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Tidal locking between a pair of co-
orbit In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
ing
astronomical bodies An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often us ...
occurs when one of the objects reaches a state where there is no longer any net change in its rotation rate over the course of a complete orbit. In the case where a tidally locked body possesses
synchronous rotation Tidal locking between a pair of co-orbiting astronomical bodies occurs when one of the objects reaches a state where there is no longer any net change in its rotation rate over the course of a complete orbit. In the case where a tidally locked b ...
, the object takes just as long to rotate around its own axis as it does to revolve around its partner. For example, the same side of the
Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
always faces the
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
, although there is some variability because the Moon's orbit is not perfectly circular. Usually, only the
satellite A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioisotope ...
is tidally locked to the larger body. However, if both the difference in mass between the two bodies and the distance between them are relatively small, each may be tidally locked to the other; this is the case for
Pluto Pluto (minor-planet designation: 134340 Pluto) is a dwarf planet in the Kuiper belt, a ring of trans-Neptunian object, bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the S ...
and
Charon In Greek mythology, Charon or Kharon (; grc, Χάρων) is a psychopomp, the ferryman of Hades, the Greek underworld. He carries the souls of those who have been given funeral rites across the rivers Acheron and Styx, which separate the wo ...
. Alternative names for the tidal locking process are gravitational locking, captured rotation, and spin–orbit locking. The effect arises between two bodies when their
gravitational interaction In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong ...
slows a body's rotation until it becomes tidally locked. Over many millions of years, the interaction forces changes to their orbits and rotation rates as a result of
energy exchange In a broad sense, an electricity market is a system that facilitates the exchange of electricity-related goods and services. During more than a century of evolution of the electric power industry, the economics of the electricity markets had un ...
and heat
dissipation In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. In a dissipative process, energy (internal, bulk flow kinetic, or system potential) transforms from an initial form to a ...
. When one of the bodies reaches a state where there is no longer any net change in its rotation rate over the course of a complete orbit, it is said to be tidally locked. The object tends to stay in this state because leaving it would require adding energy back into the system. The object's orbit may migrate over time so as to undo the tidal lock, for example, if a giant planet perturbs the object. Not every case of tidal locking involves synchronous rotation. With
Mercury Mercury commonly refers to: * Mercury (planet), the nearest planet to the Sun * Mercury (element), a metallic chemical element with the symbol Hg * Mercury (mythology), a Roman god Mercury or The Mercury may also refer to: Companies * Merc ...
, for example, this tidally locked planet completes three rotations for every two revolutions around the Sun, a 3:2 spin–orbit resonance. In the special case where an orbit is nearly circular and the body's rotation axis is not significantly tilted, such as the Moon, tidal locking results in the same hemisphere of the revolving object constantly facing its partner. However, in this case the exact same portion of the body does not always face the partner on all orbits. There can be some shifting due to
variations Variation or Variations may refer to: Science and mathematics * Variation (astronomy), any perturbation of the mean motion or orbit of a planet or satellite, particularly of the moon * Genetic variation, the difference in DNA among individuals ...
in the locked body's orbital velocity and the inclination of its rotation axis.


