Lunar precession
Encyclopedia
Precession
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...

 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
Perigee
Perigee is the point at which an object makes its closest approach to the Earth.. Often the term is used in a broader sense to define the point in an orbit where the orbiting body is closest to the body it orbits. The opposite is the apogee, the farthest or highest point.The Greek prefix "peri"...

 and apogee) of the Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...

's elliptical orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...

 precess
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...

es Eastward about once in just under 9 years. It is caused by the solar
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 tide
Tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the moon and the sun and the rotation of the Earth....

. 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
Full moon cycle
The full moon cycle is a cycle of about 14 lunations over which full moons vary in apparent size and age . The sequence is*Full moon big - *Full moon young -...

, 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
Sidereal year
A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. Hence it is also the time taken for the Sun to return to the same position with respect to the fixed stars after apparently travelling once around the ecliptic. It was equal to at noon 1 January...

.

There are approximately two such lunar apsidal precession cycles in a Saros cycle
Saros cycle
The saros is a period of 223 synodic months , that can be used to predict eclipses of the Sun and Moon. One saros after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, and a nearly identical eclipse will occur, in what is referred to as an eclipse cycle...

.

Another precession is of the node
Lunar node
The lunar nodes are the orbital nodes of the Moon, that is, the points where the orbit of the Moon crosses the ecliptic . The ascending node is where the moon crosses to the north of the ecliptic...

s of the orbit of the Moon on the plane of the ecliptic
Ecliptic
The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...

 (the plane of the lunar orbit is inclined to the ecliptic, and the points where they intersect- the nodes - precess). This is mainly caused by the flattening of the Earth; it is the period of the main nutation
Nutation
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism...

 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).

This nodal precession causes that the time for the Sun to return to the same node, the eclipse year, is about 18.623 days shorter than a sidereal year
Sidereal year
A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. Hence it is also the time taken for the Sun to return to the same position with respect to the fixed stars after apparently travelling once around the ecliptic. It was equal to at noon 1 January...

. 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
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