Periods of N-body Systems Determined Through Dimensional Analysis
Mathematical Physics
2026-05-19 v4 math.MP
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.
Keywords
Cite
@article{arxiv.2604.10559,
title = {Periods of N-body Systems Determined Through Dimensional Analysis},
author = {Dan Jonsson},
journal= {arXiv preprint arXiv:2604.10559},
year = {2026}
}
Comments
18 pages. The notion of characteristic distance developed further