Three-Body Problem in Modified Dynamics

TL;DR

This paper explores the three-body problem within a modified gravity framework, analytically solving the planar restricted case and comparing orbital behaviors to Newtonian gravity, revealing potential observational differences at galactic scales.

Contribution

It provides an analytical solution for the restricted three-body problem in modified dynamics and introduces a code to compare orbital behaviors with Newtonian gravity.

Findings

Orbits around L4 and L5 are stable under certain conditions in modified dynamics.

Orbital ejections are less frequent in modified gravity compared to Newtonian.

Contrasting orbital behaviors are observed between the two dynamics.

Abstract

General properties of the three-body problem in a model of modified dynamics are investigated. It is shown that the three-body problem in this model shares some characters with the similar problem in Newtonian dynamics. Moreover, the planar restricted three-body problem is solved analytically for this type of extended gravity and it is proved that under certain conditions, which generally happen at galactic and extragalactic scales, the orbits around $L_{4}$ and $L_{5}$ Lagrange points are stable. Furthermore, a code is provided to compare the behavior of orbits in the restricted three-body problem under Newtonian and modified dynamics. Orbit integrations based on this code show contrasting orbital behavior under the two dynamics and specially exhibit in a qualitative way that the rate of ejections is smaller in the modified dynamics compared to Newtonian gravity. These results could help us to search for observational signatures of extended gravities.