(Preprint) AAS 09-227 THE ENDGAME PROBLEM PART B: THE MULTI-BODY TECHNIQUE AND THE T-P GRAPH

ESA and NASA renewed interest on missions to Europa, Ganymede and Titan poses the question on how to best solve the Endgame problem. Endgames typically aim at a cheap insertion maneuver into the science orbit, and can be designed using either Vinfinity Leveraging Maneuvers (VILMs) or the Multi-Body dynamics. Although historically linked to insertion maneuvers, the endgame problem is symmetric and equally applies to departure. In this paper series, we analyze and draw connections between the two apparently separate approaches, providing insight to the dynamics of multi-body gravity assist problem. In this paper we study the anatomy of the Multi-Body approach using a new graphical tool, the Tisserand-Poincaré (T-P) graph. The T-P graph shows that ballistic endgames are energetically possible and it explains why they require resonant orbits patched with high altitude flybys, whereas in the VILM approach flybys alone are not effective without impulsive maneuvers in between them. We then explain how to use the T-P graph and the associated concepts to design quasi-ballistic transfers composed by endgames and begingames (the symmetric problems). Unlike previous methods, the T-P graph provides a valuable, energy based, target point for the design of the two parts of the trajectory, and a simple way to patch them. Further, the patch point calculation is straight forward and does not require the often tedious generation of manifolds and their associated intersections. We finally present two transfers. The first transfer is between low-altitude orbits at Europa and Ganymede using almost half the∆v of the Hohmann transfer; the second transfer is a 300-day quasi-ballistic transfer between halo orbits of the Jupiter-Ganymede and Jupiter-Europa. With some 50 m/s the transfer can be reduced by two months. While the results have the most relevant implications at low energy (endgame) levels, the Tisserand integral shows that ballistic multi-body transfers are feasible (given infinite time) for all energy levels across any distance gap.