On the symmetric central configurations for the planar 1+4-body problem

TL;DR

This paper investigates symmetric central configurations in the planar 1+4-body problem, providing analytical solutions under specific assumptions and numerical results for configurations with unequal infinitesimal masses.

Contribution

It offers new analytical and numerical insights into symmetric central configurations where the symmetry axis excludes infinitesimal masses.

Findings

Analytical solutions for certain symmetric configurations

Numerical results for configurations with unequal infinitesimal masses

Insights into the structure of symmetric central configurations

Abstract

We study the planar symmetric central configurations of the $1+4$-body problem where the symmetry axis does not contain any infinitesimal masses. Under certain assumptions we find analytically some central configurations, and also get some numerical results of symmetric central configurations where infinitesimal masses are not necessarily equal.