Again, it's wonderful to have taken Astronomy in college. We had a lab on this very thing! Moonrise is quite simple, actually, it is the moment when the moon appears over the horizon of the earth.
Moon rise will differ depending on where on the earth a person is standing. Keep in mind that moon rise may not be during the night! Moon rise can be in the very middle of the brightest day!
In this regard, sometimes we cannot see moon rise for many different reasons. Perhaps the light of the sun is brighter than the moon's reflection. Perhaps there is a tree or a mountain in the way.
All of these things are so (and further moon rise actually HAPPENS) due to the fact that the moon orbits the earth and it does so in exactly 27 of the earth's days. (We have to use the word "earth's" here because the earth's day differs vastly from a "day" on any other planet.)
Another interesting fact is that moon rise has absolutely nothing to do with moon phases, which is something else entirely. Moon phases, of course, have to do with the shape of the moon that we can see at different times and at different locations.
Moon rise is the first appearance of the Moon over the Earth’s horizon.The rising of the Moon changes from day to day and location to location because the Moon is orbiting round the Earth. The Moon takes just 27 days to complete an orbit around the Earth, so we can actually trace its movement in the sky every hour. And so we see the different shapes of the Moon every night.