The Moon's orbit
Encyclopedia
The Moon
completes its orbit
around the Earth
in approximately 27.3 days (a sidereal month). The Earth and Moon orbit about their barycentre (common centre of mass), which lies about km from Earth's centre (about three quarters of the Earth's radius). On average, the Moon is at a distance of about km from the centre of the Earth, which corresponds to about 60 Earth radii. With a mean orbital velocity of 1.023 km/s, the Moon moves relative to the star
s each hour by an amount roughly equal to its angular diameter
, or by about 0.5°. The Moon differs from most satellites
of other planet
s 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°.
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.
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 ° to the east (Julian Day 2000.0 rate).
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 days or about 8.85 solar orbits.
. 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
.
: for an observer on Earth it rotates westward along the ecliptic with a period of 18.6 years, or 19°21′ per year. When viewed from celestial north, the nodes move clockwise around the Earth, opposite the Earth's own spin and its rotation around the Sun. Lunar and solar eclipses can only occur when the line of nodes points toward the Sun, roughly every 5.4 months. The type of the eclipse depends on Moon's orbital position in that time window.
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°.
. Nine and a half years later, when the descending node has come to the same point, the angle is only 23°28′ − 5°8′ or 18°19′, and the declination of the Moon is a minimum. This is the minor standstill.
because of the relatively large size of the Moon; the Earth–Moon mass ratio, about 81:1, is much smaller than that of most other natural satellite
s in the Solar System. An informal criterion for a double planet system is that its barycentre must be exterior to both bodies. By that criterion, the Earth and Moon are an ordinary planet–moon system, because their mutual distance is about 60 Earth radii but their mass ratio is 81:1 so their centre of mass always lies well within the Earth.
ians were the first human civilization to keep a consistent record of lunar observations. Clay tablets from that time period found over the territory of present-day Iraq are inscribed with cuneiform
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 the full moon
. The Babylonians discovered the three main periods of the Moon's motion and used data analysis
to build lunar calendars that extended well into the future. This use of detailed, systematic observations to make predictions based on experimental data may be classified as the first scientific study in human history. However, Babylonians seem to have lacked any geometrical or physical interpretation of their data, and they could not predict future lunar eclipses (although "warnings" were issued before likely eclipse times).
Ancient Greek
astronomers were the first to introduce and analyze mathematical model
s of the motion of objects in the sky. Ptolemy
described lunar motion by using a well-defined geometric model of epicycles and evection
.
Isaac Newton
was the first to develop a complete theory of motion, mechanics. The sheer wealth of humanity's observations of the lunar motion was the main testbed of his theory.
>
There are several ways to measure how much time it takes the Moon to complete one orbit. The sidereal month is the time it takes to make one complete orbit with respect to the fixed stars, which is about 27.3 days. In contrast, the synodic month is the time it takes the Moon to reach the same phase
, which takes about 29.5 days. The synodic period is longer than the sidereal period because the Earth–Moon system moves a finite distance in its orbit around the Sun
during each sidereal month, and a longer time is required to achieve the same relative geometry. Other definitions for the duration of a lunar month include the time it takes to go from perigee to perigee (the anomalistic month), from ascending node to ascending node (the draconic month), and from two successive passes of the same ecliptic longitude (the tropical month). As a result of the slow precession of the lunar orbit, these latter three periods are only slightly different from the sidereal month. The average length of a calendric month ( of a year) is about 30.4 days.
al attraction that the Moon exerts on Earth is the major cause of tide
s in the sea; the Sun has a lesser tidal influence. If the Earth possessed a global ocean of uniform depth, the Moon would act to deform both the solid earth (by a small amount) and ocean in the shape of an ellipsoid with high points directly beneath the Moon and on the opposite side of the Earth. However, as a result of the irregular coastline and varying ocean
depths, this idealization is only partially realized. While the tidal flow period is generally synchronized to the Moon's orbit around Earth, its phase can vary. In some places on Earth there is only one high tide per day, though this is somewhat rare.
