Explanation
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. The age is the number of days since new moon.
The ellipticity of the orbit also causes the duration of a half lunation to depend 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 large full moon at the perigee, 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.
The average duration of the anomalistic month is:
- AM = 27.55454988 days
The synodic month has an average duration of:
- SM = 29.530588853 days
The full moon cycle is the beat period of these two, and has a duration of:
Read more about this topic: Full Moon Cycle
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