A proof of Saari's conjecture

TL;DR

This paper proves Saari's conjecture, demonstrating that solutions with constant moment of inertia in the classical n-body problem must behave as rotating rigid bodies, and discusses potential generalizations beyond the classical setting.

Contribution

The paper provides a rigorous proof of Saari's conjecture and explores its possible extensions beyond the classical n-body problem.

Findings

Proof of Saari's conjecture for the classical n-body problem.

Solutions with constant moment of inertia are rotating rigid bodies.

Potential generalizations of the conjecture are discussed.

Abstract

We prove Saari's conjecture, which states that for any solution to the classical $n$-body problem that has constant (polar) moment of inertia has to behave as a rotating rigid body. Additionally, we remark how Saari's conjecture can be generalised well beyond the confines of the classical $n$-body problem.