Linear Stability of Equilibrium Points in the Generalized Photogravitational Chermnykh's Problem

TL;DR

This paper analyzes the linear stability of equilibrium points in a generalized photogravitational Chermnykh's problem, considering radiation pressure, oblateness, and belt potential effects, revealing stability conditions and differences from classical models.

Contribution

It introduces a generalized model incorporating radiation, oblateness, and belt potential, and studies the stability of equilibrium points within this framework.

Findings

Collinear points are linearly unstable.

Triangular points are stable if μ<0.0385201.

The system's properties differ from the classical restricted three-body problem.

Abstract

The equilibrium points and their linear stability has been discussed in the generalized photogravitational Chermnykh's problem. The bigger primary is being considered as a source of radiation and small primary as an oblate spheroid. The effect of radiation pressure has been discussed numerically. The collinear points are linearly unstable and triangular points are stable in the sense of Lyapunov stability provided $\mu< \mu_{Routh}=0.0385201$. The effect of gravitational potential from the belt is also examined. The mathematical properties of this system are different from the classical restricted three body problem.