Binary Collisions and the Slingshot Effect

TL;DR

This paper generalizes the gravity assist or slingshot maneuver by deriving equations for arbitrary mass ratios and collision types, providing new insights into the mechanics and maximum energy gain possibilities.

Contribution

It extends previous models by deriving equations for 2D gravity assists without simplifying assumptions, covering arbitrary mass ratios and collision types.

Findings

Derived general equations for 2D gravity assist maneuvers.

Identified conditions for maximum energy gain in arbitrary mass collisions.

Provided a geometric interpretation of slingshot mechanics.

Abstract

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, 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 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.