Study on periodic orbit for the asteroid based on the dipole segment model

Asteroids are exist widely in the solar system, the study of orbital dynamics in the gravitational field of asteroids is helpful to reveal the origin and evolution of the solar system, and has potential scientific significance and engineering value. Due to the complex and irregular gravitational field characteristics of asteroids, there are abundant dynamic phenomena and mechanisms nearby, which also brings challenges to understanding the orbital dynamics and designing the periodic orbits for asteroids. In this paper, the dynamical model for the elongated asteroids is established. The model consists of a line segment and two point masses. The periodic orbits of the model are solved using the numerical technique of Poincare surface of section. The stability of the orbits is also calculated and analyzed. It is found that the shape and stability of periodic orbits are related to the islands on the Poincare map. (paper)