# Equilibrium points and basins of convergence in the triangular restricted four-body problem with a radiating body

## TL;DR

This paper investigates how radiation effects influence equilibrium points and basins of convergence in a restricted four-body problem with three primaries in an equilateral triangle, revealing instability and reduction of fixed points at high radiation levels.

## Contribution

It extends the restricted four-body problem by incorporating radiation pressure, Poynting-Robertson drag, and solar wind drag, analyzing their impact on equilibrium points and basins of convergence.

## Key findings

- Libration points become unstable if radiation factor exceeds 0.01.
- Number of equilibrium points decreases as radiation factor increases.
- Radiation effects can destabilize the system's equilibrium in realistic celestial configurations.

## Abstract

The dynamics of the four-body problem have attracted increasing attention in recent years. In this paper, we extend the basic equilateral four-body problem by introducing the effect of radiation pressure, Poynting-Robertson drag, and solar wind drag. In our setup, three primaries lay at the vertices of an equilateral triangle and move in circular orbits around their common center of mass. Here, one of the primaries is a radiating body and the fourth body (whose mass is negligible) does not affect the motion of the primaries. We show that the existence and the number of equilibrium points of the problem depend on the mass parameters and radiation factor. Consequently, the allowed regions of motion, the regions of the basins of convergence for the equilibrium points, and the basin entropy will also depend on these parameters. The present dynamical model is analyzed for three combinations of mass for the primaries: equal masses, two equal masses, different masses. As the main results, we find that in all cases the libration points are unstable if the radiation factor is larger than 0.01 and hence able to destroy the stability of the libration points in the restricted four-body problem composed by Sun, Jupiter, Trojan asteroid and a test (dust) particle. Also, we conclude that the number of fixed points decreases with the increase of the radiation factor.