The Moon makes a complete orbit around the Earth with respect to the fixed stars about once every 27.3 days[g] (its sidereal period). However, since the Earth is moving in its orbit about the Sun at the same time, it takes slightly longer for the Moon to show the same phase to Earth, which is about 29.5 days[h] (its synodic period). Unlike most satellites of other planets, the Moon orbits nearer the ecliptic plane than to the planet's equatorial plane. The Moon's orbit is subtly perturbed by the Sun and Earth in many small, complex and interacting ways. For example, the plane of the Moon's orbital motion gradually rotates, which affects other aspects of lunar motion. These follow-on effects are mathematically described by Cassini's lawsThe Moon completes its orbit around the Earth in approximately 27.5 days (a sidereal month). The Earth and Moon orbit about their barycentre (common centre of mass), which lies about 4600 km from Earth's centre (about three quarters of the Earth's radius). On average, the Moon is at a distance of about 385000 km from the centre of the Earth, which corresponds to about 60 Earth radii. With a mean orbital velocity of 1,023 m/s, the Moon moves relative to the stars each hour by an amount roughly equal to its angular diameter, or by about 0.5°. The Moon differs from most satellites of other planets in that its orbit is close to the plane of the ecliptic, and not to the Earth's equatorial plane. The lunar orbit plane is inclined to the ecliptic by about 5.1°, whereas the Moon's spin axis is inclined by only 1.5°. Properties Lunar perigee–apogee size comparison Earth's lunar orbit perturbation basics Definition of orbital parameters. The properties of the orbit described in this section are approximations. The Moon's orbit around the Earth has many irregularities (perturbations), whose study (lunar theory) has a long history. Elliptic shape The orbit of the Moon is distinctly elliptical with an average eccentricity of 0.0549. The non-circular form of the lunar orbit causes variations in the Moon's angular speed and apparent size as it moves towards and away from an observer on Earth. The mean angular daily movement relative to an imaginary observer at the barycentre is 13.176° to the east (Julian Day 2000.0 rate). Line of apsides The orientation of the orbit is not fixed in space, but precesses over time. The nearest and farthest points in the orbit are the perigee and apogee respectively. The line joining these two points (the line of apsides) rotates slowly in the same direction as the Moon itself (direct motion), making one complete revolution in 3232.6054 days or about 8.85 years Elongatio
The Moon's elongation is its angular distance east of the Sun at any time. At new moon it is zero and the Moon is said to be in conjunction. At full moon the elongation is 180° and it is said to be in opposition. In both cases the Moon is in syzygy, that is, the Sun, Moon and Earth are nearly aligned. When elongation is either 90° or 270° the Moon is said to be in quadrature. Nodes The nodes are points at which the Moon's orbit crosses the ecliptic. The Moon crosses the same node every 27.2122 days, an interval called the draconic or draconitic month. The line of nodes, the intersection between the two respective planes, has a retrograde motion: for an observer on Earth it rotates westward along the ecliptic with a period of 18.60 years, or 19.3549° per year. When viewed from celestial north, the nodes move clockwise around the Earth, opposite the Earth's own spin and its revolution around the Sun. Lunar and solar eclipses can occur when the nodes align with the Sun, roughly every 173.3 days. Lunar orbit inclination also determines eclipses; shadows cross when nodes coincide with full and new moon, when the sun, earth, and moon align in three dimensions. Inclination The mean inclination of the lunar orbit to the ecliptic plane is 5.145°. The rotation axis of the Moon is also not perpendicular to its orbital plane, so the lunar equator is not in the plane of its orbit, but is inclined to it by a constant value of 6.688° (this is the obliquity). One might be tempted to think that as a result of the precession of the Moon's orbital plane, the angle between the lunar equator and the ecliptic would vary between the sum (11.833°) and difference (1.543°) of these two angles. However, as was discovered by Jacques Cassini in 1721, the rotation axis of the Moon precesses with the same rate as its orbital plane, but is 180° out of phase (see Cassini's Laws). Thus, although the rotation axis of the Moon is not fixed with respect to the stars, the angle between the ecliptic and the lunar equator is always 1.543°. Lunar standstill During the June Solstice the Ecliptic reaches the highest declination in the southern hemisphere, ?23°29?. When at the same time the ascending node has a 90° angle with the Sun in the southern hemisphere, the declination of the Full Moon in the sky reaches a maximum at ?23°29? – 5°9? or ?28°36?. This is called the major standstill or Lunistice in the southern hemisphere. Nine and a half years later, when the descending node has a 90° angle with the December Solstice the declination of the Full Moon in the sky reaches a maximum at 23°29? + 5°9? or 28°36?. The other major standstill or Lunistice, this time in the northern hemisphere.