Relative Equilibria in the Spherical, Finite Density 3-Body Problem

TL;DR

This paper identifies and analyzes 28 relative equilibria in the spherical, finite density 3-body problem, revealing increased complexity and stability characteristics compared to the classical point-mass case.

Contribution

It extends the classical 3-body problem by including finite density effects, identifying new equilibria, and mapping their stability and bifurcation pathways.

Findings

28 distinct relative equilibria identified

Finite density increases the number of equilibria

Minimum energy configurations exist for all angular momenta

Abstract

The relative equilibria for the spherical, finite density 3 body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical 5 relative equilibria for the point-mass 3-body problem. None of the identified relative equilibria exist or are stable over all values of angular momentum. The stability and bifurcation pathways of these relative equilibria are mapped out as the angular momentum of the system is increased. This is done under the assumption that they have equal and constant densities and that the entire system rotates about its maximum moment of inertia. The transition to finite density greatly increases the number of relative equilibria in the 3-body problem and ensures that minimum energy configurations exist for all values of angular momentum.