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Any two bodies locked in an orbit rotate around a common barycenter:...

Both objects in an orbit are stretched along both sides.
Their natural rest state is in a higher, slower orbit. This causes the far side of the object to bulge outwards as it attempts to escape into this higher orbit.

Yup, that's the explanation I was trying to get out.

Why don't all these people trying to explain tides explain it the way _you_ just did intead of all that gobbledygook about the moon's gravity attracting the water, and then some vague handwaving to explain the tide opposite the moon?

You did it is just two sentences, and it is completely understandable.

(I was much older than a kid when I got interested in orbital mechanics.)

FWIW, I looked up slingshot maneuver, and I now understand it. The spacecraft steals momentum from the planet/star to impart the sideways delta-vee.
Still don't quite grasp why doing an impulse acceleration at the deepest part (closest approach) gives a multiplicative boost. Gonna have to read and re-read that a few times. It's been a long time since I messed with integrals.
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