tidal locking

{{Further information|Centers of gravity in non-uniform fields}}

File:Árapály forgatónyomaték.png

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 applied by A's gravity on bulges it has induced on B by tidal forces.{{cite book | title=Physics and Chemistry of the Solar System | first1=John | last1=Lewis | publisher=Academic Press | year=2012 | isbn=978-0323145848 | pages=242–243 | url=https://books.google.com/books?id=35uwarLgVLsC&pg=PA242 | access-date=2018-02-22 | archive-date=2023-08-06 | archive-url=https://web.archive.org/web/20230806163533/https://books.google.com/books?id=35uwarLgVLsC&pg=PA242 | url-status=live }}

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 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 to this axis. The elongated distortions are known as tidal bulges. (For the solid Earth, these bulges can reach displacements of up to around {{Convert|0.4|m|ftin|disp=or|abbr=on}}.{{cite journal | title=Impact of solid Earth tide models on GPS coordinate and tropospheric time series | display-authors=1 | last1=Watson | first1=C. | last2=Tregoning | first2=P. | last3=Coleman | first3=R. | journal=Geophysical Research Letters | volume=33 | issue=8 | pages=L08306 | date=April 2006 | doi=10.1029/2005GL025538 | bibcode=2006GeoRL..33.8306W | hdl=1885/21511 | url=http://eprints.utas.edu.au/3437/1/2005GL0255381.pdf | doi-access=free | access-date=2018-05-18 | archive-date=2021-11-26 | archive-url=https://web.archive.org/web/20211126171559/https://eprints.utas.edu.au/3437/1/2005GL0255381.pdf | url-status=live }}) 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 due to self-gravitation, the tidal distortion produces a slightly prolate spheroid, i.e. an axially symmetric ellipsoid 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.

File:tidal_acceleration_principle.svg

File:MoonTorque.svg

The angular momentum 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.

{{See also|Synchronous orbit}}

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.{{cite book

| first=Imke | last=de Pater

| date=2001

| title=Planetary Sciences

| publisher=Cambridge| isbn=978-0521482196

| page=34}} 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 about 4.5 billion years). Currently, atomic clocks show that Earth's day lengthens, on average, by about 2.3 milliseconds per century.{{cite web|last = Ray|first = R.|date = 15 May 2001|url = http://bowie.gsfc.nasa.gov/ggfc/tides/intro.html|archive-url = https://web.archive.org/web/20000818161603/http://bowie.gsfc.nasa.gov/ggfc/tides/intro.html|archive-date = 18 August 2000|title = Ocean Tides and the Earth's Rotation|publisher = IERS Special Bureau for Tides|access-date =17 March 2010}} Given enough time, this would create a mutual tidal locking between Earth and the Moon. The length of Earth's day would increase and the length of a lunar month would also increase. Earth's sidereal day would eventually have the same length as the Moon's orbital period, about 47 times the length of the Earth day at present. However, Earth is not expected to become tidally locked to the Moon before the Sun becomes a red giant and engulfs Earth and the Moon.{{cite book| last1 = Murray | first1 = C. D.|first2 = Stanley F. |last2 = Dermott| title = Solar System Dynamics| date = 1999| publisher = Cambridge University Press| isbn = 978-0-521-57295-8| page = 184 }}{{cite book| last = Dickinson| first = Terence| author-link = Terence Dickinson| title = From the Big Bang to Planet X| date = 1993| publisher = Camden House| location = Camden East, Ontario| isbn = 978-0-921820-71-0| pages = 79–81 }}

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 Pluto and its satellite Charon. They have already reached a state where Charon is visible from only one hemisphere of Pluto and vice versa.{{citation | title=On the Existence of Regular and Irregular Outer Moons Orbiting the Pluto–Charon System | display-authors=1 | last1=Michaely | first1=Erez | last2=Perets | first2=Hagai B. | last3=Grishin | first3=Evgeni | journal=The Astrophysical Journal | volume=836 | issue=1 | id=27 | pages=7 | date=February 2017 | doi=10.3847/1538-4357/aa52b2 | bibcode=2017ApJ...836...27M | arxiv=1506.08818 | s2cid=118068933 | doi-access=free }}

{{Quote

|text=A widely spread misapprehension is that a tidally locked body

permanently turns one side to its host.

|author=Heller et al. (2011)

