Orbital stability of the restricted three body problem in General Relativity

TL;DR

This paper investigates the orbital stability of a test particle in the restricted three-body problem within the framework of General Relativity, providing insights without requiring exact solutions.

Contribution

It introduces a novel approach using orbital moment and its derivative to analyze stability in relativistic three-body systems.

Findings

Stability insights can be obtained without exact solutions.

The method applies to relativistic regimes.

Provides a new perspective on orbital dynamics in General Relativity.

Abstract

We consider the problem of orbital stability of the motion of a test particle in the restricted three-body problem, by using the orbital moment and its time derivative. We show that it is possible to get some insight into the stability properties of the motion of test particles, without knowing the exact solutions of the motion equations.