Most of us think Moon does the night-duty in an office where Sun does the day-duty. Majority of our literature pictures Moon like that; someone who rises in the evening after sunset and sets when Sun rises. But the fact remains, only once in a month our Moon does like that. If you are a good observer without much knowledge in astronomy, you may know that the fact I said is right. But still, you don't know why it is like that. This time we will talk about the Moon's drama up there in the sky.
Here the situations of Moon being at different positions around Earth is shown. Sunlight will illuminate Moon as it does to Earth. As Moon is a sphere, only half of it will be illuminated at a time (Exactly this is how half of Earth experience day and other half experience night at the same time. When at one side of Earth it is noon, the opposite side of it will have a midnight as shown in picture). As Moon goes once around Earth in every 27 (approx) days, its position around Earth with respect to the Sun rays will be different on every day of this 27 days period. Just take a little time to look at the picture. Seeing from Earth, when Moon is in the direction where sunlight comes from, the part of Moon illuminated by Sun is on the back side and so we cannot see Moon at all. In other words, we are seeing the 'night' in Moon. That day is what we call New Moon. Now consider when the position of Moon is opposite to the direction of Sun, the whole of illuminated Moon is visible to us, giving us a full moon day. (From picture you can also make out that a full moon comes right ahead on sky at midnight) On all other days we can see only a part of illuminated surface of Moon which becomes larger when we go from new moon day to a full moon day. In short it is not the shadow of Earth but the shadow of Moon itself, that causes the phases.
Now let us come to the point in title. First of all, we have to remember that the rise and set of any object on sky is due to the rotation of Earth around its on axis. As we have seen, on a new moon day Sun and Moon are on the same direction and so they rise together. (Yes, Sunrise and Moonrise are together!) But on a full moon day, they are on opposite positions and so Moonrise and Sunset happens together. That means Moon can rise at any time. On a particular day it will rise 5o minutes later it rose the previous day due to its motion in its orbit around Earth.