Mechanism

Consider a pair of co-orbiting objects, A and B. The change in rotation rate necessary to tidally lock body B to the larger body A is caused by the
torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...
applied by A's
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
on bulges it has induced on B by
tidal force The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomen ...
s. The gravitational force from object A upon B will vary with distance, being greatest at the nearest surface to A and least at the most distant. This creates a gravitational
gradient In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradi ...
across object B that will distort its equilibrium shape slightly. The body of object B will become elongated along the axis oriented toward A, and conversely, slightly reduced in dimension in directions
orthogonal In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''. By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...
to this axis. The elongated distortions are known as
tidal bulge The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomen ...
s. (For the solid Earth, these bulges can reach displacements of up to around .) When B is not yet tidally locked, the bulges travel over its surface due to orbital motions, with one of the two "high" tidal bulges traveling close to the point where body A is overhead. For large astronomical bodies that are nearly
spherical A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the ce ...
due to self-gravitation, the tidal distortion produces a slightly
prolate spheroid A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circu ...
, i.e. an axially symmetric
ellipsoid An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface;  that is, a surface that may be defined as the ...
that is elongated along its major axis. Smaller bodies also experience distortion, but this distortion is less regular. The material of B exerts resistance to this periodic reshaping caused by the tidal force. In effect, some time is required to reshape B to the gravitational equilibrium shape, by which time the forming bulges have already been carried some distance away from the A–B axis by B's rotation. Seen from a vantage point in space, the points of maximum bulge extension are displaced from the axis oriented toward A. If B's rotation period is shorter than its orbital period, the bulges are carried forward of the axis oriented toward A in the direction of rotation, whereas if B's rotation period is longer, the bulges instead lag behind. Because the bulges are now displaced from the A–B axis, A's gravitational pull on the mass in them exerts a torque on B. The torque on the A-facing bulge acts to bring B's rotation in line with its orbital period, whereas the "back" bulge, which faces away from A, acts in the opposite sense. However, the bulge on the A-facing side is closer to A than the back bulge by a distance of approximately B's diameter, and so experiences a slightly stronger gravitational force and torque. The net resulting torque from both bulges, then, is always in the direction that acts to synchronize B's rotation with its orbital period, leading eventually to tidal locking.


Orbital changes

The
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
of the whole A–B system is conserved in this process, so that when B slows down and loses rotational angular momentum, its ''orbital'' angular momentum is boosted by a similar amount (there are also some smaller effects on A's rotation). This results in a raising of B's orbit about A in tandem with its rotational slowdown. For the other case where B starts off rotating too slowly, tidal locking both speeds up its rotation, and ''lowers'' its orbit.


Locking of the larger body

The tidal locking effect is also experienced by the larger body A, but at a slower rate because B's gravitational effect is weaker due to B's smaller mass. For example, Earth's rotation is gradually being slowed by the Moon, by an amount that becomes noticeable over geological time as revealed in the fossil record. Current estimations are that this (together with the tidal influence of the Sun) has helped lengthen the Earth day from about 6 hours to the current 24 hours (over ≈ ⁠4½ billion years). Currently,
atomic clock An atomic clock is a clock that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different energy levels. Electron states in an atom are associated with different energy levels, and in transitions betwee ...
s show that Earth's day lengthens, on average, by about 2.3 milliseconds per century. Given enough time, this would create a mutual tidal locking between Earth and the Moon. The length of the Earth's day would increase and the length of a
lunar month In lunar calendars, a lunar month is the time between two successive syzygies of the same type: new moons or full moons. The precise definition varies, especially for the beginning of the month. Variations In Shona, Middle Eastern, and Europ ...
would also increase. The Earth's sidereal day would eventually have the same length as the Moon's orbital period, about 47 times the length of the Earth's day at present. However, Earth is not expected to become tidally locked to the Moon before the Sun becomes a
red giant A red giant is a luminous giant star of low or intermediate mass (roughly 0.3–8 solar masses ()) in a late phase of stellar evolution. The outer atmosphere is inflated and tenuous, making the radius large and the surface temperature around or ...
and engulfs Earth and the Moon. For bodies of similar size the effect may be of comparable size for both, and both may become tidally locked to each other on a much shorter timescale. An example is the
dwarf planet A dwarf planet is a small planetary-mass object that is in direct orbit of the Sun, smaller than any of the eight classical planets but still a world in its own right. The prototypical dwarf planet is Pluto. The interest of dwarf planets to p ...
Pluto Pluto (minor-planet designation: 134340 Pluto) is a dwarf planet in the Kuiper belt, a ring of trans-Neptunian object, bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the S ...
and its satellite
Charon In Greek mythology, Charon or Kharon (; grc, Χάρων) is a psychopomp, the ferryman of Hades, the Greek underworld. He carries the souls of those who have been given funeral rites across the rivers Acheron and Styx, which separate the wo ...
. They have already reached a state where Charon is visible from only one hemisphere of Pluto and vice versa.


