Generating Periodic Orbits for Explorations of Elongated Asteroids

A practical method is proposed to search for periodic orbits of elongated asteroids. The method obtains required initial variables of periodic orbits by using the rotating mass dipole with appropriate parameters, and then implement local iterations to obtain the real orbits over an asteroid in the polyhedral model. In this paper the dipole and polyhedral models, and list detailed procedures of the searching method are introduced. A planar single lobe orbit is presented to evaluate the effectiveness of the method, with the asteroid 216 Kleopatra of the triple asteroid system as a representative elongated body. By applying the above method, ten families of periodic orbits around Kleopatra are identified and discussed with respect to their orbital stabilities and periods. One sample of the sombrero orbit is checked by calculating 1.000 hours to examine its orbital behavior. Besides the above orbits, the intriguing head-surrounding orbit is also analyzed.