A separate article treats the phenomenon of tidal resonance in oceanography. In Oceanography, a tidal Resonance occurs when the Tide excites one of the resonant modes of the ocean Oceanography (from the greek words Ωκεανός meaning Ocean and γράφω meaning to write also called oceanology or
See the article tidal acceleration for a more quantitative description of the Earth-Moon system. Tidal acceleration is an effect of the Tidal forces between an orbiting Natural satellite ( i

Tidal locking occurs when the gravitational gradient makes one side of an astronomical body always face another; for example, one side of the Earth's Moon always faces the Earth. The tidal force is a secondary effect of the Force of Gravity and is responsible for the Tides It arises because the gravitational acceleration experienced s are significant physical entities, associations or structures which current Science has confirmed to exist in Space. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 A tidally locked body takes just as long to rotate around its own axis as it does to revolve around its partner. This synchronous rotation causes one hemisphere constantly to face the partner body. In Astronomy, synchronous rotation is a planetological term describing a body orbiting another where the orbiting body takes as long to rotate Usually, only the satellite becomes tidally locked around the larger planet, but if the difference in mass between the two bodies and their physical separation is small, both may become tidally locked to the other, as is the case between Pluto and Charon. This article is about artificial satellites For natural satellites also known as moons see Natural satellite. Charon (ˈʃærən; also, as in Χάρων) discovered in 1978 is either the largest Moon of Pluto or the smaller member of a double This effect is employed to stabilize some artificial satellites. Gravity-gradient stabilization is a method of stabilizing Artificial satellites in a fixed orientation using only the orbited body's mass distribution and the Earth's gravitational

Mechanism

The change in rotation rate necessary to tidally lock a body B to a larger body A is caused by the torque applied by A's gravity on bulges it has induced on B by tidal forces. The rotation period of an astronomical object is the time it takes to complete one revolution around its Axis of rotation relative to the background stars A torque (τ in Physics, also called a moment (of force is a pseudo- vector that measures the tendency of a force to rotate an object about Gravitation is a natural Phenomenon by which objects with Mass attract one another The tidal force is a secondary effect of the Force of Gravity and is responsible for the Tides It arises because the gravitational acceleration experienced

Tidal bulges: A's gravity produces a tidal force on B which distorts its gravitational equilibrium shape slightly so that it becomes stretched along the axis oriented toward A, and conversely, is slightly compressed in the two perpendicular directions. In Geometry, two lines or planes (or a line and a plane are considered perpendicular (or orthogonal) to each other if they form congruent These distortions are known as tidal bulges. When B is not yet tidally locked, the bulges travel over its surface, with one of the two "high" tidal bulges traveling close to the point where body A is overhead. For large astronomical bodies which are near-spherical due to self-gravitation, the tidal distortion produces a slightly prolate spheroid or ellipsoid. Sphericity is a measure of how spherical (round an object is As such it is a specific example of a Compactness measure of a shape. A prolate spheroid is a Spheroid in which the polar Diameter is longer than the Equatorial diameter An ellipsoid is a type of quadric surface that is a higher dimensional analogue of an Ellipse. Smaller bodies also experience distortion, but this distortion is less regular.

Bulge dragging: The material of B exerts resistance to this periodic reshaping caused by the tidal force. Exertion is a concept describing the use of physical or perceived Energy. 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 towards A. If B's rotation period is shorter than its orbital period, the bulges are carried forward of the axis oriented towards A in the direction of rotation, whereas if B's orbital period is shorter the bulges lag behind instead.

Resulting torque: Since 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, while 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 which acts to synchronize B's rotation with its orbital period, leading eventually to tidal locking.