The tidal bulges on Earth are carried ahead of the Earth–Moon axis by a small amount as a result of the Earth's rotation. This is a direct consequence of friction
and the dissipation of energy as water moves over the ocean bottom and into or out of bays and estuaries. Each bulge exerts a small amount of gravitational attraction on the Moon, with the bulge closest to the Moon pulling in a direction slightly forward along the Moon's orbit, because the Earth's rotation has carried the bulge forward. The opposing bulge has the opposite effect, but the closer bulge dominates due to its comparative closer distance to the Moon. As a result, some of the Earth's rotational momentum is gradually being transferred to the Moon's orbital momentum, and this causes the Moon to slowly recede from Earth at the rate of approximately 38 millimetres per year. In keeping with the conservation of angular momentum, the Earth's rotation is gradually slowing, and the Earth's day thus lengthens by about 23 microseconds every year (excluding glacial 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 millimetres per year and the day lengthened at an average rate of 12 microseconds per year, both about half of their current values. See tidal acceleration
for a more detailed description and references.
The Moon is gradually receding from the Earth into a higher orbit, and calculations suggest that this would continue for about fifty billion years. By that time, the Earth and Moon would become caught up in what is called a "spin–orbit resonance" in which the Moon will circle the Earth in about 47 days (currently 27 days), and both Moon and Earth would rotate around their axes in the same time, always facing each other with the same side. However, the slowdown of the Earth's rotation is not occurring fast enough for the rotation to lengthen to a month before other effects change the situation: about 2.1 billion years from now, the increase of the Sun's radiation
will have caused the Earth's oceans to vaporize, removing the bulk of the tidal friction and acceleration.
The Moon is in synchronous rotation
, meaning that it keeps the same face turned toward the 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 moves around the Earth, and is hence not always equal to the Moon's rotational velocity. When the Moon is at its perigee
, its rotation is slower than its orbital motion, and this allows us to see up to eight degrees of longitude of its eastern (right) far side
. Conversely, when the Moon reaches its apogee, its rotation is faster than its orbital motion and this reveals eight degrees of longitude of its western (left) far side. This is referred to as longitudinal libration
.
Because the lunar orbit is also inclined to the Earth's ecliptic plane by 5.1°, the rotation axis of the Moon seems to rotate towards and away from us during one complete orbit. This is referred to as latitudinal libration, 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 the 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 a diurnal libration, which allows one to view an additional one degree's worth of lunar longitude. For the same reason, observers at both geographical pole
s of the Earth would be able to see one additional degree's worth of libration in latitude.
, i.e. from the star Polaris
, the Moon orbits the Earth counterclockwise, the Earth orbits the Sun counterclockwise, and the Moon and Earth rotate on their own axes counterclockwise.
The right-hand rule may be used instead. If the thumb of the right hand points to the north celestial pole, its fingers curl in the direction that the Moon orbits the Earth, the Earth orbits the Sun, and the direction the Moon and Earth rotate on their own axes.
In representations of the Solar System
, it is common to draw the trajectory of the Earth from the point of view of the Sun, and the trajectory of the Moon from the point of view of the Earth. This could give the impression that the Moon circles around the Earth in such a way that sometimes it goes backwards when viewed from the Sun's perspective. Since the orbital velocity of the Moon about the Earth (1 km/s) is small compared to the orbital velocity of the Earth about the Sun (30 km/s), this never occurs.
Considering the Earth-Moon system as a binary planet, their mutual centre of gravity is within the Earth, about 4624 km from its centre or 72.6% of its radius. This centre of gravity remains in line towards the Moon as the Earth completes its diurnal rotation. It is this mutual centre of gravity which defines the path of the Earth-Moon system in solar orbit. Consequently the Earth's centre veers inside and outside the orbital path during each synodic month as the Moon moves in the opposite direction.
