Central Configurations with Unequal Masses: Finiteness in Several Exceptional Cases of Five Bodies

TL;DR

This paper uses computer-assisted methods to precisely count classes of five-body central configurations for specific exceptional mass sets, extending finiteness results in celestial mechanics.

Contribution

It provides the first exact counts of five-body central configurations for certain exceptional mass cases, complementing existing theoretical finiteness results.

Findings

Exact counts of configuration classes for specific mass sets

Extension of finiteness results to new exceptional cases

Computer-assisted proof methodology applied to celestial mechanics

Abstract

We provide a computer-assisted proof of the exact count of classes of central configurations for five bodies for several sets of mass values that are exceptional from the point of view of the finiteness results of Albouy and Kaloshin in the planar case and of Hampton and Jensen in the spatial case.