Effect of oblateness, radiation and a circular cluster of material points on the stability of equilibrium points in the restricted four-body problem

TL;DR

This paper investigates how oblateness, radiation, and a circular cluster of material points influence the stability of equilibrium points in the restricted four-body problem, using numerical methods to analyze stability.

Contribution

It introduces a model incorporating oblateness, radiation, and a material point cluster into the restricted four-body problem and examines their effects on equilibrium stability.

Findings

Equilibrium points are found to be unstable.

Circular cluster and oblateness significantly affect stability.

Numerical analysis confirms instability of collinear and non-collinear points.

Abstract

Within the framework of restricted four-body problem, we study the motion of an infinitesimal mass by assuming that the primaries of the system are radiating-oblate spheroids surrounded by a circular cluster of material points. In our model, we assume that the two masses of the primaries $m_2$ and $m_3$ are equal to $\mu$ and the mass $m_1$ is $1-2\mu$. By using numerical approach, we have obtained the equilibrium points and examined their linear stability. The effect of potential created by the circular cluster and oblateness coefficients for the more massive primary and the less massive primary, on the existence and linear stability of the libration point have been critically examine via numerical computation. The stability of these points examined shows that the collinear and the non-collinear equilibrium points are unstable. The result presented in this paper have practical application in astrophysics.