Numerical study on periodic orbits near 216 Kleopatra

Searching for periodic orbits around the polyhedral model of irregularly shaped asteroids suffers from inefficient calculations. A practical method is proposed to overcome the above problem by taking the asteroid 216 Kleopatra as an example. Dynamical equations are briefly derived with respect to the two models, i.e., the rotating dipole and the homogenous polyhedron. The required initial variables of periodic orbits around the rotating mass dipole are first acquired, which are taken as initial guesses to obtain real orbits near Kleopatra in the polyhedral model. A planar single lobe orbit is presented to evaluate the effectiveness of the method. The orbital properties and its stability are also discussed.