Lunar precession

Precession is the rotation of a plane (or its associated perpendicular axis) with respect to a reference plane. The orbit of the Moon has two important such precessional motions.

First, the long axis (line of the apsides: perigee and apogee) of the Moon's elliptical orbit precesses Eastward about once in just under 9 years. It is caused by the solar tide. This is the reason that an anomalistic month (the period of time that the Moon moves from the perigee to the apogee and to the perigee again) is longer than the sidereal month (the period of time when the Moon completes one revolution with respect to the fixed stars). This apsidal 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 (8.85 years).

This apsidal precession also causes the full moon cycle, which can be interpreted as the time for the Sun to make 1 revolution with respect to the lunar perigee, to be longer (by almost 2 months) than a sidereal year.

There are approximately two such lunar apsidal precession cycles in a Saros cycle.

Another precession is that of the lunar nodes; that is, the line along which the plane of the Moon's orbit and that of Earth's orbit intersect. This is mainly caused by the flattening of the Earth; it is the period of the main nutation term in the orientation of the polar axis of the Earth. This nodal period is about twice as long (about 18.6 years) as the apsidal precession period discussed above, and the direction of motion is Westward. This is the reason that a draconic month (the period of time that the Moon takes to return to the same node) is shorter than the sidereal month. After one nodal precession period, the number of draconic months exceeds the number of sidereal months by exactly one. This period is about 6793 days (18.60 years).

As a result of this nodal precession, the time for the Sun to return to the same node, the eclipse year, is about 18.623 days shorter than a sidereal year. The number of years of the nodal period equals the length of the year divided by this deficit, minus one.

Referenced

Explanatory Supplement to the Astronomical Almanac, P.K. Seidelmann (ed.), US Naval Observatory / University Science Books (1992): pp. 114,115; p. 701