Libration points and periodic orbit families near a binary asteroid system with different shapes of the secondary

Abstract

Due to the limited capability of ground-based observations, the shapes of asteroids cannot be determined precisely, especially for the secondary of a binary system. In this paper, libration points and periodic orbit families near a binary asteroid system with different shapes of the secondary are investigated, with the binary 66391 Moshup, previously known as 1999 KW4, as an example. The gravity fields of the primary and secondary of the binary system are modelled as those of a polyhedron and a triaxial ellipsoid, respectively. With a nominal shape model for the secondary, the positions and stability of libration points are determined, and periodic orbit families emanating from each libration point are generated by numerical methods. The connections and bifurcations of periodic orbit families are analyzed through comparisons with the classic results of the circular restricted three body problem (CR3BP). Then, the effect of the shape uncertainty is investigated by changing the shape of the secondary. Libration points and associated periodic orbit families are calculated and analyzed with different shapes of the secondary. It has been found that the libration points have slight offsets on position, but their topological structures remain the same. In some cases, the halo orbit family bifurcates from the vertical Lyapunov orbit family rather than the planar Lyapunov orbit family, indicating that bifurcations of periodic orbit families are different and new connections between periodic orbit families can exist. The results will provide general insights into variations of the dynamical environments near a binary asteroid system caused by different shapes of the secondary, and will be helpful for the planetary science research and exploration mission design.