Determining novel periodic orbits around equilibrium points of asteroids

In this paper, we discover the existence of a sort of special periodic orbit around the equilibrium points of irregularly shaped asteroids and present an algorithm to accurately determine this novel orbit. Since the environment of orbital dynamics around the equilibrium points of an asteroid is similar to that in the circular restricted three-body problem (CRTBP), this article introduces the research approach used in the research of halo orbits in the CRTBP to determine the special orbits. Firstly, the dynamics of particles orbiting on irregularly shaped spinning asteroid are analyzed and then the formula to compute the positions of asteroid's equilibrium points can be deduced from the equations obtained from the analysis. Secondly, third-order approximate analytical solutions for the periodic orbit around the equilibrium points were obtained using the Lindstedt-Poincaré method. Finally, in the high-order gravitational field model, differential corrections were applied to amend the initial orbit value obtained from third-order analytical solutions in order to obtain accurate numerical solutions of this periodic orbit, which are called aureole orbits in this paper due to their similarity to the halo orbits around the Lagrangian point in the CRTBP.