It rotates so slowly, there may be no data available.
The pseudoforces are, of course, key to this argument. Although we may not yet have been able to measure them on the Moon, they do have readily measurable effects on other synchronous moons, particularly those close to the Roche limit. Simple tidal distortion produces an equilibrium shape that is a prolate spheroid, with a long axis (aligned radially) and two short axes of equal length. Add the synchronous rotation, however, and the equilibrium shape is triaxial: short polar axis, long radial axis, and an intermediate axis at right angles to these. And we observe the latter, rather than the former.
Another way to think about the rotational pseudoforces is to realize that the residuals look the same no matter where we place our rotation axis. So we can imagine the moon rotating around an external axis at the centre of its orbit, or we can decompose the motion into a uniform revolution and a superimposed rotation around an axis in the centre of the moon. The pseudoforces sum out exactly the same way.
Does that mean my thought experiment holds good too, as one of the valid ways of concieving the situation, if the sums work out whether the axis of rotation is concieved to be in the moon or at the barycenter?
Originally Posted by stroller
Imagine the moon were set, with many tons of superglue, into the rim of a wheel whose hub was at the barycentre. throughout the revolution of the wheel, the moon would remain still in relation to the rim it's set in.
So the moon doesn't 'rotate on it's own axis', it 'revolves' around the barycentres axis, at the same rate it orbits it.