Earth has to rotate a little farther
Earth rotates eastward once in roughly 24 hours relative to the Sun. During the same day, the Moon also moves eastward along its orbit by about 13 degrees relative to the stars. After Earth completes one ordinary daily rotation, it must turn a little farther before your location faces the Moon again.
That extra rotation usually makes moonrise later on the clock from one date to the next. The familiar average delay is close to 50 minutes.
Why the delay is not always 50 minutes
The Moon’s orbit is elliptical and tilted. Its speed and declination change. Your latitude and the angle at which the Moon’s path crosses your horizon matter too. Near some seasons and latitudes, much of the Moon’s daily motion runs nearly parallel to the horizon, producing a small rise-time delay. At other times the path is steep and the delay can exceed an hour.
High latitudes can produce more extreme behavior, including dates with no moonrise or no moonset within a civil day.
Phase provides a rough clock
The cumulative delay explains why new Moon rises near sunrise, first quarter around midday, Full Moon near sunset, and last quarter around midnight. Those are approximations. Exact local moonrise requires calculation for the date and coordinates, especially when terrain or a planned photograph makes minutes matter.
