Final answer:
The moon's lunar cycle, or synodic month, is approximately 29.5 days long, which is the time it takes to cycle through all phases from new moon to new moon. This is different from the moon's sidereal period, the time it takes to orbit the Earth with respect to the stars, which is 27.3217 days. The difference is due to the Earth's orbit around the Sun requiring the moon to orbit a bit more to synchronize its phases with the Sun's position.
Step-by-step explanation:
The Moon's Lunar Cycle
The moon's lunar cycle, commonly referred to as the synodic month, is approximately 29.5 days long. This duration is the time it takes for the moon to complete a full cycle of phases from new moon to new moon. However, it's important to distinguish that this is different from the moon's sidereal period, which is 27.3217 days. The sidereal period represents the time it takes for the moon to orbit the Earth with respect to the stars.
The reason for the difference between the sidereal period and the lunar cycle is due to the Earth's movement around the Sun. As the moon completes its sidereal orbit, the Earth has moved slightly in its own orbit, requiring the moon to go a bit further to reach the same phase position relative to the Sun. Therefore, a lunar month or synodic period is about 1/12 of a month longer than the actual orbital period of the moon.
During this lunar cycle, we witness the various phases of the moon, including the waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, last quarter, and waning crescent, before returning to a new moon. The changing phases represent different angles of solar illumination on the moon as viewed from Earth.