Final answer:
The Moon completes its cycle of phases in approximately 29.5 days, a period slightly longer than the sidereal month of about 27.3 days, with the difference due to Earth's movement around the Sun.
Step-by-step explanation:
Moon Phases and Their Duration
The Moon goes through a complete cycle of phases approximately every 29.5 days. This cycle is observable as the Moon transitions from a new moon, where it is not visible, to a full moon, where the entire face is illuminated, and back to a new moon again. The sidereal month, which is the time it takes for the Moon to return to the same position among the stars, is slightly shorter, totaling about 27.3217 days.
The difference in these two periods is due to the Earth's motion around the Sun; as the Earth moves, the Moon needs to 'catch up' to return to the same phase as seen from Earth. Additionally, after the full moon, the Moon starts to wane, moving through the third quarter phase where it rises around midnight and takes about a week to return to the new moon phase. Daily, the Moon moves eastward in the sky, traveling its own diameter in just under an hour, causing a delay in moonrise of about 50 minutes day to day.