# Tidal heating

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, 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;[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 $q_{tid}$ is given by

$q_{tid} = 63 \rho n^5 r^4 e^2 / 38 \mu Q$

where $r$ is the satellite’s radius, $n$ is the mean orbital motion, $e$ is the eccentricity of the orbit, $Q$ is a dimensionless dissipation factor, and $\mu$ 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.[3]