Tidal heating

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Tidal heating (also known as tidal working or tidal flexing) occurs through the tidal friction processes: orbital and rotational energy are dissipated as heat in either the surface ocean or interior of a planet or satellite. Io, a moon of Jupiter, is the most volcanically active body in the solar system, evidenced by active volcanos and no impact craters surviving on its surface. Io's heating is a result of the tug between Jupiter and the other Galilean moons.[1] The eccentricity of Io's orbit (a consequence of its participation in a 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. Saturn's moon Enceladus is similarly thought to have a liquid water ocean beneath its icy crust. The water vapor geysers which eject material from Enceladus are thought to be powered by friction generated within this moon's shifting ice crust.[2]

The total amount of tidal heating in a satellite that is spin-synchronous and has an eccentric orbit ${\displaystyle {\dot {E}}_{Tidal}}$ is given by:

${\displaystyle {\dot {E}}_{Tidal}=-{\text{Im}}(k_{2}){\frac {21}{2}}{\frac {R^{5}n^{5}e^{2}}{G}}}$

Where ${\displaystyle R}$, ${\displaystyle n}$, and ${\displaystyle e}$ are respectively the satellite's mean radius, mean orbital motion, and eccentricity.[3] ${\displaystyle {\text{Im}}(k_{2})}$ is the imaginary portion of the second order Love number which measures the efficiency of body dissipation within the satellite. This imaginary portion is a function of the satellite's bulk shear modulus and viscosity. These in turn are dependent upon temperature and melting of the satellite's interior.[4]

References

1. ^ Peale, S. J.; Cassen, P.; Reynolds, R. T. (1979), "Melting of Io by Tidal Dissipation", Science, 203 (4383): 892–894, Bibcode:1979Sci...203..892P, doi:10.1126/science.203.4383.892, PMID 17771724, retrieved 2010-10-12
2. ^ Peale, S.J. Tidally induced volcanism. Celest. Mech. & Dyn. Astr. 87, 129– 155, 2003.
3. ^ Segatz, M., T. Spohn, M. N. Ross, and G. Schubert. 1988. “Tidal Dissipation, Surface Heat Flow, and Figure of Viscoelastic Models of Io.” Icarus 75: 187. doi:10.1016/0019-1035(88)90001-2.
4. ^ Efroimsky, Michael. 2012. “Tidal Dissipation Compared to Seismic Dissipation: In Small Bodies, in Earths, and in Superearths.” The Astrophysical Journal 746: 150–86. doi:10.1088/0004-637X/746/2/150.