Motion around the out-of-plane equilibrium points in the photogravitational Copenhagen elliptic restricted three-body problem with oblateness

Abstract

This paper studies the motion of an infinitesimal mass near the out-of-plane equilibrium points (OEPs) in the elliptic restricted three-body problem (ER3BP) in the case of two equally heavy bodies (Copenhagen problem) where one of the two primaries is a radiation source and the other an oblate spheroid. We found, as in the photogravitational circular restricted three body problem, that the equations of motion of the three-dimensional photogravitational ER3BP allow the existence of OEPs if the radiation parameter has negative values. There are two out of plane equilibria that lie in the (ξ, ζ) plane in symmetrical positions with respect to the (ξ, η) plane. The positions of the OEPs are affected by the parameters involved in the systems’ dynamics. In particular, the positions change with increase in the radiation pressure, oblateness, eccentricity and semi-major axis of the orbits. As an application, the positions and linear stability of the problem are investigated numerically for the binary system B1534+12. The OEPs are found unstable.