Stability Analysis of Elliptical Restricted Three Body Problem

The study here is for the equilibrium position of the primaries with the infinitesimal body. In particular, the possible positions of the equilibrium occurred when the three bodies form an equilateral triangle. The application of this model can be seen in the motion of Trojan - asteroids. The asteroids are only influenced by the gravitational forces of the Sun and Jupiter, and the orbit of Jupiter around Sun is assumed to be a fixed ellipse.