 Diagram of the Moon's orbit with respect to the Earth. Angles are correct and relative sizes are to scale, but distances are not to scale. | |
| Semi-major axis[a] | 384,748 km (239,071 miles)[1] |
|---|---|
| Mean distance[b] | 385,000 km (239,000 miles)[2] |
| Inverse sine parallax[c] | 384,400 km (238,900 miles) |
| Perigee | 363,300 km (225,700 miles),avg. (356400–370400 km) |
| Apogee | 405,507 km (251,970 miles),avg. (404000–406700 km) |
| Meaneccentricity | 0.0549006 (0.026–0.077)[3] |
| Meanobliquity | 6.687°[5] |
| Meaninclination | |
| of orbit toecliptic | 5.15° (4.99–5.30)[3] |
| of lunar equator to ecliptic | 1.543° |
| Period of | |
| orbit around Earth (sidereal) | 27.322 days |
| orbit around Earth (synodic) | 29.530 days |
| precession of nodes | 18.5996 years |
| precession of line of apsides | 8.8504 years |
Theorbit of theMoon is, while stable, highly complex, and as such still studied bylunar theory. Most models describe the Moon's orbitgeocentrically, but while the Moon is mainly bound toEarth, it orbits with Earth, as theEarth-Moon system around their sharedbarycenter. From aheliocentric view its geocentric orbit is the result of Earthperturbating the Moon's orbit around the Sun. It orbits Earth in theprograde direction and completes onerevolution relative to theVernal Equinox and the fixed stars in about 27.3 days (atropical month and asidereal month), and one revolution relative to the Sun in about 29.5 days (asynodic month).
On average, thedistance to the Moon is about 384,400 km (238,900 mi) from Earth's centre, which corresponds to about 60 Earth radii or 1.28 light-seconds.Thebarycentre lies about 4,670 km (2,900 miles) from Earth's centre (about 73% of its radius). With a meanorbital speed around the barycentre of 1.022 km/s (2,290 mph), the Moon covers a distance of approximately its diameter, or about half a degree on thecelestial sphere, each hour.
The Moon differs from mostregular satellites of other planets in that itsorbital plane is closer to that of itsprimary – theecliptic, the plane ofEarth's orbit – than to the primary'sequatorial plane. The Moon's orbital plane isinclined about 5.1° from the ecliptic (while Earth istilted about 23.4°).
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 oflunar theory, ever so precisely studying and approximating the orbit of the Moon. Orbits in general are shaped by different forces, such asgravity and the body's velocities, giving rise tocentripetal 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 oldestthree-body problem of astronomy,[7] with possibly the need to understand it as a system determined by even more factors, including but mostly negligible also influenced by the gravity ofJupiter orany number (n) of bodies, such as the planets.[6]
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'ssphere of influence,[8] producing strongertidal forces (gravitational potential differences) on it than the Sun.
The velocity relative to the Sun of a moon is always on average equal to their primary's velocity. But in order to differentiate totrojans andquasi-satellites, true moons need to also remain and not just temporarily stay within thesphere 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 toIo 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.[10] In representations of theSolar System, it is common[clarification needed] 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.[citation needed][relevant?] However, because the orbital velocity of the Moon around Earth (1 km/s) is small compared to the orbital velocity of Earth about the Sun (30 km/s), this never happens. There are no rearward loops in the Moon's solar orbit.
Consequently, the Moon's trajectory is always convex[11][12] (as seen when looking Sunward at the entire Sun–Earth–Moon system from a great distance outside Earth–Moon solar orbit), and is nowhere concave (from the same perspective) or looped.[13][11] That is, the region enclosed[where?] by the Moon's orbit of the Sun is aconvex set.[citation needed]
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.
