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Q: How does a gravitational sling shot actually speed things up?
Physicist: A gravitational slingshot (or “gravity assist”) is a slick way to pick up speed using a moving planet’s gravity. The GEP states that the laws of physics work the same whether you’re moving (at a constant speed) or not. The total change in velocity, , experienced by the slungshot object is , where is the incoming speed (from the planet’s perspective), and is the angle between the incoming and outgoing trajectories (again from the planet’s perspective). A slingshot increases the kinetic energy of the object in question by decreasing the kinetic energy of the planet. It lowers the fuel costs a lot, but all the wandering around makes the trip quite a bit longer.
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