We often here of star systems loosing a planet or objects (satellites) getting accelerated away from a huge source of gravity (huge mass).
In: Physics
To get a gravity slingshot effect, you have to pass behind a heavy thing, like behind the moon as it’s orbiting the Earth. You’re already going fast enough to escape it, so you trace out what would be a hyperbolic orbit behind it. Except that as you pass behind it it pulls you in, and is also moving away from you, so it pulls you along with it into a slightly faster orbit, and you leave going faster.
It’s kind of the same interaction as if you physically bounced the object off the front of the moon as it’s orbiting. It bounces off faster than it was going, because the moon was going toward it. Like bouncing a rubber ball off the front of an approaching car.
If you had two mutually repulsive objects, like two objects with the same electric charge, they would “bounce” off each other this way, but without touching because their electric forces would mediate the interaction, and they would also follow a hyperbolic “orbit” that turns into straight lines at infinity. Because classical gravity is mathematically the same except that it’s attractive, you have to “bounce” off the back of it by orbiting behind it instead of bouncing off the front. So it’s more like the moon’s gravity is doing a hammer throw of the object.
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