The Moon and Earth together have acentre of mass, an orbitalbarycentre, which remains located within Earth at about 4,700 km (2,900 mi) from Earth's centre, which is roughly 3/4 of Earth's radius. This barycentre slightly moves as thedistance 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.[14]: 69 Thecentre of gravity of theEarth–Moon system is about 4,671 km (2,902 miles)[15] 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.[11]
The Sun pulls gravitationally stronger on the Moon than Earth does, making the Moon primarily orbit the Sun, not the Earth;[16][17] this in turn makes, in aheliocentricframe of reference, the Moon's orbitperturbated by Earth.[11][18]
This has led some scientists to argue that the Moon could be identified as a planet, both historically[19] and qualitatively,[20] adding that its mass would be enough to clear its orbit around the Sun if it were on its own.[21] This would imply that the Earth-Moon system is adouble planet,[14]: 70 which is conflicting with the defintion of what qualifies as aplanet by theInternational Astronomical Union (IAU) standards organization. The IAU though has no well established definition for planetarybinary 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.[22][23]
When viewed from the northcelestial pole (that is, from the approximate direction of the starPolaris) the Moon orbits Earthanticlockwise and Earth orbits the Sun anticlockwise, and the Moon and Earth rotate on their own axes anticlockwise.
Theright-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.
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The properties of the orbit described in this section are approximations. The Moon's orbit around Earth has many variations (perturbations) due to the gravitational attraction of the Sun and planets, the study of which (lunar theory) has a long history.[24]
With a meanorbital speed around the barycentre of 1.022 km/s (2,290 mph), the Moon covers a distance of approximately its diameter, or about half a degree on thecelestial sphere, each hour.[25]
The orbit of the Moon has aneccentricity of 0.0549, withperigee andapogee distances of 363,300 km (225744 mi) and 405,507 km (251970 mi) respectively (a difference of 11.6%).
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.
The Moon'selongation is its angular distance east of the Sun at any time. At new moon, it is zero and the Moon is said to be inconjunction. At full moon, the elongation is 180° and it is said to be inopposition. In both cases, the Moon is insyzygy, that is, the Sun, Moon and Earth are nearly aligned. When elongation is either 90° or 270°, the Moon is said to be inquadrature.
The orientation of the orbit is not fixed in space but rotates over time. This orbital precession is calledapsidal 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'smajor axis – the longest diameter of the orbit, joining its nearest and farthest points, theperigee andapogee, 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) – meaning precesses eastward by 360°. The Moon's apsidal precession is distinct from thenodal precession of its orbital plane andaxial precession of the moon itself.
The mean inclination of the lunar orbit to theecliptic 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.[26] 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 ofplanetesimals passing near the Moon while falling to the Earth.[27] If this had not happened, the Moon would now lie much closer to the ecliptic andeclipses would be much more frequent.[28]
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° (theobliquity). As was discovered byJacques 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.[29] 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 calledlibration in latitude.
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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 thedraconic month ordraconitic month. The line of nodes, the intersection between the two respective planes, has aretrograde motion: for an observer on Earth, it rotates westward along the ecliptic with a period of 18.6 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. An eclipse of the Moon or Sun 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 thedraconic 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. The effect of these seasons, however, 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.[30] Lunar polar sunrises and sunsets occur around the time of eclipses (solar or lunar). For example, at theSolar 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.
Thesolar eclipse of September 1 of the same year, the Moon was near its ascending 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 rises at the lunar north pole and sets at the lunar south pole.
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'sequatorial tilt (23°27′) and the Moon'sorbital inclination (5°09′) to the ecliptic. This is calledmajorlunar standstill. Around this time, the Moon'sdeclination 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 aminor lunar standstill. The last minor lunar standstill was in October 2015. At that time the descending node was lined up with the equinox (the point in the sky havingright ascension zero anddeclination 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 thehorizon every day from latitudes less than 70°43' (90° − 18°20' – 57' parallax) 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 60°27' (90° − 28°36' – 57' parallax) north or south.
Athigher 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 theseasonal 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 34arc minutes below the horizon, due toatmospheric refraction.
Because of the inclination of the Moon's orbit with respect to the Earth's equator, the Moon is above the horizon at theNorth andSouth 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 atropical 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 inGemini it will be above the horizon at the North Pole, and when it is inSagittarius it will be up at the South Pole.
The Moon's light is used byzooplankton in the Arctic when the Sun is below the horizon for months[31] and must have been helpful to the animals that lived in Arctic and Antarctic regions when the climate was warmer.