Orbital changes: 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). In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position 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 size. For example, the Earth's rotation is gradually slowing down because of the Moon, by an amount that becomes noticeable over geological time in some fossils. For similar sized bodies the effect may be of comparable size for both, and both may become tidally locked to each other. The dwarf planet Pluto and its satellite Charon are good examples of this— Charon is only visible from one hemisphere of Pluto and vice versa. A dwarf planet, as defined by the International Astronomical Union (IAU is a Celestial body Orbiting the Sun that is massive enough to be rounded Charon (ˈʃærən; also, as in Χάρων) discovered in 1978 is either the largest Moon of Pluto or the smaller member of a double

Rotation-Orbit resonance: Finally, in some cases where the orbit is eccentric and the tidal effect is relatively weak, the smaller body may end up in an orbital resonance, rather than tidally locked. In Astrodynamics, under standard assumptions, any Orbit must be of Conic section shape In Celestial mechanics, an orbital resonance occurs when two Orbiting bodies exert a regular periodic gravitational influence on each other usually due to their Here the ratio of rotation period to orbital period is some well-defined fraction different from 1:1. A well known case is the rotation of Mercury—locked to its orbit around the Sun in a 3:2 resonance.

Final configuration

There is a tendency for a moon to orient itself in the lowest energy configuration, with the heavy side facing the planet. Irregularly shaped bodies will align their long axis to point towards the planet. Both cases are analogous to how a rounded floating object will orient itself with its heavy end downwards. In many cases this planet-facing hemisphere is visibly different from the rest of the moon's surface.

The orientation of the Earth's moon might be related to this process. The lunar maria are composed of basalt, which is heavier than the surrounding highland crust, and were formed on the side of the moon on which the crust is markedly thinner. The lunar maria (singular mare, two syllables are large dark Basaltic plains on Earth 's Moon, formed by ancient Volcanic eruptions The Earth-facing hemisphere contains all the large maria. The simple picture of the moon stabilising with its heavy side towards the Earth is incorrect, however, because the tidal locking occurred over a very short timescale of a thousand years or less, while the maria formed much later.

Occurrence

Earth's Moon

Since the Moon is 1:1 tidally locked, only one side is visible from Earth. The near side of the Moon is the Lunar hemisphere that is permanently turned towards the Earth, whereas the opposite side is the Far side of the Moon EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001

The Moon's rotation and orbital periods are both just under 4 weeks, so no matter when the Moon is observed from the Earth the same hemisphere of the Moon is always seen. The far side of the Moon was not seen in its entirety until 1959, when photographs were transmitted from the Soviet spacecraft Luna 3. Far Side of the Moon, in original French, La face cachée de la lune, is a 2003 film by Robert Lepage. The year 1959 ( MCMLIX) was a Common year starting on Thursday (link will display full calendar of the Gregorian calendar. The Union of Soviet Socialist Republics (USSR was a constitutionally Socialist state that existed in Eurasia from 1922 to 1991 The Soviet spaceprobe Luna 3 (E-3 series was the third spacecraft sent successfully to the Moon and was an early triumph in the human exploration of outer space

Despite the Moon's rotational and orbital periods being exactly locked, we may actually observe about 59% of the moon's total surface with repeated observations from earth due to the phenomena of librations and parallax. In Astronomy libration (from the Latin verb librare "to balance to sway" cf Parallax is an apparent displacement or difference of orientation of an object viewed along two different lines of sight and is measured by the angle or semi-angle of inclination between Librations are primarily caused by the Moon's varying orbital speed due to the eccentricity of its orbit: this allows us to see up to about 6° more along its perimeter. In Astrodynamics, under standard assumptions, any Orbit must be of Conic section shape Parallax is a geometric effect: at the surface of the Earth we are offset from the line through the centers of Earth and Moon, and because of this we can observe a bit (about 1°) more around the side of the Moon when it is on our local horizon.

Moons

Most significant moons in the Solar System are tidally locked with their primaries, since they orbit very closely and tidal force increases rapidly (as a cubic) with decreasing distance. The Solar System consists of the Sun and those celestial objects bound to it by Gravity. This article discusses cubic equations in one variable For a discussion of cubic equations in two variables see Elliptic curve. Notable exceptions are the irregular outer satellites of the gas giant planets, which orbit much further away than the large well-known moons. A gas giant (sometimes also known as a Jovian planet after the planet Jupiter, or giant planet) is a large Planet that is not primarily

Pluto and Charon are an extreme example of a tidal lock. Charon (ˈʃærən; also, as in Χάρων) discovered in 1978 is either the largest Moon of Pluto or the smaller member of a double Charon is a relatively large moon in comparison to its primary and also has a very close orbit. In Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star This has made Pluto also tidally locked to Charon. In effect, these two celestial bodies revolve around each other (their mass center lies outside of Pluto) as if joined with a rod connecting two opposite points on their surfaces. s are significant physical entities, associations or structures which current Science has confirmed to exist in Space.

