Motion Framework of the Perturbed R3BP with Variable Masses and a Disk

Abstract

In celestial mechanics, three-body problem (3BP) is a dynamical system defining the motion of three bodies moving under their mutual  gravitational forces. However, there is no general possible solution for this system nor for a system involving more than three bodies. The  simplest description of the 3BP is called the restricted three-body problem (R3BP), in which an infinitesimal body moves under  mutual gravitational attractions of two main bodies moving in a circular or an elliptical orbit. One of the most pertinent models in  celestial mechanics or astrodynamics are the perturbed R3BP, which demonstrates more realistic status. The analysis of perturbed R3BP  is more difficult than the analysis of the classical problem. In this paper, we devote our efforts to determining motion framework of the  perturbed R3BP with variable masses and a disk. The masses of the main bodies are assumed to change with time in accordance with the  combined Mestschersky law and their motion perturbed by deflective forces due to small perturbations in the Coriolis and  centrifugal forces, and described by the Gylden-Mestschersky problem. The dynamical differential equations of a test particle in the  context of the perturbed R3BP with variable masses and a variable mass disk enclosing the configuration, has been developed. The time dependent equations of motion are derived and transformed to an autonomized system with constant terms. Further, the autonomized  equations are explored numerically by taking the mass parameter of the system in the interval which covers vast astronomical systems,  especially those containing planetary systems. These equations are solved for some initial conditions and the time series solutions, the  3D surface and contour plots are given. It is seen that the mass variation parameter proofs to be the most dominating force which  determines the nature of solutions of the system. This model can help understand dynamics of a satellite around two massive variable  mass celestial bodies in an environment surrounded by variable accumulations of material points.