On the equilibrium points of the collinear restricted 4-body problem with non-spherical bodies

Abstract

This study investigates a variation of the collinear restricted four-body problem, introducing complexity by incorporating the oblate or prolate shapes of the three primary bodies. Employing various numerical techniques, we analyze the dynamical properties of the equilibrium points within the system. In addition to identifying the coordinates of the libration points, we examine their linear stability and dynamic classifications. Our primary focus is on understanding the interplay between the system’s mass and shape parameters, revealing how they collectively influence equilibrium dynamics. Specifically, our results demonstrate that oblate-shaped peripheral bodies consistently produce six (6) equilibrium points, while prolate spheroids yield an even number – 6, 10, 14, or 18 – depending on the specific mass and shape parameters.