tangent and normal to the mobile coordinates as defined by Karimov and Sokolsky \cite{Kari}. We have applied the predictor-corrector algorithm to construct the periodic orbits in an attempt to unveil the effect of oblateness of the primaries by taking the fixed values of parameters $\mu, h, \sigma_1$ and $\sigma_2$.