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There are two important precessional motions in the Orbit of the Moon.
The long axis (line of the apsides: perigee and apogee) of the moon's elliptical orbit precesses about once in just under 9 years. It is caused by the solar tide. This precession completes one rotation in the same time as the number of sidereal months exceeds the number of anomalistic months by exactly one, after about 3233 days.
This same geometric theorem results in one less full moon cycle than lunar orbits per solar orbit, and one more year than orbits per precession cycle.
There are approximately two elliptical lunar precession cycles in a Saros cycle.
Another precession is of the lunar nodes of lunar orbit with the plane of the ecliptic. The plane of lunar orbit is inclined in relation to the ecliptic. During one nodal precession, the number of draconic months exceeds the number of lunar orbits by exactly one. This period is about 6793 days (18.6 years). The rotation of the node precedes the year by 18.623 days. The number of years in this cycle equals the year divided by this amount minus one.
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