Eccentric orbits

For orbits that do not have an eccentricity close to zero, the
rotation Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...
rate tends to become locked with the
orbital speed In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter or, if one body is much more massi ...
when the body is at
periapsis An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary (astronomy), primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two ...
, which is the point of strongest tidal interaction between the two objects. If the orbiting object has a companion, this third body can cause the rotation rate of the parent object to vary in an oscillatory manner. This interaction can also drive an increase in orbital eccentricity of the orbiting object around the primary – an effect known as eccentricity pumping. In some cases where the orbit is
eccentric Eccentricity or eccentric may refer to: * Eccentricity (behavior), odd behavior on the part of a person, as opposed to being "normal" Mathematics, science and technology Mathematics * Off-center, in geometry * Eccentricity (graph theory) of a v ...
and the tidal effect is relatively weak, the smaller body may end up in a so-called ''spin–orbit resonance'', rather than being tidally locked. Here, the ratio of the rotation period of a body to its own orbital period is some simple fraction different from 1:1. A well known case is the rotation of
Mercury Mercury commonly refers to: * Mercury (planet), the nearest planet to the Sun * Mercury (element), a metallic chemical element with the symbol Hg * Mercury (mythology), a Roman god Mercury or The Mercury may also refer to: Companies * Merc ...
, which is locked to its own orbit around the Sun in a 3:2 resonance. This results in the rotation speed roughly matching the orbital speed around perihelion. Many
exoplanet An exoplanet or extrasolar planet is a planet outside the Solar System. The first possible evidence of an exoplanet was noted in 1917 but was not recognized as such. The first confirmation of detection occurred in 1992. A different planet, init ...
s (especially the close-in ones) are expected to be in spin–orbit resonances higher than 1:1. A Mercury-like terrestrial planet can, for example, become captured in a 3:2, 2:1, or 5:2 spin–orbit resonance, with the probability of each being dependent on the orbital eccentricity.


Occurrence


Moons

All twenty known moons in the
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
that are large enough to be round are tidally locked with their primaries, because they orbit very closely and tidal force increases rapidly (as a
cubic function In mathematics, a cubic function is a function of the form f(x)=ax^3+bx^2+cx+d where the coefficients , , , and are complex numbers, and the variable takes real values, and a\neq 0. In other words, it is both a polynomial function of degree ...
) with decreasing distance. On the other hand, the irregular outer satellites of the
gas giant A gas giant is a giant planet composed mainly of hydrogen and helium. Gas giants are also called failed stars because they contain the same basic elements as a star. Jupiter and Saturn are the gas giants of the Solar System. The term "gas giant" ...
s (e.g. Phoebe), which orbit much farther away than the large well-known moons, are not tidally locked.
Pluto Pluto (minor-planet designation: 134340 Pluto) is a dwarf planet in the Kuiper belt, a ring of trans-Neptunian object, bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the S ...
and
Charon In Greek mythology, Charon or Kharon (; grc, Χάρων) is a psychopomp, the ferryman of Hades, the Greek underworld. He carries the souls of those who have been given funeral rites across the rivers Acheron and Styx, which separate the wo ...
are an extreme example of a tidal lock. Charon is a relatively large moon in comparison to its primary and also has a very close
orbit In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
. This results in Pluto and Charon being mutually tidally locked. Pluto's other moons are not tidally locked;
Styx In Greek mythology, Styx (; grc, Στύξ ) is a river that forms the boundary between Earth (Gaia) and the Underworld. The rivers Acheron, Cocytus, Lethe, Phlegethon, and Styx all converge at the centre of the underworld on a great marsh, whic ...
,
Nix Nix or NIX may refer to: Places * Nix, Alabama, an unincorporated community, United States * Nix, Texas, a ghost town in southwestern Lampasas County, Texas, United States * Nix (moon), a moon of Pluto People * Nix (surname), listing people with ...
, Kerberos, and Hydra all rotate chaotically due to the influence of Charon. Similarly, and Dysnomia are mutually tidally locked. The tidal locking situation for
asteroid moon A minor-planet moon is an astronomical object that orbits a minor planet as its natural satellite. , there are 457 minor planets known or suspected to have moons. Discoveries of minor-planet moons (and binary objects, in general) are important ...
s is largely unknown, but closely orbiting binaries are expected to be tidally locked, as well as contact binaries.