}}

For orbits that do not have an eccentricity close to zero, the rotation rate tends to become locked with the orbital speed when the body is at periapsis, 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.{{citation

| title=Pumping the Eccentricity of Exoplanets by Tidal Effect

| last1=Correia | first1=Alexandre C. M. | last2=Boué | first2=Gwenaël

| last3=Laskar | first3=Jacques | postscript=.

| journal=The Astrophysical Journal Letters

| volume=744 | issue=2 | id=L23 | pages=5 | date=January 2012

| doi=10.1088/2041-8205/744/2/L23 | bibcode=2012ApJ...744L..23C | arxiv=1111.5486| s2cid=118695308 }}

In some cases where the orbit is eccentric 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, which is locked to its own orbit around the Sun in a 3:2 resonance.{{citation |title=Spin-orbit gravitational locking-an effective potential approach |display-authors=1 |last1=Clouse |first1=Christopher |last2=Ferroglia |first2=Andrea |last3=Fiolhais |first3=Miguel C. N. |journal=European Journal of Physics |postscript= |volume=43 |issue=3 |id=035602 |pages=13 |date=May 2022 |doi=10.1088/1361-6404/ac5638 |arxiv=2203.09297 |bibcode=2022EJPh...43c5602C

|s2cid=246962304 }} This results in the rotation speed roughly matching the orbital speed around perihelion.{{citation |title=Rotational Period of the Planet Mercury |last=Colombo |first=G. |journal=Nature |volume=208 |issue=5010 |page=575 |date=November 1965 |doi=10.1038/208575a0 |bibcode=1965Natur.208..575C

|s2cid=4213296 |doi-access=free }}

Many exoplanets (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.{{citation |title=Conditions of Passage and Entrapment of Terrestrial Planets in Spin–orbit Resonances |last1=Makarov |first1=Valeri V. |journal=The Astrophysical Journal |volume=752 |issue=1 |id=73 |pages=8 |date=June 2012 |doi=10.1088/0004-637X/752/1/73 |bibcode=2012ApJ...752...73M |arxiv=1110.2658 |s2cid=119227632 |postscript= }}

File:Synchronous rotation.svg

All twenty known moons in the Solar System 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) with decreasing distance.{{cite book|last1=Schutz|first1=Bernard|title=Gravity from the Ground Up|publisher=Cambridge University Press|isbn=9780521455060|page=43|url=https://books.google.com/books?id=P_T0xxhDcsIC&pg=PA43|access-date=24 April 2017|date=2003-12-04|archive-date=2023-08-06|archive-url=https://web.archive.org/web/20230806164032/https://books.google.com/books?id=P_T0xxhDcsIC&pg=PA43|url-status=live}} On the other hand, most of the irregular outer satellites of the giant planets (e.g. Phoebe), which orbit much farther away than the large well-known moons, are not tidally locked.{{cn|date=May 2024}}

Pluto and Charon 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. This results in Pluto and Charon being mutually tidally locked. Pluto's other moons are not tidally locked; Styx, Nix, Kerberos, and Hydra all rotate chaotically due to the influence of Charon.{{cite journal | title=Resonant interactions and chaotic rotation of Pluto's small moons | last1=Showalter | first1=M. R. | last2=Hamilton | first2=D. P. | journal=Nature | date=June 2015 | volume=522 | issue=7554 | pages=45–49 | doi=10.1038/nature14469 | pmid=26040889 | bibcode=2015Natur.522...45S | s2cid=205243819 | url=https://esahubble.org/static/archives/releases/science_papers/heic1512a.pdf | access-date=2022-03-25 | archive-date=2022-06-08 | archive-url=https://web.archive.org/web/20220608040417/https://esahubble.org/static/archives/releases/science_papers/heic1512a.pdf | url-status=live }} Similarly, {{dp|Eris}} and Dysnomia are mutually tidally locked. {{dp|Orcus}} and Vanth might also be mutually tidally locked, but the data is not conclusive.{{Cite journal | last1 = Ortiz | first1 = J. L. | last2 = Cikota | first2 = A. | last3 = Cikota | first3 = S. | last4 = Hestroffer | first4 = D. | last5 = Thirouin | first5 = A. | last6 = Morales | first6 = N. | last7 = Duffard | first7 = R. | last8 = Gil-Hutton | first8 = R. | last9 = Santos-Sanz | first9 = P. | last10 = De La Cueva | first10 = I. | title = A mid-term astrometric and photometric study of trans-Neptunian object (90482) Orcus | doi = 10.1051/0004-6361/201015309 | journal = Astronomy & Astrophysics | volume = 525 | pages = A31 | date = 2010 |bibcode = 2011A&A...525A..31O |arxiv = 1010.6187 | s2cid = 56051949 }}

The tidal locking situation for asteroid moons is largely unknown, but closely orbiting binaries are expected to be tidally locked,{{cn|date=March 2022|reason=Not necessarily true given the YORP effect}} as well as contact binaries.

