Existence of Equilibrium Points and their Linear Stability in the Generalized Photogravitational Chermnykh-Like Problem with Power-law Profile

TL;DR

This paper investigates equilibrium points and their stability in a modified three-body problem with a power-law density disk, revealing new equilibrium points and stability conditions influenced by radiation, oblateness, and disk mass.

Contribution

It introduces a new equilibrium point on the line joining primaries and analyzes stability under various physical parameters, extending classical three-body problem results.

Findings

Existence of a new equilibrium point between primaries.

L2 and L3 are stable for certain disk radii.

L4 is conditionally stable for specific mass ratios.

Abstract

We consider the modified restricted three body problem with power-law density profile of disk, which rotates around the center of mass of the system with perturbed mean motion. Using analytical and numerical methods we have found equilibrium points and examined their linear stability. We have also found the zero velocity surfaces for the present model. In addition to five equilibrium points there is a new equilibrium point on the line joining the two primaries. It is found that $L_2$ and $L_3$ are stable for some values of inner and outer radius of the disk while collinear points are unstable, but $L_4$ is conditionally stable for mass ratio less than that of Routh's critical value. Lastly we have obtained the effects of radiation pressure, oblateness and mass of the disk.