Unlike most other moons in the Solar System, the trajectory of the Moon is very similar to that of its planet. The Sun's gravitational pull on the Moon is over twice as great as the Earth's pull on the Moon; consequently, the Moon's trajectory is always convex (as seen when looking inward at the entire Moon/Earth/Sun system from a great distance off), and is nowhere concave (from the perspective just mentioned) or looped. If the gravitational attraction of the Sun could be "turned off" while maintaining the Earth-Moon gravitational attraction, the Moon would continue to orbit the Earth once every sidereal month.
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
completes its orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...
around the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
in approximately 27.3 days (a sidereal month). The Earth and Moon orbit about their barycentre (common centre of mass), which lies about km from Earth's centre (about three quarters of the Earth's radius). On average, the Moon is at a distance of about km from the centre of the Earth, which corresponds to about 60 Earth radii. With a mean orbital velocity of 1.023 km/s, the Moon moves relative to the star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
s each hour by an amount roughly equal to its angular diameter
Angular diameter
The angular diameter or apparent size of an object as seen from a given position is the “visual diameter” of the object measured as an angle. In the vision sciences it is called the visual angle. The visual diameter is the diameter of the perspective projection of the object on a plane through its...
, or by about 0.5°. The Moon differs from most satellites
Natural satellite
A natural satellite or moon is a celestial body that orbits a planet or smaller body, which is called its primary. The two terms are used synonymously for non-artificial satellites of planets, of dwarf planets, and of minor planets....
of other planet
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...
s in that its orbit is close to the plane of the ecliptic
Ecliptic
The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...
, 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
Rotation
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...
is inclined by only 1.5°.
| Property | Value |
|---|---|
| Semi-major axis Semi-major axis The major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape... |
km |
| mean distance | km |
| inverse sine parallax | km |
| Distance at perigee | ~ km (- km) |
| Distance at apogee | ~ km (- km) |
| Mean eccentricity Orbital eccentricity The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit... |
(0.026 – 0.077) |
| Mean inclination Inclination Inclination in general is the angle between a reference plane and another plane or axis of direction.-Orbits:The inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit... of orbit to ecliptic |
5.14° (4.99 – 5.30) |
| Mean obliquity Axial tilt In astronomy, axial tilt is the angle between an object's rotational axis, and a line perpendicular to its orbital plane... |
6.58° |
| Mean inclination of lunar equator to ecliptic | 1.543° |
| Period of precession of nodes Lunar precession Precession is the rotation of a plane with respect to a reference plane. The orbit of the Moon has two important such precessional motions.... |
18.5996 years |
| Period of recession of line of apsides | 8.8504 years |
Properties
Perturbation (astronomy)
Perturbation is a term used in astronomy in connection with descriptions of the complex motion of a massive body which is subject to appreciable gravitational effects from more than one other massive body....
), whose study (lunar theory
Lunar theory
Lunar theory attempts to account for the motions of the Moon. There are many irregularities in the Moon's motion, and many attempts have been made over a long history to account for them. After centuries of being heavily problematic, the lunar motions are nowadays modelled to a very high degree...
) has a long history.
Elliptic shape
The orbit of the Moon is distinctly elliptical with an average eccentricityOrbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...
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 ° to the east (Julian Day 2000.0 rate).
Line of apsides
The orientation of the orbit is not fixed in space, but precessesLunar precession
Precession is the rotation of a plane with respect to a reference plane. The orbit of the Moon has two important such precessional motions....
over time. The nearest and farthest points in the orbit are the perigee
Perigee
Perigee is the point at which an object makes its closest approach to the Earth.. Often the term is used in a broader sense to define the point in an orbit where the orbiting body is closest to the body it orbits. The opposite is the apogee, the farthest or highest point.The Greek prefix "peri"...
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 days or about 8.85 solar orbits.
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 oppositionOpposition (astronomy)
In positional astronomy, two celestial bodies are said to be in opposition when they are on opposite sides of the sky, viewed from a given place . In particular, two planets are in opposition to each other when their ecliptic longitudes differ by 180°.The astronomical symbol for opposition is ☍...
