Investigation of Stable Regions of Spacecraft Motion in Binary Asteroid Systems by Terminal Condition Maps

In this paper, the stable regions of spacecraft motion in binary asteroid systems are studied and applied to design trajectories for exploration missions. Due to the non-spherical shape and the relative motion of small bodies, the motion in a binary asteroid system exhibits chaotic characteristics, which bring difficulties to proximity operations. A terminal condition map is developed to analyze the motion stability, where the initial periapsides of trajectories are classified according to their terminal states, including orbiting the asteroids, impacting on the surface or escaping from the system. The binary asteroid system 66391 Moshup is chosen as the target. The geometry of terminal condition maps is first discussed based on a synchronized model. The stable regions around asteroids are found for both planar and spatial motions, and their evolutions with orbital energy are investigated. Then, a method to trajectory design in binary asteroid systems via terminal condition maps is proposed. Opportunities for ballistic capture and escape are found in the vicinity of the asteroids by matching backward and forward terminal condition maps. Meanwhile, ΔV-assisted periodic orbits, as well as flyby trajectories, can be designed on the basis of the symmetry of maps. Finally, the terminal condition map is applied to discuss the effect of the primary and secondary’s mutual motion on the spacecraft motion. This study provides a global picture of the motion stability and makes trajectory design flexible in binary asteroid systems, which can support future binary asteroid exploration missions.