Symmetric periodic solution around asteroid 216 Kleopatra and its stability in the presence of solar radiation pressure

In this paper, the dumbbell model is used for gravity field of asteroid 216 Kleopatra. Utilizing the model results in governing equations of motion of a spacecraft around an asteroid similar to those of motion of a spacecraft in the restricted circular three-body problem. The equilibrium points and Jacobi regions are calculated and symmetric periodic orbits are computed utilizing grid search and shooting methods. The xz-plane is considered as the symmetry plane. Stability of the periodic orbits is evaluated by Floquet theory that shows all the computed orbits are unstable. By adding the solar radiation pressure term to the governing equations of motion, the symmetric periodic orbits are recomputed and index of stability are examined. The results show that the solar radiation pressure, though change the values of the index of stability, does not affect the stability of computed periodic orbits. Therefore, stabilizing a spacecraft on the unstable periodic orbits requires controlling spacecraft.