How does the oblateness coefficient influence the nature of orbits in the restricted three-body problem?

TL;DR

This study numerically examines how the oblateness coefficient of a primary affects orbit types in the restricted three-body problem, revealing its significant influence on bounded, escaping, and collisional motions.

Contribution

It provides a detailed numerical analysis of the impact of oblateness on orbit classification and phase space structure in the restricted three-body problem.

Findings

Oblateness significantly alters orbit behavior.

Identified basins for escape and collision.

Correlated escape and collision times with initial conditions.

Abstract

We numerically investigate the case of the planar circular restricted three-body problem where the more massive primary is an oblate spheroid. A thorough numerical analysis takes place in the configuration $(x,y)$ and the $(x,E)$ space in which we classify initial conditions of orbits into three categories: (i) bounded, (ii) escaping and (iii) collisional. Our results reveal that the oblateness coefficient has a huge impact on the character of orbits. Interpreting the collisional motion as leaking in the phase space we related our results to both chaotic scattering and the theory of leaking Hamiltonian systems. We successfully located the escape as well as the collisional basins and we managed to correlate them with the corresponding escape and collision times. We hope our contribution to be useful for a further understanding of the escape and collision properties of motion in this interesting version of the restricted three-body problem.