Binary collisions and the slingshot effect

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 (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][585][586][587][588][589][590] 2006) the possible trajectories are computed for both attractive or repulsive interactions yielding a further insight on the slingshot mechanics and its parametrization. http:// centra.ist.utl.pt/amaro/Collisions/Collisions.html. 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.

Geometric perspective on the one-dimensional Lenz–Ising model in a non-zero magnetic field

“…see [36,37]) and its allied fields (e.g. see [38,39]). Great physicists such as Albert Einstein [40] and Michael Faraday [41] had also thought in terms of pictures.…”

Creating deterministic collisions between two orbiting bodies

“…The geometric parametrization method has been introduced to study the two elastic collisions of planetary bodies [32]. In planetary system, the collision of two planetary bodies is used by various spacecraft to reach their target [18] and to calculate the trajectories of spacecraft between two planets [19].…”

“…In the solar system, the slingshot effect (binary collision), or gravity assist, is used by spacecraft including Galileo, Cassini, Dawn, and Voyager to reach their target [18]. The binary elastic collision (slingshot effect) is used to calculate spacecraft trajectories between two planets [19].…”