. In both cases the Moon is in syzygy
Syzygy (astronomy)
In astronomy, a syzygy is a straight line configuration of three celestial bodies in a gravitational system. The word is usually used in reference to the Sun, the Earth and either the Moon or a planet, where the latter is in conjunction or opposition. Solar and lunar eclipses occur at times of...
, 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
Quadrature (astronomy)
In astronomy, quadrature is that aspect of a heavenly body in which it makes a right angle with the direction of the Sun. It is applied especially to the apparent position of a superior planet, or of the Moon at first and last quarters....
.
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 is the intersection between the two respective planes. It has a retrograde motionRetrograde motion
Retrograde motion is motion in the direction opposite to the movement of something else, and is the contrary of direct or prograde motion. This motion can be the orbit of one body about another body or about some other point, or the rotation of a single body about its axis, or other phenomena such...
: for an observer on Earth it rotates westward along the ecliptic with a period of 18.6 years, or 19°21′ per year. When viewed from celestial north, the nodes move clockwise around the Earth, opposite the Earth's own spin and its rotation around the Sun. Lunar and solar eclipses can only occur when the line of nodes points toward the Sun, roughly every 5.4 months. The type of the eclipse depends on Moon's orbital position in that time window.
Inclination
The mean inclination of the lunar orbit to the ecliptic planePlane of the ecliptic
The plane of the ecliptic is the plane of the Earth's orbit around the Sun. It is the primary reference plane when describing the position of bodies in the Solar System, with celestial latitude being measured relative to the ecliptic plane. In the course of a year, the Sun's apparent path through...
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
Jacques Cassini
Jacques Cassini was a French astronomer, son of the famous Italian astronomer Giovanni Domenico Cassini.Cassini was born at the Paris Observatory. Admitted at the age of seventeen to membership of the French Academy of Sciences, he was elected in 1696 a fellow of the Royal Society of London, and...
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
Cassini's Laws
Cassini's laws provide a compact description of the motion of the Moon. They were established in 1693 by Giovanni Domenico Cassini, a prominent scientist of his time....
). 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
When the ascending node of the Moon's orbit coincides with the vernal equinox in the northern hemisphere, the declination of the Moon in the sky reaches a maximum at 23°29′ + 5°9′ or 28°36′. This is called the major standstillLunar standstill
At a major lunar standstill, which takes place every 18.6 years, the range of the declination of the Moon reaches a maximum. As a result, at high latitudes, the Moon appears to move in just two weeks from high in the sky to low on the horizon...
. Nine and a half years later, when the descending node has come to the same point, the angle is only 23°28′ − 5°8′ or 18°19′, and the declination of the Moon is a minimum. This is the minor standstill.
Double planet?
Some consider the Earth–Moon system to be a double planetDouble planet
In astronomy, double planet and binary planet are informal terms used to describe a binary system of two astronomical objects that each satisfy the definition of planet and that are near enough to each other to have a significant gravitational effect on each other compared with the effect of the...
because of the relatively large size of the Moon; the Earth–Moon mass ratio, about 81:1, is much smaller than that of most other natural satellite
Natural satellite
A natural satellite or moon is a celestial body that orbits a planet or smaller body, which is called its primary. The two terms are used synonymously for non-artificial satellites of planets, of dwarf planets, and of minor planets....
s in the Solar System. An informal criterion for a double planet system is that its barycentre must be exterior to both bodies. By that criterion, the Earth and Moon are an ordinary planet–moon system, because their mutual distance is about 60 Earth radii but their mass ratio is 81:1 so their centre of mass always lies well within the Earth.
History of observations and measurements
About 3000 years ago, the BabylonBabylon
Babylon was an Akkadian city-state of ancient Mesopotamia, the remains of which are found in present-day Al Hillah, Babil Province, Iraq, about 85 kilometers south of Baghdad...
ians were the first human civilization to keep a consistent record of lunar observations. Clay tablets from that time period found over the territory of present-day Iraq are inscribed with cuneiform
Cuneiform
Cuneiform can refer to:*Cuneiform script, an ancient writing system originating in Mesopotamia in the 4th millennium BC*Cuneiform , three bones in the human foot*Cuneiform Records, a music record label...
