Last week, NASA released an incredible video showing the Moon’s motion and phases over the whole year of 2013, where each frame of the video is one hour of time! It’s mesmerizing:
If you have the bandwidth, change the resolution to full, 1080p HD (using the cog icon at the bottom right) -- the extra quality is worth the watch!
The animation uses data from the Clementine lunar mission, a joint NASA and military probe in the 1990s to map the Moon, as well as images and topography measurements from the Lunar Reconnaissance Orbiter. The surface-elevation measurements were used to create the realistic shadows in the animation.
You'll noticed that the Moon appears to rock around, tipping, and tilting over the course of every month. That’s called libration, and is due to the Moon’s orbit being elliptical, as well as the Moon's rotational axis being slightly tilted with respect to its orbit.
There are many other extras to this video, like the scale on the right showing how far the Moon is from the Earth in units of the Earth’s diameter (about 13,000 kilometers, or 8,000 miles). You can watch it oscillate back and forth as it orbits, moving from 28 to 32 times the Earth’s diameter away.
At the bottom right is a huge amount of information that changes with time, including the Moon’s distance and its apparent size, measured in arcseconds. There are 3,600 arcseconds in a degree, and a full Moon is roughly 1,800 arcseconds, or a half degree across.
DIAL-A-MOON Tool: Although the video is fun to watch, NASA's website for the animation may be more useful for night photographers. This site contains all the individual frames used to animate the Moon phases and libration. Their Dial-A-Moon tool will allow you to pick any month, day, and hour of the year and see that phase of the moon (a lot easier than trying to adjust the video)!
Rising and Setting Times: Knowing the phase of the Moon is great, but a night photographer also needs to know the rising and setting times of the moon on any given day. For that you'll also need this USNO table. This table can be changed to show the rising and setting of either the sun or the Moon.
Position of the Moon: Wouldn't it also be nice to know where the Moon would be in the sky on any night and hour? The free planetarium software, Stellarium, can do this for you. All you do is tell it where you are on the earth and what time of the day or night. You can advance or go back to any day, hour, minute, and second in time (you can also speed up time and watch the sky move quickly or slowly). Using the coordinates and time you give Stellarium, you'll be able to see exactly where the moon rises and sets, or where it is in the sky at any hour (as well as all the stars, constellations, and the Milky Way)!