Earth's Moon

Earth's Moon's rotation and orbital periods are tidally locked with each other, so no matter when the Moon is observed from Earth, the same hemisphere of the Moon is always seen. The
far side of the Moon The far side of the Moon is the lunar hemisphere that always faces away from Earth, opposite to the Near side of the Moon, near side, because of synchronous rotation in the Moon's orbit. Compared to the near side, the far side's terrain is ru ...
was not seen until 1959, when photographs of most of the far side were transmitted from the
Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...
spacecraft ''
Luna 3 Luna 3, or E-2A No.1 ( rus, Луна 3}) was a Soviet spacecraft launched in 1959 as part of the Luna programme. It was the first mission to photograph the far side of the Moon and the third Soviet space probe to be sent to the neighborhood of th ...
''. When the Earth is observed from the Moon, the Earth does not appear to move across the sky. It remains in the same place while showing nearly all its surface as it rotates on its axis. Despite the Moon's rotational and orbital periods being exactly locked, about 59 percent of the Moon's total surface may be seen with repeated observations from Earth, due to the phenomena of
libration In lunar astronomy, libration is the wagging or wavering of the Moon perceived by Earth-bound observers and caused by changes in their perspective. It permits an observer to see slightly different hemispheres of the surface at different tim ...
and
parallax Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight and is measured by the angle or semi-angle of inclination between those two lines. Due to foreshortening, nearby objects ...
. Librations are primarily caused by the Moon's varying orbital speed due to the
eccentricity Eccentricity or eccentric may refer to: * Eccentricity (behavior), odd behavior on the part of a person, as opposed to being "normal" Mathematics, science and technology Mathematics * Off-center, in geometry * Eccentricity (graph theory) of a v ...
of its orbit: this allows up to about 6° more along its perimeter to be seen from Earth. Parallax is a geometric effect: at the surface of Earth observers are offset from the line through the centers of Earth and Moon, and because of this about 1° more can be seen around the side of the Moon when it is on the local horizon.


Planets

It was thought for some time that
Mercury Mercury commonly refers to: * Mercury (planet), the nearest planet to the Sun * Mercury (element), a metallic chemical element with the symbol Hg * Mercury (mythology), a Roman god Mercury or The Mercury may also refer to: Companies * Merc ...
was in synchronous rotation with the Sun. This was because whenever Mercury was best placed for observation, the same side faced inward. Radar observations in 1965 demonstrated instead that Mercury has a 3:2 spin–orbit resonance, rotating three times for every two revolutions around the Sun, which results in the same positioning at those observation points. Modeling has demonstrated that Mercury was captured into the 3:2 spin–orbit state very early in its history, probably within 10–20 million years after its formation. The 583.92-day interval between successive close approaches of
Venus Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never fa ...
to Earth is equal to 5.001444 Venusian solar days, making approximately the same face visible from Earth at each close approach. Whether this relationship arose by chance or is the result of some kind of tidal locking with Earth is unknown. The
exoplanet An exoplanet or extrasolar planet is a planet outside the Solar System. The first possible evidence of an exoplanet was noted in 1917 but was not recognized as such. The first confirmation of detection occurred in 1992. A different planet, init ...
Proxima Centauri b Proxima Centauri b (or Proxima b), sometimes referred to as Alpha Centauri Cb, is an exoplanet orbiting in the habitable zone of the red dwarf star Proxima Centauri, which is the closest star to the Sun and part of the triple star system ...
, discovered in 2016 that orbits around
Proxima Centauri Proxima Centauri is a small, low-mass star located away from the Sun in the southern constellation of Centaurus. Its Latin name means the 'nearest tarof Centaurus'. It was discovered in 1915 by Robert Innes and is the nearest-kno ...
, is almost assuredly tidally locked, expressing either synchronized rotation or a 3:2 spin–orbit resonance like that of Mercury. One form of hypothetical tidally locked
exoplanet An exoplanet or extrasolar planet is a planet outside the Solar System. The first possible evidence of an exoplanet was noted in 1917 but was not recognized as such. The first confirmation of detection occurred in 1992. A different planet, init ...
s are
eyeball planet An eyeball planet is a hypothetical type of tidally locked planet, for which tidal locking induces spatial features (for example in the geography or composition of the planet) resembling an eyeball.They are terrestrial planets where liquids may ...
s, which in turn are divided into "hot" and "cold" eyeball planets.