File:Lunation animation April 2007.gif

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. Most of the far side of the Moon was not seen until 1959, when photographs of most of the far side were transmitted from the Soviet spacecraft Luna 3.{{cite web|title=Oct. 7, 1959 – Our First Look at the Far Side of the Moon|url=http://www.universetoday.com/105326/oct-7-1959-our-first-look-at-the-far-side-of-the-moon/|website=Universe Today|date=2013-10-07|access-date=2015-02-15|archive-date=2022-08-12|archive-url=https://web.archive.org/web/20220812035122/https://www.universetoday.com/105326/oct-7-1959-our-first-look-at-the-far-side-of-the-moon/|url-status=live}}

When Earth is observed from the Moon, 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.{{Cite web|last=Cain|first=Fraser|date=2016-04-11|title=When Will Earth Lock to the Moon?|url=https://www.universetoday.com/128350/will-earth-lock-moon/|access-date=2020-08-03|website=Universe Today|language=en-US|archive-date=2022-05-28|archive-url=https://web.archive.org/web/20220528015905/https://www.universetoday.com/128350/will-earth-lock-moon/|url-status=live}}

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 and parallax. Librations are primarily caused by the Moon's varying orbital speed due to the eccentricity 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; this accounts for about a 1° difference in the Moon's surface which can be seen around the sides of the Moon when comparing observations made during moonrise and moonset.{{cite book

| title=The Moon and How to Observe It

| first=Peter

| last=Grego

| year=2006

| pages=47–50

| isbn=9781846282430

| publisher=Springer London

| url=https://books.google.com/books?id=0wh5HABxVksC&pg=PA48

| access-date=2023-03-19

| archive-date=2023-10-21

| archive-url=https://web.archive.org/web/20231021104054/https://books.google.com/books?id=0wh5HABxVksC&pg=PA48

| url-status=live

}}

It was thought for some time that Mercury 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.{{Cite journal | bibcode=2014Icar..241...26N | last1=Noyelles | first1=Benoit | last2=Frouard | first2=Julien | last3=Makarov | first3=Valeri V. | last4=Efroimsky | first4=Michael | name-list-style=amp | title=Spin–orbit evolution of Mercury revisited | journal=Icarus | date=2014 | volume=241 | doi=10.1016/j.icarus.2014.05.045 | pages=26–44 | arxiv = 1307.0136 | s2cid=53690707 }}

The 583.92-day interval between successive close approaches of Venus 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.{{cite journal |last1=Gold |first1=T. |last2=Soter |first2=S. |date=1969 |title=Atmospheric tides and the resonant rotation of Venus |journal=Icarus |volume=11 |issue=3 |pages=356–366|bibcode=1969Icar...11..356G |doi=10.1016/0019-1035(69)90068-2 }}

The exoplanet Proxima Centauri b discovered in 2016 which orbits around Proxima Centauri, is almost certainly tidally locked, expressing either synchronized rotation or a 3:2 spin–orbit resonance like that of Mercury.{{cite journal|title=Tidal locking of habitable exoplanets|url=https://link.springer.com/article/10.1007/s10569-017-9783-7|publisher=Springer|year=2017|doi=10.1007/s10569-017-9783-7|last1=Barnes|first1=Rory|journal=Celestial Mechanics and Dynamical Astronomy|volume=129|issue=4|pages=509–536|s2cid=119384474|arxiv=1708.02981|bibcode=2017CeMDA.129..509B|access-date=2021-03-29|archive-date=2021-02-26|archive-url=https://web.archive.org/web/20210226135913/https://link.springer.com/article/10.1007/s10569-017-9783-7|url-status=live}}

