A limit of nonplanar 5-body central configurations is nonplanar

TL;DR

This paper proves that a specific bifurcation phenomenon observed in larger central configurations does not occur in 5-body systems, answering a previously open question in celestial mechanics.

Contribution

It establishes that 5-body central configurations do not undergo the bifurcation into nonplanar configurations as larger systems do, resolving an open problem.

Findings

No bifurcation into nonplanar configurations for 5-body systems

Answers negatively to a previously open question

Extends understanding of central configuration bifurcations

Abstract

Moeckel (1990), Moeckel and Sim\'o (1995) proved that, while continuously changing the masses, a 946-body planar central configuration bifurcates into a spatial central configuration. We show that this kind of bifurcation does not occur with 5 bodies. Question 17 in the list Albouy & al (2012) is thus answered negatively.