Equilibrium points and locations in the photogravitational circular Robe’s restricted three-body problem with variable masses

Abstract

The restricted three-body problem (R3BP) defines the dynamics of an infinitesimal mass moving in the gravitational neighborhood of two primaries, which move in circular orbits around their center of mass on account of their mutual attraction and the infinitesimal mass not influencing the motion of the primaries. In this paper, we examine equilibrium points and their locations in the photogravitational circular Robe’s restricted three-body problem (R3BP) with variable masses. The motion of the primaries and variation in masses of the primaries are governed by the Gylden-Mestschersky problem (GMP) and the unified Mestschersky law (UML), respectively, while the second primary is assumed to be a radiation emitter. The non-autonomous equations of the governing dynamical system are deduced and transformed using the Mestschersky transformation (MT), the UML and the particular solutions of the GMP, to a system of the autonomized equations with constant coefficients under the condition that there is no fluid inside the first primary. Next, the equilibrium points (EPs) of the autonomized system are explored using perturbation method and it is seen that axial EP which is defined by the mass parameter and the radiation pressure of the second primary exists. Further, a pair of non-collinear EPs which depends on the mass parameter, radiation pressure of the second primary and a constant of the mass variations of the primaries, is found. The EPs of the non-autonomous system are obtained using the MT and differ from those of the autonomized system by time t . The EPs may be used in different problems of stellar dynamics, and also in other astrophysical applications.