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

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 $\sigma_2$.