Dynamics of a Particle in Elliptic Restricted Three-Body Problem (ER3BP) Around the Triangular Lagragian Points

Isah N

Published on: 2023-11-24

Abstract

This paper studies the stability of an infinitesimal particle (satellites, asteroids or comets) near the triangular equilibrium points (TEPs) when the primary bodies are triaxial with Poynting-Robertson (P-R) drag force of the smaller primary surrounded by circumbinary disc (disc, belt).From the equations of motion, the positions of (TEPs) are found and it consist of two Lagrangian equilibrium points L₄,₅ which lies  in the ξη- plane in symmetrical positions with respect to the orbital plane. The stability of equilibrium points were found by using both analytic technique and the energy constant c (Jacobian integral) by drawing zero velocity curves around the TEPs using the binary system archid as a case study. In both cases it was found that equilibrium points are stable. The effect of the perturbations are demonstrated numerically using the binary systems Archid and it shows the position of L₄,₅ changing with increases in triaxiality, P-R drag force and the disc. It was observed that increasing the triaxiality coefficient, values of the belt and P-R drag force did not lead to instability at the equilibrium points (EPs).