A proof of Saari's homographic conjecture

TL;DR

This paper proves Saari's homographic conjecture for a broad class of n-body problems with power law potentials, including the classical n-body problem, advancing understanding of solution behaviors in celestial mechanics.

Contribution

The paper provides a proof of Saari's homographic conjecture applicable to many n-body problems with power law potentials, extending previous partial results.

Findings

Confirmed the conjecture for a large class of problems

Unified treatment of various power law potentials

Enhanced understanding of homographic solutions in celestial mechanics

Abstract

We prove Saari's homographic conjecture for a large class of $n$-body problems with power law potentials, including the classical $n$-body problem.