Properties
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.[9]
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 movement relative to an imaginary observer at the Earth-Moon barycentre is 7001131760000000000♠13.176° per day to the east (Julian day 2000).
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
Earth's lunar orbit perturbations
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.
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.[10] 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.[11] If this had not happened, the moon would now lie much closer to the ecliptic and eclipses would be much more frequent.[12]
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° (this is the obliquity). 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 (see Cassini's Laws). 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.[13]
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 the celestial north, the nodes move clockwise around Earth, opposite to 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.
In effect, this means that the "tropical year" on the moon is only 347 days long. This is called the draconic year or eclipse year. The "seasons" on the moon fit into this period. For about half of this draconic year, the sun is north of the lunar equator (but at most 1.543°), and for the other half, it is south of the lunar equator. Obviously, the effect of these seasons is minor compared to the difference between lunar night and lunar day. At the lunar poles, instead of usual lunar days and nights of about 15 Earth days, the sun will be "up" for 173 days as it will be "down"; polar sunrise and sunset takes 18 days each year. "Up" here means that the centre of the sun is above the horizon.[14] Lunar polar sunrises and sunsets occur around the time of eclipses (solar or lunar). For example, at the Solar eclipse of March 9, 2016, the moon was near its descending node, and the sun was near the point in the sky where the equator of the moon crosses the ecliptic. When the sun reaches that point, the centre of the sun sets at the lunar north pole and rises at the lunar south pole.
Inclination to the equator and lunar standstill
Every 18.6 years, the angle between the Moon's orbit and Earth's equator reaches a maximum of 28°36′, the sum of Earth's equatorial tilt (23°27′) and the Moon's orbital inclination (5°09′) to the ecliptic. This is called major lunar standstill. Around this time, the Moon's declination will vary from −28°36′ to +28°36′. Conversely, 9.3 years later, the angle between the Moon's orbit and Earth's equator reaches its minimum of 18°20′. This is called a minor lunar standstill. The last lunar standstill was a minor standstill in October, 2015. At that time the descending node was lined up with the equinox (the point in the sky having right ascension zero and declination zero). The nodes are moving west by about 19° per year. The sun crosses a given node about 20 days earlier each year.
When the inclination of the Moon's orbit to the Earth's equator is at its minimum of 18°20′, the centre of the Moon's disk will be above the horizon every day from latitudes less than 71°40' (90° − 18°20') north or south. When the inclination is at its maximum of 28°36', the centre of the Moon's disk will be above the horizon every day only from latitudes less than 61°24' (90° − 28°36') north or south.
At higher latitudes, there will be a period of at least one day each month when the Moon does not rise, but there will also be a period of at least one day each month when the Moon does not set. This is similar to the seasonal behaviour of the Sun, but with a period of 27.2 days instead of 365 days. Note that a point on the Moon can actually be visible when it is about 34 arc minutes below the horizon, due to atmospheric refraction.
Because of the inclination of the moon's orbit with respect to the earth's equator, the moon is above the horizon at the North and South Pole for almost two weeks every month, even though the sun is below the horizon for six months at a time. The period from moonrise to moonrise at the poles is a tropical month, about 27.3 days, quite close to the sidereal period. When the sun is the furthest below the horizon (winter solstice), the moon will be full when it is at its highest point. When the moon is in Gemini it will be above the horizon at the North Pole, and when it is in Sagittarius it will be up at the South Pole.
The moon's light is used by zooplankton in the Arctic when the sun is below the horizon for months[15] and must have been helpful to the animals that lived in Arctic and Antarctic regions when the climate was warmer.
Scale model
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.
