The Dynamical Equations of the Restricted Three-Body Problem with Poynting-Robertson Drag Force and Variable Masses

Abstract

The restricted three-body problem (R3BP) is a formulation which defines the motion of a passively gravitating test particle having  infinitesimal mass and moving in the gravitational environment of two bodies, called primaries. The R3BP is still an exciting and active  research field that has been getting attention of scientists and astronomers because of its applications in dynamics of the solar and stellar systems, lunar theory, and artificial satellites. The equations of motion are usually the starting point in the investigations of the  dynamical predictions of the infinitesimal mass. Therefore, in this paper, we examine the derivations of the dynamical equations of the  R3BP with Poynting-Robertson (P-R) Drag force and variable masses. In this model formulation, both primaries are assumed to vary their  masses under the combined Mestschersky law (CML) and they move in the frame of the GyldenMestschersky equation (GME). Further,  the bigger primary is assumed to be emitting radiation force, which is a component of the radiation pressure and the P-R drag. The non- autonomous dynamical equations of the model are derived and converted into the autonomized equations with constant coefficients  using the Mestschersky transformation (MT), the CML, the particular solutions of the GMP, and a transformation for the time dependent  velocity of light. We observed that the P-R drag of the bigger primary depends on the mass parameter, radiation pressure, velocity of  light and the mass variation constant . The derived systems of equations with variable and constant coefficients can be used to model  the long-term motion of satellites and planets in binary systems.