Orbit of the Moon

The Moon orbits Earth in the prograde direction and completes one revolution relative to the stars in about 27.32 days (a sidereal month) and one revolution relative to the Sun in about 29.53 days (a synodic month). Earth and the Moon orbit about their barycenter (common center of mass), which lies about 4,600 km (2,900 mi) from Earth's center (about three-quarters of the radius of Earth). On average, the distance to the Moon is about 385,000 km (239,000 mi) from Earth's center, which corresponds to about 60 Earth radii.Scale model of the Earth–Moon system: Sizes and distances are to scale. It represents the mean distance of the orbit and the mean radii of both bodies. The Moon orbits Earth in the prograde direction and completes one revolution relative to the stars in about 27.32 days (a sidereal month) and one revolution relative to the Sun in about 29.53 days (a synodic month). Earth and the Moon orbit about their barycenter (common center of mass), which lies about 4,600 km (2,900 mi) from Earth's center (about three-quarters of the radius of Earth). On average, the distance to the Moon is about 385,000 km (239,000 mi) from Earth's center, which corresponds to about 60 Earth radii. With a mean orbital velocity of 1.022 km/s (0.635 miles/s), the Moon covers a distance approximately its diameter, or about half a degree on the celestial sphere, each hour. The Moon differs from most satellites of other planets in that its orbit is close to the ecliptic plane instead of that of its primary (in this case, Earth's) equatorial plane. The Moon's orbital plane is inclined by about 5.1° with respect to the ecliptic plane, whereas the Moon's equatorial plane is tilted by only 1.5°. The properties of the orbit described in this section are approximations. The Moon's orbit around Earth has many irregularities (perturbations), the study of which (lunar theory) has a long history. The orbit of the Moon is a nearly circular ellipse about the Earth (the semimajor and -minor axes are 384,400 km and 383,800 km, respectively; a difference of only 0.14%). The equation of the ellipse yields an eccentricity of 0.0549, and, perigee and apogee distances of 362,600 km and 405,400 km respectively (a difference of 12%). Since nearer objects appear larger, the Moon's apparent size changes as it moves toward and away from an observer on Earth. An event referred to as a 'Supermoon' occurs when the Moon is at its closest to Earth (perigee). The variance in the Moon's orbital distance corresponds with changes in its tangential and angular speeds, as stated in Kepler's second law. The mean angular movement relative to an imaginary observer at the Earth-Moon barycentre is 13.176° per day to the east (Julian day 2000). 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. The orientation of the orbit is not fixed in space, but rotates over time. This orbital precession is also called apsidal precession and is the rotation of the Moon's orbit within the orbital plane, i.e. the axes of the ellipse change direction. The Moon's major axis – the longest diameter of the orbit, joining its nearest and farthest points, the perigee and apogee, respectively – makes one complete revolution every 8.85 Earth years, or 3,232.6054 days, as it rotates slowly in the same direction as the Moon itself (direct motion). The Moon's apsidal precession is distinct from the nodal precession of its orbital plane and axial precession of moon itself. The mean inclination of the lunar orbit to the ecliptic plane is 5.145°. Theoretical considerations show that the present inclination relative to the ecliptic plane arose by tidal evolution from an earlier near-Earth orbit with a fairly constant inclination relative to Earth's equator. It would require an inclination of this earlier orbit of about 10° to the equator to produce a present inclination of 5° to the ecliptic. It is thought that originally the inclination to the equator was near zero, but it could have been increased to 10° through the influence of planetesimals passing near the Moon while falling to the Earth. If this had not happened, the Moon would now lie much closer to the ecliptic and eclipses would be much more frequent.