Central Configurations of the Five-Body Problem with Equal Masses

TL;DR

This paper classifies all isolated central configurations of the five-body problem with equal masses using computational methods, providing a comprehensive understanding of these configurations.

Contribution

It introduces a complete classification of five-body central configurations with equal masses using polyhedral homotopy and Krawczyk methods, advancing computational approaches in celestial mechanics.

Findings

All isolated central configurations are approximated and verified.

The methods efficiently handle large Albouy-Chenciner equations.

The classification enhances understanding of five-body gravitational arrangements.

Abstract

In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. This is accomplished by using the polyhedral homotopy method to approximate all the isolated solutions of the Albouy-Chenciner equations. The existence of exact solutions, in a neighborhood of the approximated ones, is then verified using the Krawczyk method. Although the Albouy-Chenciner equations for the five-body problem are huge, it is possible to solve them in a reasonable amount of time.