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 the full moon
Full moon
Full moon lunar phase that occurs when the Moon is on the opposite side of the Earth from the Sun. More precisely, a full moon occurs when the geocentric apparent longitudes of the Sun and Moon differ by 180 degrees; the Moon is then in opposition with the Sun.Lunar eclipses can only occur at...
. The Babylonians discovered the three main periods of the Moon's motion and used data analysis
Data analysis
Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of highlighting useful information, suggesting conclusions, and supporting decision making...
to build lunar calendars that extended well into the future. This use of detailed, systematic observations to make predictions based on experimental data may be classified as the first scientific study in human history. However, Babylonians seem to have lacked any geometrical or physical interpretation of their data, and they could not predict future lunar eclipses (although "warnings" were issued before likely eclipse times).
Ancient Greek
Ancient Greece
Ancient Greece is a civilization belonging to a period of Greek history that lasted from the Archaic period of the 8th to 6th centuries BC to the end of antiquity. Immediately following this period was the beginning of the Early Middle Ages and the Byzantine era. Included in Ancient Greece is the...
astronomers were the first to introduce and analyze mathematical model
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
s of the motion of objects in the sky. Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
described lunar motion by using a well-defined geometric model of epicycles and evection
Evection
Evection , in astronomy, is the largest inequality produced by the action of the Sun in the monthly revolution of the Moon around the Earth. The evection, formerly called the moon's second anomaly, was approximately known in ancient times, and its discovery is attributed to Ptolemy...
.
Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
was the first to develop a complete theory of motion, mechanics. The sheer wealth of humanity's observations of the lunar motion was the main testbed of his theory.
Lunar periods
| Name | Value (days) | Definition |
|---|---|---|
| sidereal month | with respect to the distant stars (13.36874634 passes per solar orbit) | |
| synodic month | with respect to the Sun (phases of the Moon, 12.36874634 passes per solar orbit) | |
| tropical month | with respect to the vernal point (precesses in ~26,000 years) | |
| anomalistic month | with respect to the perigee (recesses in days = 8.8504 years) | |
| draconic (nodical) month | with respect to the ascending node (precesses in days = 18.5996 years) |
There are several ways to measure how much time it takes the Moon to complete one orbit. The sidereal month is the time it takes to make one complete orbit with respect to the fixed stars, which is about 27.3 days. In contrast, the synodic month is the time it takes the Moon to reach the same phase
Lunar phase
A lunar phase or phase of the moon is the appearance of the illuminated portion of the Moon as seen by an observer, usually on Earth. The lunar phases change cyclically as the Moon orbits the Earth, according to the changing relative positions of the Earth, Moon, and Sun...
, which takes about 29.5 days. The synodic period is longer than the sidereal period because the Earth–Moon system moves a finite distance in its orbit around the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
during each sidereal month, and a longer time is required to achieve the same relative geometry. Other definitions for the duration of a lunar month include the time it takes to go from perigee to perigee (the anomalistic month), from ascending node to ascending node (the draconic month), and from two successive passes of the same ecliptic longitude (the tropical month). As a result of the slow precession of the lunar orbit, these latter three periods are only slightly different from the sidereal month. The average length of a calendric month ( of a year) is about 30.4 days.
Tidal evolution
The gravitationGravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
al attraction that the Moon exerts on Earth is the major cause of tide
Tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the moon and the sun and the rotation of the Earth....
s in the sea; the Sun has a lesser tidal influence. If the Earth possessed a global ocean of uniform depth, the Moon would act to deform both the solid earth (by a small amount) and ocean in the shape of an ellipsoid with high points directly beneath the Moon and on the opposite side of the Earth. However, as a result of the irregular coastline and varying ocean
Ocean
An ocean is a major body of saline water, and a principal component of the hydrosphere. Approximately 71% of the Earth's surface is covered by ocean, a continuous body of water that is customarily divided into several principal oceans and smaller seas.More than half of this area is over 3,000...
depths, this idealization is only partially realized. While the tidal flow period is generally synchronized to the Moon's orbit around Earth, its phase can vary. In some places on Earth there is only one high tide per day, though this is somewhat rare.
