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This popped up into my mind just now. The Moon is tidally locked to Earth, and also has a significantly eccentric orbit. This means that its orbital velocity near periapsis is considerably faster than its orbital velocity at apoapsis.

Thus, for the Moon to always show one side to Earth, its rotation around its own axis has to slow down and speed up depending on where it is in its orbit, but doesn't that violate the law of conservation of angular momentum? And if its rotation around its axis was constant then it would get out of sync and not be tidally locked, no?

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    $\begingroup$ Just for a reference point, "considerably faster" here means about 10% faster. That's not negligible, but also not the kind of orders-of-magnitude speed difference that you'd see with a really eccentric orbit like e.g. that of a comet or a satellite in a Molniya orbit. $\endgroup$ – Ilmari Karonen Aug 9 '20 at 14:22
  • $\begingroup$ The moon is tidally-locked anyway because moons don't care what astrophysicists say is possible. $\endgroup$ – Studoku Aug 10 '20 at 15:03
  • $\begingroup$ silence contrarian $\endgroup$ – ChristieToWin Aug 10 '20 at 19:29
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You are right, that would be weird if the Moon speeds up and slows down this way to always show the exact same side to the Earth. That's why it doesn't.

At some point in the orbit the Moon's rotation (its phase) lags behind and at some point it is too fast. It is (pretty much) constant and does not adjust to the varying orbital velocity. That's (one reason) why it wobbles. And this wobble is what's called libration.

But the Moon is still tidally locked as its rotation period is still equal to its orbital period.

Lunar libration

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With a more eccentric orbit, tidal control of the rotation does not lead to a librating lock. Mercury is in a 3:2 spin-orbit resonance. Hyperion's spin is chaotic: it gets a quasi-random kick each close approach to Saturn. So, your question is a good one, and the phenomena are rich. The Moon is merely an example of the simplest case.

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    $\begingroup$ Mercury's rotation is such that the Sun stands nearly still in its sky at perihelion when the tide is strongest. $\endgroup$ – Anton Sherwood Aug 13 '20 at 3:06

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