Gravitational Slingshot Effect

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
In astronautical mechanics, the gravitational slingshot maneuver, which NASA calls a "gravity assist", exploits the gravitational attraction of a planet to alter the speed and trajectory of an interplanetary spacecraft. A spacecraft can thereby be accelerated by a near planetary flyby to enable considerable savings of fuel in missions to the outer planets, such as Jupiter and Saturn. At first sight, this might seem like a cosmic something-for-nothing scam. But the physics depends straightforwardly on conservation of momentum and energy and the huge planet-to-spacecraft mass ratio, which leaves the planetary orbit essentially undisturbed.
[more]
Contributed by: S. M. Blinder (April 2010)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The encounter of the spacecraft with the planet can be simulated by an elastic collision. In the simplest case of a head-on collision, the initial state can be represented by the diagram:
¤ and the final state by:
¤
. The planet is so massive compared to the spacecraft that its motion is essentially unperturbed. In the actual situation, the final speed of the spacecraft is given by
, where
is the initial angle between
and
.
References: Gravity Assist (Wikipedia).
Permanent Citation