As the Moon orbits around the Earth, we see different phases, ranging from (the invisible) New Moon through First Quarter, Full Moon, Third Quarter, and back to New Moon.
There are several different periods which astronomers use to describe the motion of the Moon.
sidereal period is the time it takes for the Moon to move by 360 degrees around the Earth, as seen by an observer floating high above the plane of the solar system. The sidereal period of the Moon's orbit is about 27.3 days.
synodic period is the time from one Full Moon to the next Full Moon (or from one New Moon to the next New Moon). This is a little longer than the sidereal period because the Moon has to "catch up" to the motion of the Earth around the Sun. The synodic period of the Moon's orbit is about 29.5 days
turns out that the synodic and sidereal periods of a moon around its planet are related to the planet's orbital period around the Sun:
1 1 1
--------------- = --------------- - -----------------------
synodic period sidereal period planet's orbital period
If you look more closely at the Moon over the course of a full cycle, you'll start to see small variations in its size -- due to the eccentricity of the Moon's orbit around the Earth -- and very small changes in the visibility of regions near the limbs -- again due to the eccentricity of the Moon's orbit.






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