The Effect of Radiation Pressure on the Equilibrium Points in the Generalised Photogravitational Restricted Three Body Problem

TL;DR

This paper investigates how radiation pressure and Poynting-Robertson effects influence equilibrium points in a generalized photogravitational restricted three-body problem, revealing shifts, stability changes, and instability conditions.

Contribution

It extends the classical three-body problem by incorporating radiation pressure, oblateness, and P-R effects, analyzing their impact on equilibrium points and stability.

Findings

Collinear points shift from the axis due to radiation pressure.

Radiation pressure reduces stability zones of equilibrium points.

P-R effect induces Lyapunov instability in the system.

Abstract

The existence of equilibrium points and the effect of radiation pressure have been discussed numerically. The problem is generalized by considering bigger primary as a source of radiation and small primary as an oblate spheroid. We have also discussed the Poynting-Robertson(P-R) effect which is caused due to radiation pressure. It is found that the collinear points $L_1,L_2,L_3$ deviate from the axis joining the two primaries, while the triangular points $L_4,L_5$ are not symmetrical due to radiation pressure. We have seen that $L_1,L_2,L_3$ are linearly unstable while $L_4,L_5$ are conditionally stable in the sense of Lyapunov when P-R effect is not considered. We have found that the effect of radiation pressure reduces the linear stability zones while P-R effect induces an instability in the sense of Lyapunov.