Study on periodic orbits around the dipole segment model for dumbbell-shaped asteroids

Equilibrium points and periodic orbits in irregular gravitational fields are significant for an understanding of dynamical behaviors around asteroids as well as deep space exploring missions. The dipole segment is a good alternative model to study qualitative dynamical properties near dumbbell-shaped asteroids. In this paper, the dipole segment model and its equilibrium points are simply introduced. The stability of the two triangular equilibrium points of the system is numerically examined. Next, periodic orbits are presented around the dipole segment model in two different cases, in which triangular equilibria are linearly stable and unstable, respectively. New types of periodic orbits are illustrated in detail, including their orbital shapes, periods and the Jacobi integral. The orbital stability, topological classification and bifurcations of these orbits are also analyzed with numerical continuations.