Crash test for the Copenhagen problem with oblateness

TL;DR

This paper investigates the complex dynamics of the restricted three-body problem with an oblate primary, analyzing escape, collision, and bounded motions, revealing fractal basin boundaries and energy dependence.

Contribution

It provides a detailed numerical analysis of phase space structures, escape and collision basins, and fractal boundaries in the oblate primary three-body problem, linking results to chaotic scattering and leaking systems.

Findings

High complexity of the dynamical system.

Strong dependence of escape basins on orbital energy.

Presence of fractal basin boundaries indicating sensitive dependence on initial conditions.

Abstract

The case of the planar circular restricted three-body problem where one of the two primaries is an oblate spheroid is investigated. We conduct a thorough numerical analysis on the phase space mixing by classifying initial conditions of orbits and distinguishing between three types of motion: (i) bounded, (ii) escape and (iii) collisional. The presented outcomes reveal the high complexity of this dynamical system. Furthermore, our numerical analysis shows a strong dependence of the properties of the considered escape basins with the total orbital energy, with a remarkable presence of fractal basin boundaries along all the escape regimes. 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 also determined the escape and collisional basins and computed the corresponding escape/crash times. The highly fractal basin boundaries observed are related with high sensitivity to initial conditions thus implying an uncertainty between escape solutions which evolve to different regions of the phase space. We hope our contribution to be useful for a further understanding of the escape and crash mechanism of orbits in this version of the restricted three-body problem.