Stars

Close
binary star A binary star is a system of two stars that are gravitationally bound to and in orbit around each other. Binary stars in the night sky that are seen as a single object to the naked eye are often resolved using a telescope as separate stars, in wh ...
s throughout the universe are expected to be tidally locked with each other, and
extrasolar planet An exoplanet or extrasolar planet is a planet outside the Solar System. The first possible evidence of an exoplanet was noted in 1917 but was not recognized as such. The first confirmation of detection occurred in 1992. A different planet, init ...
s that have been found to orbit their primaries extremely closely are also thought to be tidally locked to them. An unusual example, confirmed by
MOST Most or Möst or ''variation'', may refer to: Places * Most, Kardzhali Province, a village in Bulgaria * Most (city), a city in the Czech Republic ** Most District, a district surrounding the city ** Most Basin, a lowland named after the city ** A ...
, may be
Tau Boötis Tau Boötis, Latinised from τ Boötis, is an F-type main-sequence star approximately 51 light-years away in the constellation of Boötes. It is a binary star system, with the secondary star being a red dwarf. As of 1999, an extrasol ...
, a star that is probably tidally locked by its planet
Tau Boötis b Tau Boötis b, or more precisely Tau Boötis Ab, is an extrasolar planet approximately 51 light-years away. The planet and its host star is one of the planetary systems selected by the International Astronomical Union as part of NameExoWorlds, th ...
. If so, the tidal locking is almost certainly mutual.


Timescale

An estimate of the time for a body to become tidally locked can be obtained using the following formula: : t_ \approx \frac where * \omega\, is the initial spin rate expressed in
radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that c ...
s per second, * a\, is the
semi-major axis In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the long ...
of the motion of the satellite around the planet (given by the average of the
periapsis An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary (astronomy), primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two ...
and
apoapsis An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any ellip ...
distances), * I\, \approx 0.4\; m_s R^2 is the
moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceler ...
of the satellite, where m_s is the mass of the satellite and R is the mean radius of the satellite, * Q\, is the dissipation function of the satellite, * G\, is the
gravitational constant The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in ...
, * m_p\, is the mass of the planet (i.e., the object being orbited), and * k_2\, is the tidal
Love number The Love numbers (''h'', ''k'', and ''l'') are dimensionless parameters that measure the rigidity of a planetary body and the susceptibility of its shape to change in response to a tidal potential. In 1909, Augustus Edward Hough Love introduced ...
of the satellite. Q and k_2 are generally very poorly known except for the Moon, which has k_2/Q=0.0011. For a really rough estimate it is common to take Q \approx 100 (perhaps conservatively, giving overestimated locking times), and : k_2 \approx \frac, where * \rho\, is the density of the satellite * g\approx Gm_s/R^2 is the surface gravity of the satellite * \mu\, is the rigidity of the satellite. This can be roughly taken as 3 N·m−2 for rocky objects and 4 N·m−2 for icy ones. Even knowing the size and density of the satellite leaves many parameters that must be estimated (especially ''ω'', ''Q'', and ''μ''), so that any calculated locking times obtained are expected to be inaccurate, even to factors of ten. Further, during the tidal locking phase the semi-major axis a may have been significantly different from that observed nowadays due to subsequent
tidal acceleration Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite (e.g. the Moon) and the primary planet that it orbits (e.g. Earth). The acceleration causes a gradual recession of a satellite in a prograde orbit away from ...
, and the locking time is extremely sensitive to this value. Because the uncertainty is so high, the above formulas can be simplified to give a somewhat less cumbersome one. By assuming that the satellite is spherical, k_2\ll1\, , Q = 100, and it is sensible to guess one revolution every 12 hours in the initial non-locked state (most asteroids have rotational periods between about 2 hours and about 2 days) : t_ \approx 6\ \frac \times 10^\ \text, with masses in kilograms, distances in meters, and \mu in newtons per meter squared; \mu can be roughly taken as 3 N·m−2 for rocky objects and 4 N·m−2 for icy ones. There is an extremely strong dependence on semi-major axis a. For the locking of a primary body to its satellite as in the case of Pluto, the satellite and primary body parameters can be swapped. One conclusion is that, ''other things being equal'' (such as Q and \mu), a large moon will lock faster than a smaller moon at the same orbital distance from the planet because m_s\, grows as the cube of the satellite radius R. A possible example of this is in the Saturn system, where Hyperion is not tidally locked, whereas the larger
Iapetus In Greek mythology, Iapetus (; ; grc, Ἰαπετός, Iapetós), also Japetus, is a Titan, the son of Uranus and Gaia and father of Atlas, Prometheus, Epimetheus, and Menoetius. He was also called the father of Buphagus and Anchiale in other ...
, which orbits at a greater distance, is. However, this is not clear cut because Hyperion also experiences strong driving from the nearby Titan, which forces its rotation to be chaotic. The above formulae for the timescale of locking may be off by orders of magnitude, because they ignore the frequency dependence of k_2/Q. More importantly, they may be inapplicable to viscous binaries (double stars, or double asteroids that are rubble), because the spin–orbit dynamics of such bodies is defined mainly by their viscosity, not rigidity.


