Central configurations on the plane with $N$ heavy and $k$ light bodies

TL;DR

This paper investigates planar central configurations involving heavy and light bodies, deriving equations for the limit as light masses approach zero, and computes configurations for specific cases using rigorous computer methods.

Contribution

It introduces equations for the limit of light masses in central configurations and computes all configurations for certain small cases using rigorous computer methods.

Findings

Derived equations for the limit of light masses in central configurations.

Computed all configurations for N=2, k=3,4 cases.

Results are consistent with the derived limit problem.

Abstract

We study the problem of planar central configurations with $N$ heavy bodies and $k$ bodies with arbitrary small masses. We derive the equation which describe the limit of light masses going to zero, which can be seen as the equation for central configurations in the anisotropic plane. Using computer rigorous computations we compute all central configurations for $N=2$ and $k=3,4$ and for the derived limit problem. We show that the results are consistent.