On Oct 7, 12:13*pm, Crown-Horned Snorkack
wrote:

Suppose that the Moon were somehow turned 180 degrees in longitude,
and stopped there...

Then it would still be tidally locked. Stopped is stopped.
Furthermore, turning the Moon 180° still aligns the long axis with the
Earth-Moon line... so it's still locked in that sense as well. Even if
you turned it just 90°, you wouldn't necessarily have a change in
rotational state (although you might have some significant Moon-quakes
- i'n not sure what the relaxation timescale is under those
conditions).

What would its period of free libration then be? Still 1056 days?

Hmm. What liberation are you refering to? I was thinking about the
liberation due to the eccentricity of the lunar orbit. There are
diurnal liberations of the Moon (due to viewing angle from the limbs
of the Earth), monthly liberations of the Moon (due to the orbital
eccentricity and therefore varying orbital speed), and even longer
term components (due to the precession of the lunar orbit with respect
to the Earth's equatorial bulge). But none of these are due to a
variation in the rotation - they are due to variations in orbital
elements. The rotation is very constant.

--
Brian Davis