Survey of Mars Ballistic Capture Trajectories using Periodic Orbits

A systematic approach is devised to find ballistic captures in the planar elliptic restricted three-body problem. Simple symmetric periodic orbits around the secondary body of the circular problem, computed through a global grid search, are used as generators for ballistic captures in the elliptic problem. Combining a scaling factor that maps states from the circular to the elliptic case and restricting the motion to emanate from periodic solutions, the search space for ballistic capture is reduced to three dimensions. Results in the Sun-Mars system indicate an abundance of long time-of-flight regular solutions with a variety of characteristics, including low osculating eccentricities.