Survey of Mars Ballistic Capture Trajectories Using Periodic Orbits as Generating Mechanisms

A systematic approach is devised to find ballistic captures in the planar elliptic restricted three-body problem. Simple symmetric periodic orbits around the smaller primary in the circular problem are used as generators for ballistic captures. Combining a scaling factor that maps states from the circular to the elliptic model, 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-duration, regular solutions with a variety of characteristics, including low osculating eccentricities. A large-scale survey is completed using three families of periodic orbits encompassing more than 2600 periodic solutions. Discretizing over the mapping parameter, the Mars true anomaly, and the generating periodic orbits, 37 million ballistic captures are evaluated and classified for potential use. The existence of sample solutions into a high-fidelity ephemeris model is evidenced.