The tidal locking situation for asteroid moons is largely unknown, but closely-orbiting binaries are expected to be tidally locked, as well as, obviously, contact binaries. An asteroid moon is an Asteroid that Orbits another asteroid as its Natural satellite. In the study of asteroids a contact binary is caused when two asteroids gravitate toward each other until they touch forming an oddly-shaped single body

Planets

Until radar observations in 1965 proved otherwise, it was thought that Mercury was tidally locked with the Sun. Year 1965 ( MCMLXV) was a Common year starting on Friday (link will display full calendar of the 1965 Gregorian calendar. Instead, it turned out that Mercury has a 3:2 spin-orbit resonance, rotating three times for every two revolutions around the Sun; the eccentricity of Mercury's orbit makes this resonance stable. The original reason astronomers thought it was tidally locked was because whenever Mercury was best placed for observation, it was always at the same point in its 3:2 resonance, so showing the same face, which would be also the case if it were totally locked.

A curious aspect of Venus' orbit and rotation periods is that the 583. The VENUS ( V ictoria E xperimental N etwork U nder the S ea project is a cabled sea floor observatory operated by the University 92-day interval between successive close approaches to the Earth is almost exactly equal to 5 Venusian solar days (precisely, 5. 001444 of these), 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 the Earth is unknown [1].

Stars

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. A binary star is a Star system consisting of two Stars orbiting around their Center of mass. An extrasolar planet, or exoplanet, is a Planet beyond the Solar System, orbiting around other Stars As of September 2008 312 An unusual example, confirmed by MOST, is Tau Boötis, a star tidally locked by a planet. The Microvariability and Oscillations of STars telescope better known simply as MOST, is Canada 's first and (as of mid-2005 only Space telescope. Tau Boötis (τ Boo / τ Boötis is a Yellow-white dwarf approximately 51 Light-years away in the Constellation of Boötes. The tidal locking is almost certainly mutual. [2]

Timescale

An estimate of the time for a body to become tidally locked can be obtained using the following formula [3]:

$t_{\textrm{lock}} \approx \frac{w a^6 I Q}{3 G m_p^2 k_2 R^5}$

where

• $w\,$ is the initial spin rate (revolutions per second)
• $a\,$ is the semi-major axis of the motion of the satellite around the planet
• $I\approx 0.4 m_s R^2$ is the moment of inertia of the satellite. In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae This article is about the moment of inertia of a rotating object.
• $Q\,$ is the dissipation function of the satellite.
• $G\,$ is the gravitational constant
• $m_p\,$ is the mass of the planet
• $m_s\,$ is the mass of the satellite
• $k_2\,$ is the tidal Love number of the satellite
• $R\,$ is the radius of the satellite. The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass Augustus Edward Hough Love ( 17 April 1863, Weston-super-Mare - 5 June 1940, Oxford) often known as A

Q and k2 are generally very poorly known except for the Earth's Moon which has k2 / Q = 0. 0011. However, for a really rough estimate one can take Q≈100 (perhaps conservatively, giving overestimated locking times), and

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

where

• $\rho\,$ is the density of the satellite
• $g\approx Gm_s/R^2$ is the surface gravity of the satellite
• $\mu\,$ is rigidity of the satellite. This can be roughly taken as 3×1010 Nm-2 for rocky objects and 4×109 Nm-2 for icy ones.

As can be seen, even knowing the size and density of the satellite leaves many parameters that must be estimated (especially w, Q, and $\mu\,$), so that any calculated locking times obtained are expected to be inaccurate, to even factors of ten. Further, during the tidal locking phase the orbital radius 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. Tidal acceleration is an effect of the Tidal forces between an orbiting Natural satellite ( i

Since 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)

$t_{\textrm{lock}}\quad \approx\quad 6\ \frac{a^6R\mu}{m_sm_p^2}\quad \times 10^{10}\ \textrm{ years},$

with masses in kg, distances in meters, and μ in Nm-2. μ can be roughly taken as 3×1010 Nm-2 for rocky objects and 4×109 Nm-2 for icy ones.

