Binary collisions and the slingshot effect

We derive the equations for the gravity assist manoeuvre in the general 2D case without the constraints of circular planetary orbits or widely different masses as assumed by Broucke (AIAA/AAS 1988) and obtain the slingshot conditions and maximum energy gain for arbitrary mass ratios of two colliding rigid bodies. Using the geometric view developed in an earlier paper by the authors (Rica da Silva, A., Lemos, J.P.S.: Am. J. Phys. 74, 584–590, 2006) the possible trajectories are computed for both attractive or repulsive interactions yielding a further insight on the slingshot mechanics and its parametrization. . The general slingshot manoeuvre for arbitrary masses is explained as a particular case of the possible outcomes of attractive or repulsive binary collisions, and the correlation between asymptotic information and orbital parameters is obtained in general.