How is a gravitational slinghot work?

How is a gravitational slinghot work?

You may have seen this type of science-fiction scene more than once: some trap to the star and escape of a supernova / escaping of a supernova / fuel-escaping can find a planet! So they head for it, rocket burns, then lift and use gravity to the slingshot. Hooray! Cue the victorious music. So it…

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