On the minimum distance between masses of relative equilibria of the n-body problem

2014/01/14 by Pieter Tibboel, Tibboel, Pieter
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Cosmology and Gravitation Theories #Dynamical Systems (math.DS) #FOS: Mathematics #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.1401.3059

openalex publication_date 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if for relative equilibrium solutions of a generalisation of the n-body problem of celestial mechanics the masses and rotation are given, then the minimum distance between the point masses of such a relative equilibrium has a universal lower bound that is not equal to zero. We furthermore prove that the set of such relative equilibria is compact.

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