Analysis of albedo as well as disc effects at the Jacobi constant and their stability of equilibrium points in the generalized restricted four-body problem

Abstract

The valuable facets of the dynamics are its stability and the components that disturb stability behavior. Our purpose in this research work is to examine the fundamental analysis of equilibrium points and their linear stability under the solar radiation pressure, albedo force effects, and radiatingoblateness in the generalized restricted four-body problem. The significant elements of this problem are mass parameter µ and other disturbing parameters to the unique influential potential function and its required derivatives to the primaries. An important relation in albedo parameters and their possible range is derived. The analysis of the albedo and disc effect is observed on the Jacobi’s constant and the positions of the existing equilibrium points and their stability regions are discussed. The inhibited zone of motion by the infinitesimal body is shown for different planetary systems. The particular as well as the joint effect of solar radiation pressure at first, albedo at second, and radiating-oblateness at both primaries of the mass, a disc is observed. The scatter diagram of locations of the mass as well as equilibrium points plotted for planetary systems. The behavior of monotonicity of the existing equilibrium points is analyzed for the presence as well as the absence of perturbations of taken planetary systems. Due to such prevalence, the considered perturbing forces give a significant perturbation in the RFBP. This current study can be extended later to the design of orbits for the different planetary systems.