Why does the daily moonrise time vary by as much as 60 minutes, and as little as 30 minutes during the same month?

It depends on how far the Moon dips below the horizon from one day to the next. Our satellite moves, on average, 13.2° per day relative to the background stars. But the angle at which the Moon’s orbit (tilted 5° to Earth’s orbit around the Sun) intercepts the eastern horizon varies considerably during any given month. When the angle is steep, the Moon will lie well below the horizon at the same time the following night and Earth must rotate more to bring it into view. When the angle is shallow, Luna dips only a few degrees below the horizon from one night to the next and rises with much less lag time.

Take November 2015 as an example. From 40° north latitude, the biggest lag in moonrise occurs with the waning gibbous Moon on the 30th, which rises 60 minutes later than it did the previous night. The smallest delay happens at the waxing gibbous phase on the 21st, which comes up 36 minutes later than it did the previous day.

A number of other variables play into the time difference. The Moon’s orbital speed is not constant, so its motion relative to the stars can be up to 12 percent faster or slower than the average during the month. Latitude also changes the numbers significantly because it alters the angle at which the lunar orbit meets the eastern horizon. In Nov­ember 2015, the moonrise delay ranges from 42 to 58 minutes at 30° north and from 30 to 63 minutes at 50° north. In general, the closer you live to the equator, the less variation you will see.