About1000 BC, theBabylonians were the first human civilization known to have kept a consistent record of lunar observations. Clay tablets from that period, which have been found in Iraq, are inscribed withcuneiform writing recording the times and dates of moonrises and moonsets, the stars that the Moon passed close by, and the time differences between rising and setting of both the Sun and the Moon around the time of afull moon.Babylonian astronomy discovered the three main periods of the Moon's motion and useddata analysis to build lunar calendars that extended well into the future.[24] This use of detailed, systematic observations to make predictions based on experimental data may be classified as the firstscientific study in human history. However, the Babylonians seem to have lacked any geometric or physical interpretation of their data, and they could not predict future lunar eclipses (though "warnings" were issued before likely eclipse times).
Ancient Greek astronomers were the first to introduce and analyzemathematical models of the motion of objects in the sky.Ptolemy described lunar motion by using a well-defined geometric model ofepicycles andevection.[24]
The relation of the Moon, Earth and Sun has been studied since antiquity and has therefore been called the oldestthree-body problem.[7]
Isaac Newton was the first to develop a complete theory of motion,Newtonian mechanics. The observations of the lunar motion were the main test of his theory.[24]
| Name | Value (days) | Definition |
|---|---|---|
| Sidereal month | 27.321662 | with respect to the distant stars (13.36874634 passes per solar orbit) |
| Synodic month | 29.530589 | with respect to the Sun (phases of the Moon, 12.36874634 passes per solar orbit) |
| Tropical month | 27.321582 | with respect to thevernal point (precesses in ~26,000 years) |
| Anomalistic month | 27.554550 | with respect to theperigee (precesses in3232.6054 days = 8.850578 years) |
| Draconic month | 27.212221 | with respect to the ascending node (precesses in6793.4765 days = 18.5996 years)[citation needed] |
There are several different periods associated with the lunar orbit.[32] Thesidereal month is the time it takes to make one complete orbit around Earth with respect to the fixed stars. It is about 27.32 days. Thesynodic month is the time it takes the Moon to reach the same visualphase. This varies notably throughout the year,[33] but averages around 29.53 days. The synodic period is longer than the sidereal period because the Earth–Moon system moves in its orbit around the Sun during each sidereal month, hence a longer period is required to achieve a similar alignment of Earth, the Sun, and the Moon. Theanomalistic month is the time between perigees and is about 27.55 days. The Earth–Moon separation determines the strength of the lunar tide raising force.
The draconic month is the time fromascending node to ascending node. The time between two successive passes of the same ecliptic longitude is called thetropical month. The latter periods are slightly different from the sidereal month.
The average length of acalendar month (a twelfth of a year) is about 30.4 days. This is not a lunar period, though the calendar month is historically related to the visible lunar phase.
Thegravitational attraction that the Moon exerts on Earth is the cause oftides in both the ocean and the solid Earth; the Sun has a smaller tidal influence. The solid Earth responds quickly to any change in the tidal forcing, the distortion taking the form of an ellipsoid with the high points roughly beneath the Moon and on the opposite side of Earth. This is a result of the high speed ofseismic waves within the solid Earth.
However the speed of seismic waves is not infinite and, together with the effect of energy loss within the Earth, this causes a slight delay between the passage of the maximum forcing due to the Moon across and the maximum Earth tide. As the Earth rotates faster than the Moon travels around its orbit, this small angle produces a gravitational torque which slows the Earth and accelerates the Moon in its orbit.
In the case of the ocean tides, the speed of tidal waves in the ocean[34] is far slower than the speed of the Moon's tidal forcing. As a result, the ocean is never in near equilibrium with the tidal forcing. Instead, the forcing generates the long ocean waves which propagate around the ocean basins until eventually losing their energy through turbulence, either in the deep ocean or on shallow continental shelves.
Although the ocean's response is the more complex of the two, it is possible to split the ocean tides into a small ellipsoid term which affects the Moon plus a second term which has no effect. The ocean's ellipsoid term also slows the Earth and accelerates the Moon, but because the ocean dissipates so much tidal energy, the present ocean tides have an order of magnitude greater effect than the solid Earth tides.
Because of the tidal torque, caused by the ellipsoids, some of Earth's angular (or rotational) momentum is gradually being transferred to the rotation of the Earth–Moon pair around their mutual centre of mass, called the barycentre.
