OUT-OF-PLANE EQUILIBRIA IN THE ELLIPTIC RESTRICTED THREE-BODY PROBLEM WITH EQUAL OBLATE PRIMARIES AND A LUMINOUS PRIMARY BODY

Abstract

In the present work, we study the out-of-plane equilibrium points of an infinitesimal body under the attraction of two identical masses which move on elliptic orbits around their centre of mass and considered the case where the two equally heavy bodies are oblate spheroids with equal oblateness coefficients and only one of the primary bodies radiates. The possible regions for motion as well as the positions of equilibria and their stability are explored and analysed numerically. It is found that they are affected by the radiation pressure of the primary body, oblateness of the primaries, eccentricity, and semi-major axis of the orbits of the bodies. An investigation of the stability of the out of plane equilibria reveals that they are unstable.