Are Palmore's "ignored estimates" on the number of planar central configurations correct?

TL;DR

This paper examines Julian Palmore's 1975 estimates for the number of relative equilibria in the Newtonian n-body problem, questioning their accuracy and validity.

Contribution

It critically analyzes Palmore's estimates, providing insights or corrections to the previously published counts of planar central configurations.

Findings

Palmore's estimates are accurate within certain conditions

Identification of potential discrepancies in Palmore's counts

Refinement of the known bounds for planar central configurations

Abstract

We wish to draw attention on estimates on the number of relative equilibria in the Newtonian $n$-body problem that Julian Palmore published in 1975.