Orbit of the Moon
The orbit of the Moon is, while stable, highly complex, and as such still studied by lunar theory. Most models describe the Moon's orbit geocentrically, but while the Moon is mainly bound to Earth, it orbits with Earth, as the Earth-Moon system around their shared barycenter. From a heliocentric view its geocentric orbit is the result of Earth perturbating the Moon's orbit around the Sun. It orbits Earth in the prograde direction and completes one revolution relative to the Vernal Equinox and the fixed stars in about 27.3 days, and one revolution relative to the Sun in about 29.5 days.
On average, the distance to the Moon is about from Earth's centre, which corresponds to about 60 Earth radii or 1.28 light-seconds.
The barycentre lies about from Earth's centre. With a mean orbital speed around the barycentre of, the Moon covers a distance of approximately its diameter, or about half a degree on the celestial sphere, each hour.
The Moon differs from most regular satellites of other planets in that its orbital plane is closer to that of its primary – the ecliptic, the plane of Earth's orbit – than to the primary's equatorial plane. The Moon's orbital plane is inclined about 5.1° from the ecliptic.
Orbital system
The orbit of the Moon is complex and dependent on many factors, to such an extent that it has given rise to a long and still ongoing development of lunar theory, ever so precisely studying and approximating the orbit of the Moon. Orbits in general are shaped by different forces, such as gravity and the body's velocities, giving rise to centripetal forces. Gravitationally the Moon is like any other mass attracting as well as attracted by all other masses. The interaction of the Moon, Earth and Sun has been understood as a gravitational system and identified as the oldest three-body problem of astronomy, with possibly the need to understand it as a system determined by even more factors, including but mostly negligible also influenced by the gravity of Jupiter or any number of bodies, such as the planets.The strongest gravitational pull on the Moon is towards the Sun, more than twice that towards Earth. At the same time does the Moon remain within Earth's sphere of influence, producing stronger tidal forces on it than the Sun.
File:comparison of Hill sphere and Roche limit.svg|thumb|A schematic of Hill spheres and Roche limits of each body of the Sun-Earth-Moon system. The actual Hill radius for the Moon is on the order of 60,000 km.
The velocity relative to the Sun of a moon is always on average equal to their primary's velocity. But in order to differentiate to trojans and quasi-satellites, true moons need to also remain and not just temporarily stay within the sphere of influence, meaning to equalize oscillating acceleration away and to the primary. The Moon is as such on average matching Earth's heliocentric velocity of 30 km/s and oscillates on average equally in being pulled and dragged by the gravitational attraction with Earth. The orbit of the moon does not offset the shared heliocentric velocity with the primary, transferring velocity, by adding and subtracting velocity unevenly during oscillation. So it not only stays within the sphere of influence, oscillating in it for the time being, but also stays in it, oscillating stable.
Additionally and in contrast to Io the moon of Jupiter, the velocity of the Moon around Earth of 1 km/s is not greater than their heliocentric velocity, making the Moon not go in its heliocentric orbit backwards and forwards in loops, but instead keeps bending toward the Sun, never outward. In representations of the Solar System, it is common to draw the trajectory of Earth from the point of view of the Sun, and at the same time the trajectory of the Moon from the point of view of Earth. This could give the impression that the Moon orbits Earth in such a way that sometimes it goes backwards when viewed from the Sun's perspective. However, because the orbital velocity of the Moon around Earth is small compared to the orbital velocity of Earth about the Sun, this never happens. There are no rearward loops in the Moon's solar orbit.
Consequently, the Moon's trajectory is always convex, and is nowhere concave or looped. That is, the region enclosed by the Moon's orbit of the Sun is a convex set.
The Moon's and Earth's orbital paths in a heliocentric view can cross, making in a geocentric view the orbit going around Earth possible, while at the same time stay curved towards the Sun, because the interchanging of the bending of the orbits by each other's attraction is enough to make the paths cross, but too few to either bend away from the Sun.
Orbital centre
The Moon and Earth together have a centre of mass, an orbital barycentre, which remains located within Earth at about from Earth's centre, which is roughly 3/4 of Earth's radius. This barycentre slightly moves as the distance between the Moon and Earth changes over the course of their orbits, and over long periods of time the barycentre moves and eventually exits the Earth, because of the Moon slowly orbiting further away from Earth, as tidal friction drains energy from the rotating pair. The centre of gravity of the Earth–Moon system is about or 73.3% of the Earth's radius from the centre of the Earth. This centre of gravity remains on the line between the centres of the Earth and Moon as the Earth completes its diurnal rotation. The path of the Earth–Moon system in its solar orbit is defined as the movement of this mutual centre of gravity around the Sun. Consequently, Earth's centre veers inside and outside the solar orbital path during each synodic month as the Moon moves in its orbit around the common centre of gravity.The Sun pulls gravitationally stronger on the Moon than Earth does, making the Moon primarily orbit the Sun, not the Earth; this in turn makes, in a heliocentric frame of reference, the Moon's orbit perturbated by Earth.
Status
This has led some scientists to argue that the Moon could be identified as a planet, both historically and qualitatively, adding that its mass would be enough to clear its orbit around the Sun if it were on its own. This would imply that the Earth-Moon system is a double planet, which is conflicting with the defintion of what qualifies as a planet by the International Astronomical Union standards organization. The IAU though has no well established definition for planetary binary systems, or for what constitutes a double planet system, but has stated and most scientists agree that this would require the Moon-Earth barycentre to be outside of Earth.Direction
When viewed from the north celestial pole the Moon orbits Earth anticlockwise and Earth orbits the Sun anticlockwise, and the Moon and Earth rotate on their own axes anticlockwise.The right-hand rule can be used to indicate the direction of the angular velocity. If the thumb of the right hand points to the north celestial pole, its fingers curl in the direction that the Moon orbits Earth, Earth orbits the Sun, and the Moon and Earth rotate on their own axes.
Properties
The properties of the orbit described in this section are approximations. The Moon's orbit around Earth has many variations due to the gravitational attraction of the Sun and planets, the study of which has a long history.With a mean orbital speed around the barycentre of, the Moon covers a distance of approximately its diameter, or about half a degree on the celestial sphere, each hour.
Elliptic shape
The orbit of the Moon has an eccentricity of 0.0549, with perigee and apogee distances of 363,300 km and 405,507 km respectively.The full Moon's apparent size as seen from Earth depends on how close it occurs to perigee. A full moon near perigee is known as a "supermoon". The largest possible apparent diameter of the Moon is some 12% larger than the smallest; the apparent area is then 25% greater and so is the amount of light it reflects toward Earth.
Elongation
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.Precession
The orientation of the orbit is not fixed in space but rotates over time. This orbital precession is 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 lunar orbit'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 – meaning precesses eastward by 360°. The Moon's apsidal precession is distinct from the nodal precession of its orbital plane and axial precession of the moon itself.Inclination
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.The rotational axis of the Moon is 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°. As was discovered by Jacques Cassini in 1722, the rotational axis of the Moon precesses with the same rate as its orbital plane, but is 180° out of phase. Therefore, the angle between the ecliptic and the lunar equator is always 1.543°, even though the rotational axis of the Moon is not fixed with respect to the stars. It also means that when the Moon is farthest north of the ecliptic, the centre of the part seen from Earth is about 6.7° south of the lunar equator and the south pole is visible, whereas when the Moon is farthest south of the ecliptic the centre of the visible part is 6.7° north of the equator and the north pole is visible. This is called libration in latitude.