# Gravitational Slingshot Effect

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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.

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Contributed by: S. M. Blinder (April 2010)

Open content licensed under CC BY-NC-SA

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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).

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