Poynting-Robertson Effect on the Lyapunov Stability of Equilibrium Points in the Generalized Photogravitational Chermnykh's Problem

TL;DR

This paper investigates how the Poynting-Robertson effect influences the stability of equilibrium points in a generalized photogravitational problem involving radiation and oblateness, revealing that all points become Lyapunov unstable due to this effect.

Contribution

It extends the classical Chermnykh's problem by incorporating the Poynting-Robertson effect, radiation, oblateness, and belt potential, analyzing their combined impact on equilibrium stability.

Findings

Equilibrium points shift from classical positions due to the P-R effect.

All equilibrium points are Lyapunov unstable under the P-R effect.

The gravitational potential from the belt influences equilibrium positions.

Abstract

The Poynting-Robertson(P-R) effect on Lyapunov stability of equilibrium points is being discussed in the the generalized photogravitational Chermnykh's problem when bigger primary is a sours of radiation and smaller primary is an oblate spheriod. We derived the equations of motion, obtained the equilibrium points and examined the linear stability of the equilibrium points for various values of parameter which have been used in the present problem. We have examined the effect of gravitational potential from the belt. The positions of the equilibrium points are different from the position in classical case. We have seen that due to the P-R effect all the equilibrium points are unstable in Lyapunov sense.