Equilibrium stability in the triangular restricted four-body problem with non-spherical primaries

Abstract

This paper investigates the Lagrangian configuration of the restricted four-body problem in which the three primaries are non-spherical, specifically either prolate or oblate. By using various standard numerical methods, the positions of equilibrium points and their linear stability and dynamical type were determined. The impact of mass and shape of the primaries on the system’s equilibrium points and their linear stability were systematically explored by discretizing the parameter space for the non-sphericity parameter within a specified interval. The study revealed that the system always has an even number of equilibrium points, ranging from 8 to 22. Linearly stable points always exist, except for the case where there are 10 equilibrium points, where all the points are unstable.