The Stability of Triangular Lagragian Points in the Photogravitational Elliptic Restricted Three – Body Problem (ER3BP) with Triaxial Primaries Surrounded by a Belt with A P-R Drag Force

Abstract

Abstract

This paper studies the motion of an infinitesimal particle near the triangular equilibrium points (TEPs) in the elliptic restricted three body problem (ER3BP) when the primaries are radiating- triaxial rigid bodies and are affected by the Poynting-Robertson (P-R) drag force enclosed in a circumbinary disc (disc,belt). We present the equations of motion, obtained the positions of (TEPs) and found that there exist two Lagragian equilibria points L_4,5 which lies  in the ξη- plane in symmetrical positions with respect to the orbital plane.The parameters involved in the system affect their positions.The position changes with an increase in triaxiality, radiation, P-R drag force and the disc. The positions and linear stability of the  TEPs are investigated numerically using  the  binary systems Archid  and it was observed that the effect  of P-R drag force of the smaller primary is not sufficient in  causing instability at the EPs  but  the radiation pressure force.We observed that when the triaxiality coefficient, values of the belt and P-R drag force are varied increasingly in the absence of radiation equilibrium points (EPs) are stable in the linear sense but becomes unstable on introducing  radiation.Thus radiation is the cause of instability when both primaries are radiating and triaxial with the smaller primary having an effective P-R drag force enclosed in a circumbinary disc and not the P-R drag.