Stability of equilibrium points in a CR3BP with oblate bodies enclosed by a circular cluster of material points

Abstract

We have investigated an improved version of the classic restricted three-body problem where both primaries are considered oblate and are enclosed by a homogeneous circular planar cluster of material points centered at the mass center of the system. In this dynamical model we have examined the effect on the number and on the linear stability of the equilibrium locations of the small particle due to both, the primaries’ oblateness and the potential created by the circular cluster. We have drawn the zero-velocity surfaces and we have found that in addition to the usual five Lagrangian equilibrium points of the classic restricted three-body problem, there exist two new collinear points L _n1,L _n2 due to the potential from the circular cluster of material points. Numerical investigations reveal that with the increase in the mass of the circular cluster of material points, L _n2 comes nearer to the more massive primary, while L _n1 moves away from it. Owing to oblateness of the bodies, L _n1 comes nearer to the more massive primary, while L _n2 moves towards the less massive primary. The collinear equilibrium points remain unstable, while the triangular points are stable for 0<μ<μ _c and unstable for $\mu_{c} \le \mu \le \frac{1}{2}$, where μ _c is the critical mass ratio influenced by oblateness of the primaries and the potential from the circular cluster of material points. The oblateness and the circular cluster of material points have destabilizing tendency.