A question came up on Outdoors StackExchange, How to tell time at night. I wrote an answer to that question, and in my answer I said that a standard sundial wouldn't work without some fiddling, but that an astronomer would know what fiddling was required. (I invite/encourage any qualified astronomers to go there and answer the question, BTW.)
So I did some searching around, and some thinking about it. Here's the question. Suppose we have an ordinary horizontal sundial, at a fixed latitude (in the Northern hemisphere), which has been calibrated to correctly show solar time at that latitude. The sundial works.
Now, suppose there's a Full moon. What adjustments would be necessary, what additional information is needed, what would it take to transform/convert the ordinary sundial into a moondial? The definition of "success" would be that we could look at the shadow and get the "correct" time, where correct might mean up to the precision of an ordinary sundial which might neglect the Equation of Time (is a different equation needed?). One website I read said that no adjustment was necessary, but I'm not sure I agree.
If that's not too bad, how would the answer change if we were some days off of a full moon? (Obviously, if we are sufficiently far off then there will not be enough light to make a discernible shadow.)
EDIT:
I've been thinking about it a lot, and thinking about the E.o.T.. The EoT has two (dominant) parts: the Kepler eccentricity part, and the oblique axis part. At first I thought the Kepler part wouldn't matter, but then I learned that the Moon/Earth eccentricity (0.055) is even bigger than the Earth/Sun eccentricity (0.017). So it would seem any reliable moondial would need to be corrected for this problem.
I'm still wrapping my head around the obliqueness part. I understand that the style of the gnomon must be angled from the horizontal (equal to the latitude), but that's to make sure the style points toward true north. In fact, even if a horizontal sundial is used at an incorrect latitude, we can fix it by angling the whole sundial so the style points north. Clearly the Moon is in another orbital plane (apparently by about 5 degrees, I'm guessing that's an average), but if we change the angle of the style to compensate for the Moon then it wouldn't be pointing north anymore. So, at the moment, I'm thinking to leave the sundial as-is and then figure (somehow) the sine-wave that describes the Moon's obliqueness.
The further this goes the more it looks like I'm talking about figuring an Equation of Moon Time or similar.
Best Answer
For a perfect full moon, simply change AM to PM and vice versa. For other phases, there's a different offset. First and third quarters would be six hour offsets, etc., though I would have to think a while before stating which was plus and minus. During a total solar eclipse, the times would exactly coincide, and approximately so for a new moon. (Good luck finding the shadow cast by new moonlight.)
Technically, for best precision you ought to account for the equation of time and the slight change in Moon phase over the course of a Moon-day. Also, since the Moon's orbit is inclined with respect to the Earth's, you can't use the same latitude setting all the time, but this is a frikking repurposed sundial we're talking about. If you're really after precise timekeeping, use a technology invented in the last thousand years.