One form of hypothetical tidally locked exoplanets are eyeball planets, which in turn are divided into "hot" and "cold" eyeball planets.{{cite web|url=http://nautil.us/blog/forget-earth_likewell-first-find-aliens-on-eyeball-planets|title=Forget "Earth-Like"—We'll First Find Aliens on Eyeball Planets|publisher=Nautilus|language=en|author=Sean Raymond|date=20 February 2015|access-date=5 June 2017|archive-date=23 June 2017|archive-url=https://web.archive.org/web/20170623082602/http://nautil.us/blog/forget-earth_likewell-first-find-aliens-on-eyeball-planets|url-status=dead}}{{cite news |last=Starr |first=Michelle |title=Eyeball Planets Might Exist, And They're as Creepy as They Sound |url=https://www.sciencealert.com/eyeball-planets-might-exist-yep-they-re-exactly-as-creepy-as-they-sound |date=5 January 2020 |work=ScienceAlert.com |access-date=6 January 2020 |archive-date=6 January 2020 |archive-url=https://web.archive.org/web/20200106014046/https://www.sciencealert.com/eyeball-planets-might-exist-yep-they-re-exactly-as-creepy-as-they-sound |url-status=live }}

Close binary stars throughout the universe are expected to be tidally locked with each other, and extrasolar planets 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, may be Tau Boötis, a star that is probably tidally locked by its planet Tau Boötis b.{{cite web |url=http://www.space.com/scienceastronomy/050523_star_tide.html |title=Role Reversal: Planet Controls a Star |date=2005-05-23 |first=Michael |last=Schirber |publisher=space.com |access-date=2018-04-21 |archive-date=2008-08-04 |archive-url=https://web.archive.org/web/20080804180104/http://www.space.com/scienceastronomy/050523_star_tide.html |url-status=live }} If so, the tidal locking is almost certainly mutual.{{cite journal | title=Life on a tidally-locked planet | last=Singal | first=Ashok K. | journal=Planex Newsletter | volume=4 | issue=2 | page=8 | date=May 2014 | bibcode=2014arXiv1405.1025S | arxiv=1405.1025 }}{{cite journal | title=MOST detects variability on tau Bootis possibly induced by its planetary companion | url=http://www.aanda.org/articles/aa/full/2008/17/aa8952-07/aa8952-07.html | last1=Walker | first1=G. A. H. | last2=Croll | first2=B. | last3=Matthews | first3=J. M. | last4=Kuschnig | first4=R. | last5=Huber | first5=D. | last6=Weiss | first6=W. W. | last7=Shkolnik | first7=E. | last8=Rucinski | first8=S. M. | last9=Guenther | first9=D. B. | display-authors=1 | year=2008 | journal=Astronomy and Astrophysics | volume=482 | issue=2 | pages=691–697 | doi=10.1051/0004-6361:20078952 | arxiv=0802.2732 | bibcode=2008A&A...482..691W | s2cid=56317105 | access-date=2019-05-16 | archive-date=2021-02-25 | archive-url=https://web.archive.org/web/20210225212508/https://www.aanda.org/articles/aa/full/2008/17/aa8952-07/aa8952-07.html | url-status=live }}

An estimate of the time for a body to become tidally locked can be obtained using the following formula:{{cite journal | author= B. Gladman| display-authors= etal| title= Synchronous Locking of Tidally Evolving Satellites| journal= Icarus| date= 1996| volume= 122| issue= 1| pages= 166–192 | doi = 10.1006/icar.1996.0117| bibcode=1996Icar..122..166G| doi-access= free}} (See pages 169–170 of this article. Formula (9) is quoted here, which comes from S. J. Peale, Rotation histories of the natural satellites, in {{cite book | editor= J. A. Burns | title= Planetary Satellites| date= 1977| publisher= University of Arizona Press |pages= 87–112| location= Tucson}})

:$$

t_{\text{lock}} \approx \frac{\omega a^6 I Q}{3 G m_p^2 k_2 R^5}

where

• $\backslash omega\backslash ,$ is the initial spin rate expressed in radians per second,
• $a\backslash ,$ is the semi-major axis of the motion of the satellite around the planet (given by the average of the periapsis and apoapsis distances),
• $I\backslash ,$ $\backslash approx\; 0.4\backslash ;\; m\_s\; R^2$ is the moment of inertia of the satellite, where $m\_s$ is the mass of the satellite and $R$ is the mean radius of the satellite,
• $Q\backslash ,$ is the dissipation function of the satellite,
• $G\backslash ,$ is the gravitational constant,
• $m\_p\backslash ,$ is the mass of the planet (i.e., the object being orbited), and
• $k\_2\backslash ,$ is the tidal Love number 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 $Q\; \backslash approx\; 100$ (perhaps conservatively, giving overestimated locking times), and

