On a planar circular restricted charged three-body problem

TL;DR

This paper introduces a planar circular restricted charged three-body problem incorporating both gravitational and Coulomb forces, analyzing equilibrium solutions and their stability under various force conditions.

Contribution

It extends the classical three-body problem by including Coulomb forces and provides conditions for equilibrium existence and stability in this new model.

Findings

Existence conditions for triangular equilibrium solutions.

Linear stability analysis of these solutions.

Criteria for collinear equilibrium solutions.

Abstract

We introduce a circular restricted charged three-body problem on the plane. In this model, the gravitational and Coulomb forces, due to the primary bodies, act on a test particle; the net force exerted by some primary body on the test particle can be attractive, repulsive or null. The restricted problem is obtained by the general planar charged three-body problem considering one mass of the three bodies going to zero. We obtain necessary restrictions for the parameters that appear in the problem, in order to be well defined. Taking into account such restriction, we study the existence and linear stability of the triangular equilibrium solutions, as well as its location in the configuration space. We also obtain necessary and sufficient conditions for the existence of the collinear equilibrium solutions.