This slightly greater orbital angular momentum causes the Earth–Moon distance to increase at approximately 38 millimetres per year.[35]Conservation of angular momentum means that Earth's axial rotation is gradually slowing, and because of this its day lengthens by approximately 24 microseconds every year (excludingglacial rebound). Both figures are valid only for the current configuration of the continents.Tidal rhythmites from 620 million years ago show that, over hundreds of millions of years, the Moon receded at an average rate of 22 mm (0.87 in) per year (2200 km or 0.56% or the Earth-Moon distance per hundred million years) and the day lengthened at an average rate of 12 microseconds per year (or 20 minutes per hundred million years), both about half of their current values. From 650 to 280 million years ago, through two intervals where Earth's rotation decelerated, the Moon moved approximately 20,000 km further away, which increased the daylength on Earth by 2.2 hours.[36]
The present high rate may be due to nearresonance between natural ocean frequencies and tidal frequencies.[37] Another explanation is that in the past the Earth rotated much faster, a day possibly lasting only 9 hours on the early Earth. The resulting tidal waves in the ocean would have then been much shorter and it would have been more difficult for the long wavelength tidal forcing to excite the short wavelength tides.[38]
The Moon is gradually receding from Earth into a higher orbit. This has resulted in the length of aanomalistic month having increased from 20 days to today's 27.55 days over the course of 3.2 billion years.[39] Calculations suggest that this would continue for about 50 billion years.[40][41] By that time, Earth and the Moon would be in a mutual spin–orbit resonance ortidal locking, in which the Moon will orbit Earth in about 47 days (currently 27 days), and both the Moon and Earth would rotate around their axes in the same time, always facing each other with the same side. This has already happened to the Moon—the same side always faces Earth—and is also slowly happening to the Earth. However, the slowdown of Earth's rotation is not occurring fast enough for the rotation to lengthen to a month before other effects change the situation: approximately 2.3 billion years from now, the increase of the Sun'sradiation will have caused Earth's oceans to evaporate,[42] removing the bulk of the tidal friction and acceleration.
The Moon is insynchronous rotation, meaning that it keeps the same face toward Earth at all times. This synchronous rotation is only true on average because the Moon's orbit has a definite eccentricity. As a result, the angular velocity of the Moon varies as it orbits Earth and hence is not always equal to the Moon's rotational velocity which is more constant. When the Moon is at its perigee, its orbital motion is faster than its rotation. At that time the Moon is a bit ahead in its orbit with respect to its rotation about its axis, and this creates a perspective effect which makes up to eight degrees of longitude of its easternfar side visible. Conversely, when the Moon reaches its apogee, its orbital motion is slower than its rotation, revealing eight degrees of longitude of its western far side. This is referred to asoptical libration in longitude.
The Moon's axis of rotation is inclined by in total 6.7° relative to the normal to the plane of the ecliptic. This leads to a similar perspective effect in the north–south direction that is referred to asoptical libration in latitude, which allows one to see almost 7° of latitude beyond the pole on the far side. Finally, because the Moon is only about 60 Earth radii away from Earth's centre of mass, an observer at the equator who observes the Moon throughout the night moves laterally by one Earth diameter. This gives rise to adiurnal libration, which allows one to view an additional one degree's worth of lunar longitude. For the same reason, observers at both of Earth'sgeographical poles would be able to see one additional degree's worth of libration in latitude.
Besides these "optical librations" caused by the change in perspective for an observer on Earth, there are also "physical librations" which are actualnutations of the direction of the pole of rotation of the Moon in space: but these are very small.
The moon's Hill sphere has a radius of 60,000 kilometres, about one-sixth of the distance between it and Earth.
| Included | Earth →Solar System →Local Interstellar Cloud →Local Bubble →Gould Belt →Orion Arm →Milky Way →Milky Way subgroup →Local Group→Local Sheet→Local Volume→Virgo Supercluster→Laniakea Supercluster →Pisces–Cetus Supercluster Complex →Local Hole →Observable universe →Universe Each arrow (→) may be read as "within" or "part of". |
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| Related | |
