Abstract

In this paper, we have deduced the dynamical differential equations of a dust grain in a system with albedo, radiation pressure under effects of variable accumulations of material points and masses. The system consists of a dust grain passively gravitating in the field of two bodies whose masses are changing with time and the three bodies are enclosed by a variable mass accumulation of material points. The analysis considers the bigger body as a radiation source while the smaller one is an albedo body. Further, the masses of the main bodies and the accumulations change over time according to the Mestschersky Unified Law (MUL), while the motion of the main bodies is governed by the Gylden-Mestschersky equation. It is observed that the equations of motion of this problem differ from the restricted three-body problem with variable masses due to the influence of the radiation, albedo factors and the varying mass of the accumulations around the bodies. Additionally, to derive the relation that connects the albedo and radiation pressure, we assume that the luminosities and radius of both bodies vary and we introduced a transformation to describe it. Finally, the model is applied to three systems, which are: Proxima-Centauri-Dust disk, Sun-Mars-Asteroid belt and Sun-Saturn-Kuiper belt. The time series, surface and contour plots are presented to demonstrate the impacts of the model parameters on the dynamics of the dust grain. This study can be instrumental in mission design for space exploration and also aid in understanding the stability of celestial bodies like asteroid motion near the Lagrange points of the systems.

Keywords

R3BP, Variable Masses, Accumulation, Albedo, Radiation Pressure