Editing Tidal locking (section)

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

[[File:Árapály forgatónyomaték.png|thumbnail|Here, the body's tidal bulges (green) are misaligned with the direction of the attracting force (red). The local tidal forces (blue) exert a net torque that twists the body back toward realignment.]]

Consider a pair of co-orbiting objects, A and B. The change in [[Rotation period|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 force]]s.<ref>{{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 }}</ref>

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 [[Mechanical equilibrium|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 bulge]]s. (For the solid Earth, these bulges can reach displacements of up to around {{Convert|0.4|m|ftin|disp=or|abbr=on}}.<ref>{{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 }}</ref>) 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 [[Sphericity|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.

===Orbital changes===
[[File:tidal_acceleration_principle.svg|thumb|300px|In (1), a satellite orbits in the same direction as (but slower than) its parent body's rotation. The nearer tidal bulge (red) attracts the satellite more than the farther bulge (blue), slowing the parent's rotation while imparting a net positive force (dotted arrows showing forces resolved into their components) in the direction of orbit, lifting it into a higher orbit (tidal acceleration).<br/>In (2) with the rotation reversed, the net force opposes the satellite's direction of orbit, lowering it (tidal deceleration).]]
[[File:MoonTorque.svg|thumb|alt=Tidal Locking|If rotational frequency is larger than orbital frequency, a small torque counteracting the rotation arises, eventually locking the frequencies (situation depicted in green)]]
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.

===Locking of the larger body===
{{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.<ref>{{cite book
 | first=Imke | last=de Pater
 | date=2001
 | title=Planetary Sciences
 | publisher=Cambridge| isbn=978-0521482196
 | page=34}}</ref> 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 clock]]s show that Earth's day lengthens, on average, by about 2.3 milliseconds per century.<ref>{{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}}</ref> 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 [[Orbit of the Moon|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.<ref>{{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 }}</ref><ref>{{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 }}
</ref>

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 (moon)|Charon]]. They have already reached a state where Charon is visible from only one hemisphere of Pluto and vice versa.<ref name=Michaely2017>{{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 }}</ref>

===Eccentric orbits===
{{Quote
|text=A widely spread misapprehension is that a tidally locked body
permanently turns one side to its host.
|author=Heller et al. (2011)<ref name=Heller_Leconte_Barnes_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 &ndash; an effect known as eccentricity pumping.<ref name=Correia2012>{{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 }}</ref>

In some cases where the orbit is [[eccentricity (orbit)|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 (planet)|Mercury]], which is locked to its own orbit around the Sun in a 3:2 resonance.<ref name=Clouse_et_al_2022>{{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 }}</ref> This results in the rotation speed roughly matching the orbital speed around perihelion.<ref>{{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 }}</ref>

Many [[exoplanet]]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.<ref name=Makarov2012>{{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= }}</ref>