Full moon cycle

The full moon cycle is a cycle of about 14 lunations over which full moons vary in apparent size and age (time since new moon). The sequence is

The apparent size of the Moon varies because the orbit of the Moon is elliptical, and as a consequence at one time it is nearer to the Earth (perigee) than half an orbit later (apogee). The orbital period of the Moon from perigee to apogee and back to perigee is called the anomalistic month.

The appearance, or phase, of the Moon is due to its motion with respect to the Sun. It varies in a period of time called a lunation, also called synodic month; its duration is about 2 days longer than an anomalistic month. The age is the number of days since new moon.

As a consequence, the apparent diameter of a full moon varies, depending on when it occurs in the anomalistic month: larger near the Earth (near perigee); or smaller when more distant (near apogee).

Also, like all celestial bodies, the speed of the Moon varies in its elliptic orbit: faster near perigee, and slower near apogee. So the time of the half lunation between a new moon and the next full moon varies, depending on where in the elliptical orbit it begins, and so affects the age of the full moon.

The full moon cycle is slightly less than 14 synodic months and slightly less than 15 anomalistic months. Its significance is that when you start with a full moon at the perigee - which appears large, then subsequent full moons will occur ever later after the passage of the perigee; after 1 full moon cycle, the accumulated difference between the number of completed anomalistic months and the number of completed synodic months is exactly 1, and the full moon occurs again at perigee, giving a large apparent moon.

The average duration of the anomalistic month is:

The synodic month has an average duration of:

The full moon cycle is the beat period of these two, and has a duration of:

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