Note the extremely strong dependence on orbital radius a.

For the locking of a primary body to its moon as in the case of Pluto, satellite and primary body parameters can be interchanged.

One conclusion is that other things being equal (such as Q and μ), a large moon will lock faster than a smaller moon at the same orbital radius from the planet because $m_s\,$ grows much faster with satellite radius than R. A possible example of this is in the Saturn system, where Hyperion is not tidally locked, while the larger Iapetus, which orbits at a greater distance, is. TemplateInfobox Planet.--> Hyperion (haɪˈpɪəriən, or as in TemplateInfobox Planet.--> Iapetus (aɪˈæpɨtəs, or as in Greek This is not clear cut because Hyperion also experiences strong driving from the nearby Titan, which forces its rotation to be chaotic. TemplateInfobox Planet.--> Titan (ˈtaɪtən, or as

List of known tidally locked bodies

Solar System

Locked to the Sun

• Mercury (in a 3:2 rotation:orbit resonance)

Locked to the Earth

Locked to Mars

Locked to Jupiter

Locked to Saturn

Locked to Uranus

Locked to Neptune

Locked to Pluto

• Charon (Pluto being itself locked to Charon)

Extra-solar

• Tau Boötis is known to be locked to the close-orbiting giant planet Tau Boötis Ab. The Sun (Sol is the Star at the center of the Solar System. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 TemplateInfobox Planet.--> Deimos (ˈdaɪməs; also /ˈdiːməs/ TemplateInfobox Planet.--> Metis (, or as in Greek Μήτις Adrastea (, or as in Greek Αδράστεια also known as Jupiter XV, is the second by distance and the smallest of the four inner moons of Jupiter TemplateInfobox Planet.--> Amalthea (, or as in Greek Αμάλθεια TemplateInfobox Planet.--> Thebe (, or as in Greek Θήβη TemplateInfobox Planet.--> Io (ˈaɪoʊ, or as Greek TemplateInfobox Planet.--> Europa (jʊˈroʊpə; or as TemplateInfobox Planet.--> Ganymede (ˈgænɨmiːd, or as Greek TemplateInfobox Planet.--> Callisto (kəˈlɪstoʊ, or as Greek For the moon of Jupiter known by this name 1955-1975 see Carme (moon. TemplateInfobox Planet.--> Atlas (ˈætləs, or as Greek Άτλας TemplateInfobox Planet.--> Prometheus (proʊˈmiːθiəs,, or There is also an Asteroid called 55 Pandora. TemplateInfobox Planet.--> Epimetheus (ˌɛpɨˈmiːθiəs,, or Saturn X redirects here For the spurious moon reported in 1905 see Themis (moon TemplateInfobox Planet. --> Mimas (ˈmaɪməs, or as Greek TemplateInfobox Planet.--> This article is about the moon of TemplateInfobox Planet.--> Telesto (tɨˈlɛstoʊ, or as Greek TemplateInfobox Planet.--> Tethys (ˈtiːθɨs, /ˈtɛθɨs/, or TemplateInfobox Planet.--> Calypso (kəˈlɪpsoʊ, or as in Greek TemplateInfobox Planet.--> Dione (daɪˈoʊni, or as in Greek TemplateInfobox Planet.--> Rhea (ˈriːə, or as in Greek TemplateInfobox Planet.--> Titan (ˈtaɪtən, or as TemplateInfobox Planet.--> Iapetus (aɪˈæpɨtəs, or as in Greek TemplateInfobox Planet.--> Miranda (mɨˈrændə) is the smallest TemplateInfobox Planet.--> Ariel (ˈɛəriəl) is a moon Umbriel (ˈʌmbriəl) is a moon of Uranus discovered on October 24, 1851 by William Lassell. Titania (, also) is the largest moon of Uranus and the eighth largest moon in the Solar System. Neptune ( English|AmE] ] is the eighth and farthest Planet from the Sun in the Solar System. There is also an Asteroid called 9313 Protea. TemplateInfobox Planet.--> Triton (ˈtraɪtən, or as in Greek Charon (ˈʃærən; also, as in Χάρων) discovered in 1978 is either the largest Moon of Pluto or the smaller member of a double Tau Boötis (τ Boo / τ Boötis is a Yellow-white dwarf approximately 51 Light-years away in the Constellation of Boötes. A gas giant (sometimes also known as a Jovian planet after the planet Jupiter, or giant planet) is a large Planet that is not primarily Tau Boötis b, occasionally cataloged as Tau Boötis Ab, is an Extrasolar planet approximately 50 Light-years away around the primary star of [4]

