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The Moon's rotation is firmly tidally locked to the Earth and the Earth's rotation is firmly tidally unlocked with respect to the Moon. I gather that Mercury's rotation is tidally locked in a 3:2 resonance - which sounds a little precarious. Are there any bodies which are on the verge of being tidally locked (very nonuniform rotation) or are barely tidally locked (very large libration)? Are there any bodies whose rotation is actually chaotic for such reasons?

[Edit] Note, this question is about the physical libration rather than the apparent or optical libration caused by the body being observing from different perspectives.

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    $\begingroup$ Libration is not an expression of the "quality" of tidal locking. It is an expression of the excentricity and obliquity of the orbit of the tidally-locked body. $\endgroup$ Dec 11, 2020 at 8:18
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    $\begingroup$ Great question! This is not the same thing but it's quite an interesting related situation: Is Venus in some way tidally locked to… Earth? $\endgroup$
    – uhoh
    Dec 11, 2020 at 14:52
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    $\begingroup$ @planetmaker that's not correct. You've only described optical libration. Now read about true libration which is what the OP is describing. Our Moon does both, the latter is small now, but it would have been quite wild at some point the past. $\endgroup$
    – uhoh
    Dec 11, 2020 at 14:59
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    $\begingroup$ @uhoh That paper on the Moon's libration is surely a classic. There's something special about papers like this that were written well before the age of computers. $\endgroup$
    – Roger Wood
    Dec 12, 2020 at 4:14
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    $\begingroup$ The magnitude of tidal forces decreases with a power of 7..8 of the distance of two bodies (as far as I remember). This means that tidal locking either occurs very quickly (on astronomical time scales) or never. The chances to find an object in the middle of the transition from unlocked to locked is thus very small. $\endgroup$ Dec 12, 2020 at 8:07

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The answer to this question is negative, if "almost tidally locked" signifies a small but persistent deviation from an exact resonance. The anwser, however, is positive if "almost tidally locked" implies large-magnitude libration.

Within a tidal two-body problem, a secondary body experiences two torques exerted on it by the primary: a tidal torque ${\cal{T}}_{tide}$ and a torque generated by the permanent dynamical triaxiality of the secondary's figure, ${\cal{T}}_{tri}$ (in practitioners' argo, the "triaxial torque").

For bodies that are rigid or have a solid crust, the triaxiality-caused elevation above the mean level is typically much larger than the hight of the tidal bulge. As a result of this, in a spin-orbit resonance (a synchronous resonance, like the Moon; or higher resonance, like Mercury), ${\cal{T}}_{tri} \gg {\cal{T}}_{tide}$.

Two important caveats are in order, though:
(a) In a spin-orbit resonance, the rotator is subject to forced physical libration of a magnitude $\simeq e^2$.
(b) Outside spin-orbit resonances, ${\cal{T}}_{tri}$ averages out due to rotation, and $ {\cal{T}}_{tide}$ plays a key role.

Usually (the Moon being a notable exception), forced physical libration is predominantly longitudinal. Its evolution is analogous to ordinary pendulum. The torque ${\cal{T}}_{tri}$ splits into two parts, one playing the role of restoring force, another of exterior forcing. Like a pendulum, the rotator is impelled to deviate from the exact equilibrium position, but is pushed back by the restoring part of the torque.

For gas and liquid bodies lacking dynamical triaxiality, we have ${\cal{T}}_{tri} =0$. So dynamics is governed by ${\cal{T}}_{tide}$. Calculation demonstrates that in this situation the rotator always ends up in a so-called pseudosynchronous state, a regime wherein the rotator has an excess angular velocity (as compared to the mean motion $n$) proportional to $6ne^2$. This calculation is presented, with an error, in this standard text, eqn (5.14). A correct calculation can be found in our paper. (Be mindful that the value of said excess in angular velocity is rheology-dependent.)

(2) Now, do pseudosynchronous rotators in the solar system exist? Not to the best of my knowledge.

(3) Are there intensely librating objects? Yes, there are.

Owing to its potatoe shape, Phobos is librating in longitude with a magnitude of $1.2^{\,o}$. Epimetheus has a more regular shape but a larger dynamical triaxiality due to its internal inhomogeneity, so its longitudinal libration magnitude is $5.9^{\,o}$. This is a lot. Libration more than doubles tidal dissipation in Phobos, and boosts tidal dissipation in Epimetheus by a factor of 26 -- more than an order of magnitude.

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    $\begingroup$ great answer, thank you. I suppose at some point these systems go from very non-uniform rotation to having huge libration with occasional 360 degree turns to having a relatively stable very large libration. As others point out, the period of transition is probably very brief in comparison with other time-scales. PS. I wasn't aware of Epimetheus/Janus. That pair sounds quite wild! Do you think Ttide has played a role in how Venus has ended up or is it all about atmospheric convection? $\endgroup$
    – Roger Wood
    Sep 7, 2023 at 3:19
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    $\begingroup$ @RogerWood The spin state of Venus is an equilibrium between gravitational and thermal atmospheric tidal torques, see ui.adsabs.harvard.edu/abs/2003Icar..163....1C/abstract My colleagues and I are actually working on this topic, developing some dissident idea -- which may work out or may as well fail. Bound by omerta, I cannot say more at this point :) $\endgroup$ Sep 7, 2023 at 5:35
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    $\begingroup$ @RogerWood Speaking of Epimetheus and Janus. Both moons are rotationally synchronised with Saturn (up to libration). What makes them unusual is their orbital dance planetary.org/articles/janus-epimetheus-swap $\endgroup$ Sep 7, 2023 at 5:43
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    $\begingroup$ I always thought Venus' spin was explained by convection rather than tidal effects. That looks like an interesting paper. Thanks for the feedback. $\endgroup$
    – Roger Wood
    Sep 7, 2023 at 19:02
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    $\begingroup$ @RogerWood Yes, chaos also kicks in. If the libration magnitudes about both the 1:1 spin-orbit resonance (SOR) and the neighbouring 3:2 SOR become large, then these resonances may overlap. The rotator will be switching chaotically between the two SORs. When the body is very triaxial, or when forcing is very strong, the spin becomes totally chaotic, with many neighbouring SORs overlapping. To add insult to injury, rotation about the z axis may become unstable -- in which case wobble emerges. You may want to look up Alice Quillen's works on tumble excitation in moons, if interested. $\endgroup$ Sep 7, 2023 at 19:21

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