Shouldn’t the gravity of the planet force the craft to expend fuel to escape the gravity?
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It’s not the gravity we’re using, but the planet’s motion around the sun. Throw a ball against the wall, it comes back at about the same speed. Throw a ball against a truck moving towards you, and the ball bounces back faster than the truck itself is going. Kind of the same thing, but using gravity to impart the energy instead of bouncing.
The planet actually loses energy in speeding up a spacecraft, although it’s a meaningless amount given the mass of the planet. The planet gains energy if the slingshot is used to slow the spacecraft by coming at it from the other direction.
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