The tidal bulges on Earth are carried ahead of the Earth–Moon axis by a small amount as a result of the Earth's rotation. This is a direct consequence of friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...
and the dissipation of energy as water moves over the ocean bottom and into or out of bays and estuaries. Each bulge exerts a small amount of gravitational attraction on the Moon, with the bulge closest to the Moon pulling in a direction slightly forward along the Moon's orbit, because the Earth's rotation has carried the bulge forward. The opposing bulge has the opposite effect, but the closer bulge dominates due to its comparative closer distance to the Moon. As a result, some of the Earth's rotational momentum is gradually being transferred to the Moon's orbital momentum, and this causes the Moon to slowly recede from Earth at the rate of approximately 38 millimetres per year. In keeping with the conservation of angular momentum, the Earth's rotation is gradually slowing, and the Earth's day thus lengthens by about 23 microseconds every year (excluding glacial 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 millimetres per year and the day lengthened at an average rate of 12 microseconds per year, both about half of their current values. See tidal acceleration
Tidal acceleration
Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite , and the primary planet that it orbits . The "acceleration" is usually negative, as it causes a gradual slowing and recession of a satellite in a prograde orbit away from the primary, and a corresponding...
for a more detailed description and references.
The Moon is gradually receding from the Earth into a higher orbit, and calculations suggest that this would continue for about fifty billion years. By that time, the Earth and Moon would become caught up in what is called a "spin–orbit resonance" in which the Moon will circle the Earth in about 47 days (currently 27 days), and both Moon and Earth would rotate around their axes in the same time, always facing each other with the same side. However, the slowdown of the Earth's rotation is not occurring fast enough for the rotation to lengthen to a month before other effects change the situation: about 2.1 billion years from now, the increase of the Sun's radiation
Radiation
In physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space. There are two distinct types of radiation; ionizing and non-ionizing...
will have caused the Earth's oceans to vaporize, removing the bulk of the tidal friction and acceleration.
Libration
Synchronous rotation
In astronomy, synchronous rotation is a planetological term describing a body orbiting another, where the orbiting body takes as long to rotate on its axis as it does to make one orbit; and therefore always keeps the same hemisphere pointed at the body it is orbiting...
, meaning that it keeps the same face turned toward the Earth at all times. This synchronous rotation is only true on average, because the Moon's orbit has a definite eccentricity
Orbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...
. As a result, the angular velocity of the Moon varies as it moves around the Earth, and is hence not always equal to the Moon's rotational velocity. When the Moon is at its perigee
Perigee
Perigee is the point at which an object makes its closest approach to the Earth.. Often the term is used in a broader sense to define the point in an orbit where the orbiting body is closest to the body it orbits. The opposite is the apogee, the farthest or highest point.The Greek prefix "peri"...
, its rotation is slower than its orbital motion, and this allows us to see up to eight degrees of longitude of its eastern (right) far side
Far side of the Moon
The far side of the Moon is the lunar hemisphere that is permanently turned away, and is not visible from the surface of the Earth. The far hemisphere was first photographed by the Soviet Luna 3 probe in 1959, and was first directly observed by human eyes when the Apollo 8 mission orbited the Moon...
. Conversely, when the Moon reaches its apogee, its rotation is faster than its orbital motion and this reveals eight degrees of longitude of its western (left) far side. This is referred to as longitudinal libration
Libration
In astronomy, libration is an oscillating motion of orbiting bodies relative to each other, notably including the motion of the Moon relative to Earth, or of Trojan asteroids relative to planets.-Lunar libration:...
.
