# On the uniqueness of trapezoidal four-body central configurations

## TL;DR

This paper proves that for the Newtonian four-body problem, there is at most one trapezoidal central configuration for each cyclic order of the masses, using a topological approach.

## Contribution

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

## Key findings

- Proves at most one trapezoidal configuration per mass order
- Uses topological methods to establish uniqueness
- Contributes to understanding of four-body central configurations

## Abstract

We study central configurations of the Newtonian four-body problem that form a trapezoid. Using a topological argument we prove that there is at most one trapezoidal central configuration for each cyclic ordering of the masses.