Final answer:
The Moon's sidereal month, which is the time for a complete orbit relative to the stars, is 27.3217 days, while the synodic month, the time from one lunar phase to the same phase, is 29.5306 days.
Step-by-step explanation:
The Moon orbits around the Earth in what we call a sidereal month which is 27.3217 days long. This is the period for the Moon to complete one orbit relative to the stars. However, because the Earth is also moving in its orbit around the Sun, we commonly refer to the synodic month when referring to the lunar phases, which is 29.5306 days. This is the time it takes for the Moon to reach the same phase, such as from full moon to full moon.
The difference between the sidereal month and the synodic month arises due to the Earth's motion around the Sun. As the Earth moves, the Moon has to travel a bit further to return to the same phase relative to the Sun. The motion of the Moon in the night sky is apparent on a daily basis, as it moves eastward among the stars by its own diameter in just under an hour, causing a 50-minute delay in moonrise from one day to the next.