:$$

k_2 \approx \frac{1.5}{1+\frac{19\mu}{2\rho g R}},

where

• $\backslash rho\backslash ,$ is the density of the satellite
• $g\backslash approx\; Gm\_s/R^2$ is the surface gravity of the satellite
• $\backslash mu\backslash ,$ is the rigidity of the satellite. This can be roughly taken as 3{{e|10}} N/m² for rocky objects and 4{{e|9}} N/m² 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, 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, $k\_2\backslash ll1\backslash ,\; ,\; Q\; =\; 100$, 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_{\text{lock}} \approx 6\ \frac{a^6R\mu}{m_sm_p^2} \times 10^{10}\ \text{years},

{{cite book

| title=Planetary Habitability And Stellar Activity

| first=Arnold

| last=Hanslmeier

| date=2018

| page=99

| isbn=9789813237445

| publisher=World Scientific Publishing Company

| url=https://books.google.com/books?id=plZoDwAAQBAJ&pg=PA99

| access-date=2023-03-19

| archive-date=2023-10-04

| archive-url=https://web.archive.org/web/20231004190153/https://books.google.com/books?id=plZoDwAAQBAJ&pg=PA99

| url-status=live

}}

with masses in kilograms, distances in meters, and $\backslash mu$ in newtons per meter squared; $\backslash mu$ can be roughly taken as 3{{e|10}} N/m² for rocky objects and 4{{e|9}} N/m² 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 $\backslash mu$), a large moon will lock faster than a smaller moon at the same orbital distance from the planet because $m\_s\backslash ,$ 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, 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.{{Cite journal|bibcode=2015AJ....150...98E |author=Efroimsky, M. |title=Tidal Evolution of Asteroidal Binaries. Ruled by Viscosity. Ignorant of Rigidity. |journal=The Astronomical Journal |id=98 |date=2015 | volume=150 |issue=4 |doi=10.1088/0004-6256/150/4/98 |arxiv = 1506.09157 | pages=12 |s2cid=119283628 }}

All the bodies below are tidally locked, and all but Mercury are moreover in synchronous rotation. (Mercury is tidally locked, but not in synchronous rotation.)

• 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.{{cite journal|author=F. J. Ballesteros|author2=A. Fernandez-Soto|author3=V. J. Martinez|title=Title: Diving into Exoplanets: Are Water Seas the Most Common?|date=2019|doi=10.1089/ast.2017.1720|journal=Astrobiology|pmid=30789285|volume=19|issue=5|pages=642–654|hdl=10261/213115|s2cid=73498809|hdl-access=free}} Tau Boötis is known to be locked to the close-orbiting giant planet Tau Boötis b.

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:

{{colbegin|colwidth=18em}}

• Daphnis
• Aegaeon
• Methone
• Anthe
• Pallene
• Helene
• Polydeuces

{{colend}}

{{colbegin|colwidth=18em}}

• Cordelia
• Ophelia
• Bianca
• Cressida
• Desdemona
• Juliet
• Portia
• Rosalind
• Cupid
• Belinda
• Perdita
• Puck
• Mab

