Periodic orbits in the doubly synchronous binary asteroid systems and their applications in space missions

This paper investigates the periodic motion of a particle in the doubly synchronous binary asteroid systems. Two typical doubly synchronous systems, 809 Lundia and 3169 Ostro, are discussed in detail. Under the Roche figure assumption, the two bodies of doubly synchronous system can be modeled as two triaxial ellipsoids. The Ivory’s theorem is used to derive the gravitational potential of the system. Then, a global numerical method, which combines grid searching and differential correction, is developed for systematically searching periodic orbits in the doubly synchronous systems. A total of 30 and 28 families of periodic orbits around Lundia and Ostro are found, respectively. Furthermore, on the basis of the analysis of morphology, stabilities and invariant manifolds, the potential applications of these periodic orbit families are studied. Several quasi-circular orbit families with low instability index are found to be suitable for the observation of the two typical binary systems. The invariant manifolds of some periodic orbits near the equilibrium points can provide the fuel-free trajectories to achieve the ballistic landing to the surface of the asteroids and transfer between the binary asteroids.