THE STABILITY OF OUT-OF-PLANE EQUILIBRIUM POINTS IN THE ELLIPTIC RESTRICTED THREE-BODY PROBLEM AT J_4 OF THE BIGGER PRIMARY

Abstract

This paper examines the positions and stability of out-of-plane equilibrium points within the framework of the Elliptic Restricted Three-Body Problem (ER3BP) at  of the bigger primary in the field of stellar binary systems: HD188753 and Alpha Centauri around their common centre of mass in elliptic orbits. It is found that, the positions and stability of the out-of-plane equilibrium points are significantly affected by the oblateness, semi-major axis and the eccentricity of their orbits. The positions  of the infinitesimal body lie in the plane almost directly above and below the center of the bigger oblate primary. The effects of the perturbed parameters on the positions and stability are shown numerically for the aforementioned binary systems. The status of the out-of-plane equilibrium points as evidenced in most cases remain the same and are unstable even when only the bigger primary is viewed in the out-of-plane.