When something “falls” it accelerates.
Gravity is only so strong.
When this “slingshot” maneuver is used, they basically do a whole lot of math that calculates at juuust what distance they need to enter the planet”s gravity well to circle and escape the drain rather than spiral into it. For the brief moment it is ” falling” toward the planet, it picks up just enough extra speed that it is able to reach the escape velocity of the relative altitude to the planet and sling off in a line or tangent from the brief orbit it created.
Its the same that can happen with a basketball circling a net. Or a golf putt circling the hole.
If there is enough energy in the ball and its on juuust the right (wrong for the player, lol) part of the rim, it can loop the rim, gain a bit of extra speed from starting to fall into the basket, then use that extra speed to actually skip back up and out if the angle was right.
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