Investigating the planar circular restricted three-body problem with strong gravitational field

TL;DR

This paper explores how varying the strength of gravitational fields affects orbital dynamics in a modified three-body problem, revealing significant impacts on orbit types and escape/collision behaviors through extensive numerical analysis.

Contribution

It introduces a novel investigation of the planar circular restricted three-body problem with variable gravitational strength controlled by potential power p, analyzing orbit classifications and phase space structures.

Findings

Gravitational potential strength significantly influences orbit types.

Identified and mapped escape and collision basins in phase space.

Linked orbit behaviors to chaotic scattering and leaking Hamiltonian systems.

Abstract

The case of the planar circular restricted three-body problem where one of the two primaries has a stronger gravitational field with respect to the classical Newtonian field is investigated. We consider the case where two primaries have the same mass, so as the the only difference between them to be the strength of the gravitational field which is controlled by the power $p$ of the potential. A thorough numerical analysis takes place in several types of two dimensional planes in which we classify initial conditions of orbits into three main categories: (i) bounded, (ii) escaping and (iii) collision. Our results reveal that the power of the gravitational potential has a huge impact on the nature of orbits. Interpreting the collision 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 collision basins and we managed to correlate them with the corresponding escape and collision time of the orbits. 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.