Investigating the impact of non-spherical bodies and three-body interactions on equilibrium dynamics in the circular restricted three-body problem

In this paper, we study a modified version of the classical restricted 3-body problem, which introduces an additional mutual interaction force. Moreover, we extend our analysis to include non-spherical shapes, specifically prolate or oblate shapes, for the primary bodies within the system. Our main objective is to investigate how the additional interaction and non-sphericity of the primaries influence the locations and dynamical characteristics of the equilibrium points in the system. To accomplish this, we employ standard numerical methods and techniques. Through a meticulous examination of the system's parameter space, we have identified a range of 1 to 13 libration points. We have observed that the total number of equilibrium points is directly related to the sign and intensity of the three-body interaction term. Consequently, our findings reveal a substantial difference when compared to scenarios where only three-body interactions or the non-sphericity of the primaries are considered independently.