List of known tidally locked bodies


Solar System


Extra-solar

* The most successful detection methods of exoplanets (transits and radial velocities) suffer from a clear observational bias favoring the detection of planets near the star; thus, 85% of the exoplanets detected are inside the tidal locking zone, which makes it difficult to estimate the true incidence of this phenomenon.
Tau Boötis Tau Boötis, Latinised from τ Boötis, is an F-type main-sequence star approximately 51 light-years away in the constellation of Boötes. It is a binary star system, with the secondary star being a red dwarf. As of 1999, an extrasol ...
is known to be locked to the close-orbiting
giant planet The giant planets constitute a diverse type of planet much larger than Earth. They are usually primarily composed of low-boiling-point materials (volatiles), rather than rock or other solid matter, but massive solid planets can also exist. Ther ...
Tau Boötis b Tau Boötis b, or more precisely Tau Boötis Ab, is an extrasolar planet approximately 51 light-years away. The planet and its host star is one of the planetary systems selected by the International Astronomical Union as part of NameExoWorlds, th ...
.


Bodies likely to be locked


Solar System

Based on comparison between the likely time needed to lock a body to its primary, and the time it has been in its present orbit (comparable with the age of the Solar System for most planetary moons), a number of moons are thought to be locked. However their rotations are not known or not known enough. These are:


Probably locked to Saturn

*
Daphnis In Greek mythology, Daphnis (; grc, Δάφνις, from , ''daphne'', "Bay Laurel") was a Sicilian shepherd who was said to be the inventor of pastoral poetry. Family According to tradition, he was the son of Hermes and a nymph, despite which ...
* Aegaeon * Methone * Anthe * Pallene * Helene * Polydeuces


