Analysis of albedo and disc effects in the generalized restricted four-body problem

Abstract

This manuscript explores the Generalized Restricted Four-Body Problem within the context of radiation pressure, the albedo effect, oblateness, and a disc-like structure that orbits around the primary bodies. We have considered that one of the primaries is a bigger primary, and the rest of the two smaller primaries are of equal masses, in which one of the smaller primaries is considered as a black body. Moreover, the perturbing forces by the effect of radiation pressure and oblateness are considered in the bigger primary. The effect of albedo and oblateness due to the second smaller primary is also taken into count. This study yields nine equilibrium points corresponding to various parameter values, including three collinear and six non-collinear equilibria. We conduct an analysis of the equilibrium points, their linear stability, and the motion around them. In the context of the considered parameter set, certain collinear equilibrium points exhibit stability, while others are unstable. Additionally, most of the non-collinear equilibrium points display linear stability. We also investigate variations in Jacobi’s constant and the positions of existing equilibrium points caused by the albedo and disc effects. It is found that the value of Jacobi constant CLj decreases with an increase in the mass parameter μ at the collinear points, which results in an expansion in the prohibited region. The inhibited zone of motion of the infinitesimal body is shown for different sets of parameters.