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

Probably locked to Uranus

Probably locked to Neptune

Probably locked to other dwarf planets and minor planets
Numerous asteroid and TNO moons are expected to be locked to their primaries. Daphnis (ˈdæfnɨs, or as Greek Δαφνίς is an Inner satellite of Saturn. TemplateInfobox Planet.--> Helene (ˈhɛlɨni, sometimes, or as TemplateInfobox Planet.--> Cordelia (kor-dee'-lee-ə There is also an Asteroid called 171 Ophelia. There is also an Asteroid called 218 Bianca. There is also an Asteroid called 548 Kressida. There is also a Minor planet called 666 Desdemona. There is also an Asteroid called 1285 Julietta. Portia (por'-shə ˈpɔrʃə is an Inner satellite of Uranus. There is also an Asteroid called 900 Rosalinde. TemplateInfobox Planet.--> Belinda (bə-lin'-də bɨˈlɪndə Perdita (pər'-di-tə ˈpɝdɨtə is an Inner satellite of Uranus. TemplateInfobox Planet.--> Puck (ˈpʌk puk' is an TemplateInfobox Planet.--> Oberon (ˈoʊbərɒn) is the outermost Neptune ( English|AmE] ] is the eighth and farthest Planet from the Sun in the Solar System. See also Discovery It was first discovered by Harold J Reitsema, William B A dwarf planet, as defined by the International Astronomical Union (IAU is a Celestial body Orbiting the Sun that is massive enough to be rounded Minor planet is a term used since the 19th century to describe objects such as Asteroids that are in Orbit around the Sun but are not Planets Asteroids, sometimes called Minor planets or planetoids', are bodies—primarily of the inner Solar System —that are smaller than planets but A trans-Neptunian object (TNO is any object in the Solar system that Orbits the sun at a greater distance on average than Neptune. However, in the absence of direct observation reliable candidates are difficult to verify. While locking timescales can be estimated, the age of the primary+satellite system is difficult to gauge; most are thought to be the results of collisions in the last few hundred million years.

Extra-solar

• Gliese 581 c may be tidally locked to its parent star Gliese 581. Gliese 581 c (ˈgliːzə is a " Super-earth " Gliese 581 (ˈgliːzə is a Red dwarf Star with spectral type M3V located 20 [5]

References

1. ^ Gold T. In Astronomy, synchronous rotation is a planetological term describing a body orbiting another where the orbiting body takes as long to rotate Tidal acceleration is an effect of the Tidal forces between an orbiting Natural satellite ( i Gravity-gradient stabilization is a method of stabilizing Artificial satellites in a fixed orientation using only the orbited body's mass distribution and the Earth's gravitational , Soter S. (1969), Atmospheric tides and the resonant rotation of Venus, Icarus, v. 11, p 356-366
2. ^ SPACE.com - Role Reversal: Planet Controls a Star
3. ^ B. Gladman et al (1996). "Synchronous Locking of Tidally Evolving Satellites". Icarus 122: 166. doi:10.1006/icar.1996.0117. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.   (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 (1977) in J. A. Burns: Planetary Satellites. University of Arizona Press, 87-112.  )
4. ^ SPACE.com - Role Reversal: Planet Controls a Star
5. ^ USATODAY.com

tidal locking

-noun

1. (astronomy) The locking of the rotation of a satellite (moon or planet) to its orbit, such that one side always faces the body around which it is orbiting.
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