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The slingshot effect is elastic - i.e., the KE before equals
the KE after.
The mass of the planet is so much more than the mass of the
satellite that one sees a visible change in the speed of the
satellite but not the planet.
It's just like a bowling ball striking a stationary tennis
ball. The bowling continues on with no visible change in
speed, whereas the tennis ball moves at twice the speed of
the bowling ball (a slingshot in one dimension!)