What is the difference between a sidereal month and a synodic month? Which is longer? Why?

A sidereal month is the time it takes for the Moon to complete one orbit around the Earth, relative to the background stars. In other words, it is the time required for the Moon to return to the same position in the sky as observed from Earth when considering the distant stars as a reference point. The duration of a sidereal month is approximately 27.3 days.

A synodic month, on the other hand, is the time it takes for the Moon to return to the same phase (e.g., Full Moon to Full Moon, or New Moon to New Moon) as observed from Earth. In other words, it is the time required for the Moon to complete one cycle of its phases, considering the Sun's position as a reference point. The duration of a synodic month is approximately 29.5 days.

When comparing the two, we can see that a synodic month is longer than a sidereal month. The synodic month lasts about 29.5 days, while the sidereal month lasts approximately 27.3 days.

The main reason for the difference in lengths between a sidereal and a synodic month is the motion of the Earth around the Sun. During the time the Moon takes to complete one orbit around the Earth (sidereal month), the Earth has also moved slightly in its orbit around the Sun. As a result, it takes an additional ~2.2 days for the Moon to "catch up" and return to the same position concerning the Sun and show the same phase to an observer on Earth, which is the duration of a synodic month. In summary, the difference between a sidereal month and a synodic month is the reference point used to measure the time it takes for the Moon to orbit the Earth. A sidereal month is based on the background stars, while a synodic month is based on the Sun's position. A synodic month is longer than a sidereal month, with durations of approximately 29.5 days and 27.3 days, respectively. The difference in their lengths can be attributed to the motion of the Earth around the Sun.