Okay, so it has been known for a long time that by (very) carefully timing stellar occultations, one can learn a great deal about stellar sizes and previously unresolved binary stars.

However, I'm interested in the specifics of how this is done, in two respects:

1.) When observing a stellar occultation, I'm guessing that scientists use the sidereal lunar motion corrected for the rotation of the Earth. However, that begs the question: is the sidereal lunar motion we see usually listed that of the Moon as seen from a hypothetical nonrotating Earth (which should just be 360 degrees devided by the Moon's orbital period), or does it include the effect of Earth's rotation, however slight?

2.) Is the sidereal lunar rate only applicable to the Moon's apparent (as opposed to actual) equator? Part of me thinks it is, as a star being occulted at a higher latitude is "moving" increasingly tangential to the lunar disk. If that's the case, then perhaps the sidereal rate varies relative to the cosine of its apparent latitude.

On the other hand, part of me thinks this idea is absurd, because it's obvious that the sidereal rate at its equator (edge of the disk) and (apparent) poles must be the same, as the Moon is a single body.