LOCATIONS OF TRIANGULAR EQUILIBRIUM POINTS OF THE RESTRICTED THREE-BODY PROBLEM WITH POYNTING-ROBERTSON DRAG AND VARIABLE MASSES

Abstract

The restricted three-body problem (R3BP) is a fascinating problem that has been receiving attentions of astronomers and scientists because of its vast implications in diverse scientific fields, including among others; celestial mechanics, galactic dynamics, chaos theory and molecular physics. In this paper, we examine the locations of the triangular equilibrium points of the R3BP with Poynting-Robertson (P-R) drag forces and variable masses. The primaries are assumed to vary under the unified Mestschersky law and their dynamics defined by the Gylden-Mestschersky equation, while the smaller primary is assumed to be a radiation emitter with P-R drag. The dynamical equations are obtained for both the non-autonomous with variable coefficients and autonomized system with constant coefficients. Further, the locations of the triangular points of the autonomized systems are obtained using perturbation method. It is seen that the positions are defined by the mass parameter, radiation pressure and P-R drag of the smaller primary. The triangular points of the non-autonomous equations are obtained with help of the Mestschersky transformation, and differ from those of the autonomized system due to a function of time. The equilibrium points have several applications in space missions, satellites constellations and station-keeping.