Periods of N-body Systems Determined Through Dimensional Analysis

TL;DR

This paper extends dimensional analysis to derive generalized Kepler's third law for n-body systems, aligning with existing conjectures in classical and quantum contexts without solving equations of motion.

Contribution

It introduces a method to generalize Kepler's third law to n-body systems using dimensional analysis, avoiding direct solutions of equations.

Findings

Derived generalized Kepler's third law for n-body systems.

Results agree with Sun's conjecture on classical n-body periods.

Aligns with Semay and Sun's quantum n-body period conjecture.

Abstract

A generalization of classical dimensional analysis, presented in a separate article, makes it possible to derive Kepler's third law for the period of a two-body system, up to a multiplicative constant, without solving the equations of motion. Here we show how to derive generalizations of Kepler's third law to n-body systems by the same technique. Our results agree with conjectures by Sun on the period of a classical n-body system and by Semay and Sun on the quantum-theoretical counterpart of the period of a classical n-body system.