Because the lunar orbit is also inclined to the Earth's ecliptic plane by 5.1°, the rotation axis of the Moon seems to rotate towards and away from us during one complete orbit. This is referred to as latitudinal libration, 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 the 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 a diurnal libration, which allows one to view an additional one degree's worth of lunar longitude. For the same reason, observers at both geographical pole
Geographical pole
A geographical pole is either of the two points—the north pole and the south pole—on the surface of a rotating planet where the axis of rotation meets the surface of the body...
s of the Earth would be able to see one additional degree's worth of libration in latitude.
Path of Earth and Moon around Sun
When viewed from the north celestial poleCelestial pole
The north and south celestial poles are the two imaginary points in the sky where the Earth's axis of rotation, indefinitely extended, intersects the imaginary rotating sphere of stars called the celestial sphere...
, i.e. from the star Polaris
Polaris
Polaris |Alpha]] Ursae Minoris, commonly North Star or Pole Star, also Lodestar) is the brightest star in the constellation Ursa Minor. It is very close to the north celestial pole, making it the current northern pole star....
, the Moon orbits the Earth counterclockwise, the Earth orbits the Sun counterclockwise, and the Moon and Earth rotate on their own axes counterclockwise.
The right-hand rule may be used instead. If the thumb of the right hand points to the north celestial pole, its fingers curl in the direction that the Moon orbits the Earth, the Earth orbits the Sun, and the direction the Moon and Earth rotate on their own axes.
In representations of the Solar System
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...
, it is common to draw the trajectory of the Earth from the point of view of the Sun, and the trajectory of the Moon from the point of view of the Earth. This could give the impression that the Moon circles around the Earth in such a way that sometimes it goes backwards when viewed from the Sun's perspective. Since the orbital velocity of the Moon about the Earth (1 km/s) is small compared to the orbital velocity of the Earth about the Sun (30 km/s), this never occurs.
Considering the Earth-Moon system as a binary planet, their mutual centre of gravity is within the Earth, about 4624 km from its centre or 72.6% of its radius. This centre of gravity remains in line towards the Moon as the Earth completes its diurnal rotation. It is this mutual centre of gravity which defines the path of the Earth-Moon system in solar orbit. Consequently the Earth's centre veers inside and outside the orbital path during each synodic month as the Moon moves in the opposite direction.
Unlike most other moons in the Solar System, the trajectory of the Moon is very similar to that of its planet. The Sun's gravitational pull on the Moon is over twice as great as the Earth's pull on the Moon; consequently, the Moon's trajectory is always convex (as seen when looking inward at the entire Moon/Earth/Sun system from a great distance off), and is nowhere concave (from the perspective just mentioned) or looped. If the gravitational attraction of the Sun could be "turned off" while maintaining the Earth-Moon gravitational attraction, the Moon would continue to orbit the Earth once every sidereal month.
See also
- Lunar theoryLunar theoryLunar theory attempts to account for the motions of the Moon. There are many irregularities in the Moon's motion, and many attempts have been made over a long history to account for them. After centuries of being heavily problematic, the lunar motions are nowadays modelled to a very high degree...
- Ernest William BrownErnest William BrownErnest William Brown FRS was a British mathematician and astronomer, who spent the majority of his career working in the United States....
- Orbital elementsOrbital elementsOrbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are generally considered in classical two-body systems, where a Kepler orbit is used...
- Lunar Laser Ranging ExperimentLunar laser ranging experimentThe ongoing Lunar Laser Ranging Experiment measures the distance between the Earth and the Moon using laser ranging. Lasers on Earth are aimed at retroreflectors planted on the moon during the Apollo program, and the time for the reflected light to return is determined...
- List of orbits
- Milankovitch cyclesMilankovitch cyclesMilankovitch theory describes the collective effects of changes in the Earth's movements upon its climate, named after Serbian civil engineer and mathematician Milutin Milanković, who worked on it during First World War internment...
- SupermoonSupermoonA "supermoon" is the coincidence of a full moon with the closest approach the Moon makes to the Earth on its elliptical orbit, or perigee, leading to the technical name for a supermoon of the perigee-syzygy of the Earth-Moon-Sun system...