Existence and Stability of Equilibrium Points under Combined Effects of Oblateness and Triaxiality in the Restricted Problem of Four Bodies

The restricted four-body problem consists of an infinitesimal body which is moving under the Newtonian gravitational attraction of three finite bodies m1,m2,m3 The three bodies (primaries) lie always at the vertices of an equilateral triangle, while each moves in circle about the centre of mass of the system fixed at the origin of the coordinate system. The fourth body does not affect the motion of the three bodies. We consider that the dominant primary body m1 and smaller primary m2 are respectively triaxial and oblate spheroidal bodies. We investigate the existence and locations of the equilibrium points and study their linear stability for the case of two equal masses. The result shows that the non-sphericity of the bodies plays an important role on the existence and evolution of the equilibrium points and influences in a very definitive way their position, as well as, their stability.