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| '''Tidal heating''' (also known as '''tidal working''') occurs through the [[tidal friction]] processes: orbital and rotational energy are dissipated as heat in the crust of the moons and planets involved. [[Io (moon)|Io]], a moon of [[Jupiter]], is the most volcanically active body in the [[solar system]], with no impact craters surviving on its surface. This is because the tidal force of Jupiter deforms Io;<ref>{{Citation
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| | title = Melting of Io by Tidal Dissipation
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| | url = http://links.jstor.org/sici?sici=0036-8075%2819790302%293%3A203%3A4383%3C892%3AMOIBTD%3E2.0.CO%3B2-8
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| | year = 1979
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| | journal = Science
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| | pages = 892–894
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| | volume = 203
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| | issue = 4383
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| | last1 = Peale | first1 = S. J.
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| | last2 = Cassen | first2 = P.
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| | last3 = Reynolds | first3 = R. T.
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| | accessdate = 2010-10-12
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| | doi = 10.1126/science.203.4383.892 | pmid=17771724|bibcode = 1979Sci...203..892P }}</ref> the [[orbital eccentricity|eccentricity]] of Io's orbit (a consequence of its participation in a [[Orbital resonance|Laplace resonance]]) causes the height of Io's tidal bulge to vary significantly (by up to 100 m) over the course of an orbit; the friction from this tidal flexing then heats up its interior. A similar but weaker process is theorised to have melted the lower layers of the ice surrounding the rocky mantle of Jupiter's next large moon, [[Europa (moon)|Europa]]. Saturn's moon [[Enceladus (moon)|Enceladus]] is similarly thought to have a liquid water ocean beneath its icy crust. The [[cryovolcano|water vapor geysers]] which eject material from Enceladus are thought to be powered by friction generated within this moon's shifting ice crust.<ref>Peale, S.J. Tidally induced volcanism. Celest. Mech. & Dyn. Astr. 87, 129–
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| 155, 2003.</ref>
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| The total amount of tidal heating <math>q_{tid}</math> is given by
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| :<math>q_{tid} = 63 \rho n^5 r^4 e^2 / 38 \mu Q</math>
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| where <math>r</math> is the satellite’s radius, <math>n</math> is the mean orbital motion, <math>e</math> is the eccentricity of the orbit, <math>Q</math> is a dimensionless dissipation factor, and <math>\mu</math> is the shear modulus. The role of tidal heating is sometimes expressed by dimensionless number C equal to quotient of tidal heating and total internal heating.<ref>Czechowski, L., 2006, Parameterized model of convection driven by tidal and radiogenic heating, Adv. Space Res, 38, 4, 788-793</ref>
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| ==See also==
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| * [[Cryovolcano]]
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| * [[Tidal acceleration]]
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| * [[Tidal locking]]
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| ==References==
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| {{Reflist}}
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| [[Category:Planetary science]]
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| [[Category:Tides]]
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| {{Geophysics-stub}}
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| {{Planetary-science-stub}}
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