Secular dynamics around uniformly rotating asteroids

The dynamical behaviours of spacecrafts moving around uniformly rotating asteroids are investigated in this work. Based on the generalized inertia integrals of asteroids, the expression of the disturbing potential is derived as a trigonometric series in terms of the mean anomaly, geographical longitude of ascending node and argument of pericentre. In thismanner, averaged models can be achieved by eliminating the short-period terms or both the short- and long-period terms in the disturbing function. In the averaged models, families of stationary solutions with constant semi-major axis, eccentricity, inclination and argument of pericentre are identified. Based on the consideration that the equations of motion in the non-averaged model are composed of secular and periodic parts, the analytical solution of osculating elements for nonresonant motions is given as a summation of mean elements and periodic oscillations. Taking asteroid 216 Kleopatra as an example, we find that the analytical orbits have an excellent correspondence with the numerically integrated orbits, indicating that the analytical solution is applicable in predicting dynamical behaviours in non-averaged models.