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How does gravitational slingshotting work?

Asked by SmashTheState (14245points) April 29th, 2015

I don’t understand the physics of slingshotting. Velocity is gained by diving into a gravitational field, but then you have to escape that same gravitational field, giving up the potential energy you gained by falling into it. Yet you end up with a net gain in velocity – slingshotting. Where does the energy come from?

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