Revealing the equilibrium dynamics of a binary system of prolate or oblate elliptical galaxies.

In this work, we focus on a binary stellar system consisting of two elliptical galaxies. Specifically, our investigation centers around prolate and oblate elliptical galaxies, which we model using the circular restricted three-body problem. Employing various standard numerical methods, we determine the positions of equilibrium points and analyze their linear stability and dynamical characteristics. To comprehensively explore the influence of mass and shape on the equilibrium points and their linear stability, we systematically investigate and discretize the parameter space of the system. Our study reveals a consistent pattern of an odd number of equilibrium points, which varies from 5 to 11. Notably, the system consistently displays linearly stable points, with the number of collinear points varying between 3 and 5. [ABSTRACT FROM AUTHOR]