Probably locked to Uranus

*
Cordelia Cordelia is a feminine given name. It was borne by the tragic heroine of Shakespeare's ''King Lear'' (1606), a character based on the legendary queen Cordelia. The name is of uncertain origin. It is popularly associated with Latin '' cor'' ( geni ...
*
Ophelia Ophelia () is a character in William Shakespeare's drama ''Hamlet'' (1599–1601). She is a young noblewoman of Denmark, the daughter of Polonius, sister of Laertes and potential wife of Prince Hamlet, who, due to Hamlet's actions, ends up in ...
*
Bianca Bianca is a feminine given name. It means "white" and is an Italian cognate of Blanche. Variants * Blanche: French * Bianca: Italian * Bianka ( Polish, Hungarian, Slovak, German, English, French, Icelandic, Finnish, Dutch, Norwegian, C ...
*
Cressida Cressida (; also Criseida, Cresseid or Criseyde) is a character who appears in many Medieval and Renaissance retellings of the story of the Trojan War. She is a Trojan woman, the daughter of Calchas, a Greek seer. She falls in love with Troilus, ...
*
Desdemona Desdemona () is a character in William Shakespeare's play ''Othello'' (c. 1601–1604). Shakespeare's Desdemona is a Venetian beauty who enrages and disappoints her father, a Venetian senator, when she elopes with Othello, a Moorish Venetian ...
*
Juliet Juliet Capulet () is the female protagonist in William Shakespeare's romantic tragedy ''Romeo and Juliet''. A 13-year-old girl, Juliet is the only daughter of the patriarch of the House of Capulet. She falls in love with the male protagonist R ...
* Portia * Rosalind *
Cupid In classical mythology, Cupid (Latin Cupīdō , meaning "passionate desire") is the god of desire, lust, erotic love, attraction and affection. He is often portrayed as the son of the love goddess Venus (mythology), Venus and the god of war Mar ...
*
Belinda Belinda is a feminine given name of unknown origin, apparently coined from Italian ''bella'', meaning "beautiful". Alternatively it may be derived from the Old High German name ''Betlinde'', which possibly meant "bright serpent" or "bright linde ...
* Perdita * Puck * Mab


Probably locked to Neptune

*
Naiad In Greek mythology, the naiads (; grc-gre, ναϊάδες, naïádes) are a type of female spirit, or nymph, presiding over fountains, wells, springs, streams, brooks and other bodies of fresh water. They are distinct from river gods, who ...
*
Thalassa Thalassa (; grc-gre, Θάλασσα, Thálassa, sea; Attic Greek: , ''Thálatta'') was the general word for 'sea' and for its divine female personification in Greek mythology. The word may have been of Pre-Greek origin. Mythology According t ...
* Despina *
Galatea Galatea is an ancient Greek name meaning "she who is milk-white". Galatea, Galathea or Gallathea may refer to: In mythology * Galatea (Greek myth), three different mythological figures In the arts * ''Aci, Galatea e Polifemo'', cantata by H ...
*
Larissa Larissa (; el, Λάρισα, , ) is the capital and largest city of the Thessaly region in Greece. It is the fifth-most populous city in Greece with a population of 144,651 according to the 2011 census. It is also capital of the Larissa regiona ...


Extrasolar

*
Gliese 581c Gliese 581c (Gl 581c or GJ 581c) is a planet orbiting within the Gliese 581 system. It is the second planet discovered in the system and the third in order from the star. With a mass at least 5.5 times that of the Earth, it is classified as a ...
,
Gliese 581g Gliese 581g , unofficially known as Zarmina (or Zarmina's World), was a candidate exoplanet postulated to orbit within the Gliese 581 system, twenty light-years from Earth. It was discovered by the Lick–Carnegie Exoplanet Survey, and was the si ...
,
Gliese 581b Gliese 581b or Gl 581b is an extrasolar planet orbiting within the Gliese 581 system. It is the first planet discovered of three confirmed in the system so far, and the second in order from the star. Discovery The planet was discovered by a tea ...
, and
Gliese 581e Gliese 581e or Gl 581e is an extrasolar planet orbiting within the Gliese 581 system, located approximately 20.4 light-years away from Earth in the Libra constellation. It is the third planet discovered in the system (fourth if the disputed plane ...
may be tidally locked to their parent star
Gliese 581 Gliese 581 () is a red dwarf star of spectral type M3V at the center of the Gliese 581 planetary system, about 20 light years away from Earth in the Libra constellation. Its estimated mass is about a third of that of the Sun, and it is t ...
.
Gliese 581d Gliese 581d (often shortened to Gl 581d or GJ 581d) is a proposed extrasolar planet orbiting within the Gliese 581 system, approximately 20.4 light-years away in the Libra constellation. It is the third planet claimed in the system and (assumi ...
is almost certainly captured either into the 2:1 or the 3:2 spin–orbit resonance with the same star. * All planets in the TRAPPIST-1 system are likely to be tidally locked.


See also

* * Earth tide#Effects * * * * * * *


References

{{DEFAULTSORT:Tidal Locking Celestial mechanics Orbits Locking