On the Uniqueness of Co-circular Four Body Central Configurations

TL;DR

This paper proves that in the Newtonian four-body problem, there can be at most one co-circular central configuration for each specific ordering of the masses on the circle, using a topological approach.

Contribution

It establishes the uniqueness of co-circular four-body central configurations for each mass ordering, a novel result in celestial mechanics.

Findings

At most one co-circular configuration per mass order

Topological methods used for proof

Clarifies structure of four-body central configurations

Abstract

We study central configurations lying on a common circle in the Newtonian four-body problem. Using a topological argument we prove that there is at most one co-circular central configuration for each cyclic ordering of the masses on the circle.