Shouldn't tidal locking be impossible for a satellite that has a considerably eccentric orbit?

Question

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?

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. — Ilmari Karonen, Aug 09 '20 at 14:22
The moon is tidally-locked anyway because moons don't care what astrophysicists say is possible. — Comic Sans Seraphim, Aug 10 '20 at 15:03

score 27 · Accepted Answer · edited Aug 10 '20 at 11:13

27

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.

edited Aug 10 '20 at 11:13

Ruslan

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answered Aug 08 '20 at 23:26

SpaceCore

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+1! Possibly of interest: Roughly express how much of our Moon's apparent libration amplitude seen from the Geocenter is due to different effects? and also How “locked” are Pluto and Charon? How much does each librate as seen from the other? – uhoh Aug 09 '20 at 03:16

John Doty · Answer 2 · 2020-08-09T19:39:20.813

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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.

edited Aug 09 '20 at 19:39

answered Aug 09 '20 at 14:35

John Doty

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Mercury's rotation is such that the Sun stands nearly still in its sky at perihelion when the tide is strongest. – Anton Sherwood Aug 13 '20 at 03:06

Shouldn't tidal locking be impossible for a satellite that has a considerably eccentric orbit?

2 Answers2