{{colend}}

{{colbegin|colwidth=18em}}

• Naiad
• Thalassa
• Despina
• Galatea
• Larissa

{{colend}}

• Orcus and Vanth{{cite journal

|first1 = Michael E. |last1 = Brown

|first2 = Bryan |last2 = Butler

|title = Masses and densities of dwarf planet satellites measured with ALMA

|journal = The Planetary Science Journal

|date = July 2023

|volume = 4

|issue = 10

|id =

|pages = 11

|doi-access = free

|doi = 10.3847/PSJ/ace52a

|arxiv = 2307.04848

|bibcode = 2023PSJ.....4..193B

|s2cid = }}

• Gliese 581c,{{cite news | url=https://www.usatoday.com/printedition/news/20070425/1a_bottomstrip25_dom.art.htm | work=USA Today | title=Out of our world: Earthlike planet | first=Dan | last=Vergano | date=2007-04-25 | access-date=2010-05-25 | archive-date=2011-05-23 | archive-url=https://web.archive.org/web/20110523021921/http://www.usatoday.com/printedition/news/20070425/1a_bottomstrip25_dom.art.htm | url-status=live }} Gliese 581g,{{cite journal|url=http://news.sciencemag.org/sciencenow/2010/09/astronomers-find-most-earth-like.html|title=Astronomers Find Most Earth-like Planet to Date|journal=Science, USA|date=September 29, 2010|access-date=September 30, 2010|archive-url=https://web.archive.org/web/20101002020745/http://news.sciencemag.org/sciencenow/2010/09/astronomers-find-most-earth-like.html|archive-date=October 2, 2010}}{{Cite web|url=https://www.telegraph.co.uk/science/space/8033124/Gliese-581g-the-most-Earth-like-planet-yet-discovered.html|title=Gliese 581g the most Earth like planet yet discovered|publisher=The Daily Telegraph, UK|date=September 30, 2010|access-date=September 30, 2010|archive-url=https://web.archive.org/web/20101002104629/http://www.telegraph.co.uk/science/space/8033124/Gliese-581g-the-most-Earth-like-planet-yet-discovered.html|archive-date=October 2, 2010}} Gliese 581b,{{cite web |title=Gliese 581 |url=http://www.openexoplanetcatalogue.com/planet/Gliese%20581%20b/ |website=Open Exoplanet Catalogue |access-date=16 May 2019 |archive-date=7 April 2022 |archive-url=https://web.archive.org/web/20220407173703/http://www.openexoplanetcatalogue.com/planet/Gliese%20581%20b/ |url-status=live }} and Gliese 581e{{cite web |title=Gliese 581 |url=https://library.eb.com.au/levels/adults/article/Gliese-581/475108 |website=Encyclopedia Britannica |access-date=16 May 2019 |archive-date=6 August 2023 |archive-url=https://web.archive.org/web/20230806164036/https://library.eb.com.au/?target=%2Flevels%2Fadults%2Farticle%2FGliese-581%2F475108 |url-status=live }} may be tidally locked to their parent star Gliese 581. Gliese 581d is almost certainly captured either into the 2:1 or the 3:2 spin–orbit resonance with the same star.{{Cite journal | bibcode=2012ApJ...761...83M | last1=Makarov | first1=V. V. | last2=Berghea | first2=C. | last3=Efroimsky | first3=M. | name-list-style=amp | title=Dynamical Evolution and Spin–Orbit Resonances of Potentially Habitable Exoplanets: The Case of GJ 581d. | journal=The Astrophysical Journal | id=83 | date=2012 | issue=2 | volume=761 | doi=10.1088/0004-637X/761/2/83 | pages=83 | arxiv=1208.0814 | s2cid=926755 }}
• All planets in the TRAPPIST-1 system are likely to be tidally locked.{{cite press release|title=NASA Telescope Reveals Largest Batch of Earth-Size, Habitable-Zone Planets Around Single Star|url=https://www.nasa.gov/press-release/nasa-telescope-reveals-largest-batch-of-earth-size-habitable-zone-planets-around|publisher=NASA|date=22 February 2017|access-date=23 February 2017|archive-date=5 March 2017|archive-url=https://web.archive.org/web/20170305055703/https://www.nasa.gov/press-release/nasa-telescope-reveals-largest-batch-of-earth-size-habitable-zone-planets-around/|url-status=live}}{{Cite journal | last1=Gillon | first1=Michaël | last2=Triaud | first2=Amaury H. M. J. | last3=Demory | first3=Brice-Olivier | last4=Jehin | first4=Emmanuël | last5=Agol | first5=Eric | last6=Deck | first6=Katherine M. | last7=Lederer | first7=Susan M. | last8=de Wit | first8=Julien | last9=Burdanov | first9=Artem | date=2017-02-23 | title=Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1 | journal=Nature | language=en | volume=542 | issue=7642 | pages=456–460 | doi=10.1038/nature21360 | issn=0028-0836 | pmc=5330437 | pmid=28230125 | arxiv=1703.01424 | bibcode=2017Natur.542..456G }}

{{Portal|Physics|Astronomy|Stars|Spaceflight|Outer space|Solar System}}

• {{annotated link|Conservation of angular momentum}}
• {{annotated link|Gravity-gradient stabilization}}
• {{annotated link|Kozai mechanism}}
• {{annotated link|Orbital resonance}}
• {{annotated link|Planetary habitability}}
• Pseudo-synchronous rotation – a near synchronization of revolution and rotation at periastron
• {{annotated link|Roche limit}}
• {{annotated link|Synchronous orbit}}
• {{annotated link|Tidal acceleration}}
• {{annotated link|Rotation around a fixed axis}}

{{Reflist|30em}}

{{The Moon|state=collapsed}}

{{DEFAULTSORT:Tidal Locking}}

Category:Celestial mechanics

Category:Orbits

Locking