Lonely planets and light belts: the Statistical Mechanics of Gravitational Systems

TL;DR

This paper introduces a new stability concept called $-N$-stability for gravitational systems with a dominant central mass, providing insights into their thermodynamic behavior and aligning with Solar System observations.

Contribution

It proposes the $-N$-stability notion for gravitational systems, addressing limitations of traditional thermodynamic stability and connecting theoretical models with Solar System data.

Findings

The model fits Solar System data well.

The $-N$-stability concept offers a new perspective on gravitational system stability.

Provides a reasonable interpretation of global properties of planetary systems.

Abstract

In this paper we propose a notion of stability, that we call $\epsilon -N$-stability, for systems of particles interacting via Newton's gravitational potential, and orbiting a much bigger object. For these systems the usual thermodynamical stability condition, ensuring the possibility to perform the thermodynamical limit, fails, but one can use as relevant parameter the maximum number of particles $N$ that guarantees the $\epsilon -N$-stability. With some judicious but not particularly optimized estimates, borrowed from the classical theory of equilibrium statistical mechanics, we show that our model has a good fit with the data observed in the Solar System, and it gives a reasonable interpretation of some of its global properties.