A continuation approach for computing periodic orbits around irregular-shaped asteroids. An application to 433 Eros

The orbital dynamics in the gravitational environment of irregular asteroids is an important issue for space missions and a quite complex problem. In this paper we propose a methodological approach for computing periodic orbits around rotating, irregular-shaped asteroids. Our study starts from the families of periodic orbits of a triaxial ellipsoid model that can approximate the gravitational field of an irregular body. The families of periodic orbits of the triaxial ellipsoid have particular structures and symmetries. By using a particular periodic orbit, which belongs in a family of the ellipsoid model, we introduce and apply the method of shape continuation in order to obtain a corresponding periodic orbit in the gravitational field of an irregular body, which in our study is approximated with a sufficient number of mascons. Then, by applying analytic continuation to this orbit, we can compute a family of periodic orbits in the asymmetric gravitational field. This family can be assumed as a perturbed family, with respect to that of the ellipsoid, with the strength of the perturbation being dependent on the irregular shape of the asteroid and the distance of the orbits from its surface. We apply our methodology to the asteroid 433 Eros and present results on particular planar and 3D orbits. Similarities and differences between families of the ellipsoid and the asteroid model are indicated and discussed.