Geometric parametrization of binary elastic collisions
  A geometric view of the possible outcomes of elastic collisions of two massive bodies is developed that integrates laboratory, center of mass, and relative body frames in a single diagram. From these diagrams all the scattering properties of binary collisions can be obtained. The particular case of gravitational scattering by a moving massive object corresponds to the slingshot maneuver, and its maximum velocity is obtained. 
Amaro J. Rica da Silva and Jos\'e P. S. Lemos