Tidal heating

Tidal heating (also known as tidal working or tidal flexing) occurs through the

.

Moons of Gas Giants

Tidal heating is responsible for the geologic activity of the most volcanically active body in the

Earth

Munk & Wunsch (1998) estimated that Earth experiences 3.7 TW (0.0073 W/m²) of tidal heating, of which 95% (3.5 TW or 0.0069 W/m²) is associated with ocean tides and 5% (0.2 TW or 0.0004 W/m²) is associated with

Heller et al. (2021) estimated that shortly after the Moon was formed, when the Moon orbited 10-15 times closer to Earth than it does now, tidal heating might have contributed ~10 W/m² of heating over perhaps 100 million years, and that this could have accounted for a temperature increase of up to 5°C on the early Earth.[5]^[6]

Moon

Harada et al. (2014) proposed that tidal heating may have created a molten layer at the core-mantle boundary within Earth's Moon.^[7]

Io

Jupiter's closest moon Io experiences considerable tidal heating.

Formula

The tidal heating rate, ${\displaystyle {\dot {E}}_{\text{Tidal}}}$, in a satellite that is

(${\displaystyle I=0}$), and has an eccentric orbit is given by: where ${\displaystyle R}$, ${\displaystyle n}$, ${\displaystyle a}$, and ${\displaystyle e}$ are respectively the satellite's mean radius, mean orbital motion, orbital distance, and eccentricity.^[8] ${\displaystyle M_{h}}$ is the host (or central) body's mass and ${\displaystyle \operatorname {Im} (k_{2})}$ represents the imaginary portion of the second-order Love number which measures the efficiency at which the satellite dissipates tidal energy into frictional heat. This imaginary portion is defined by interplay of the body's rheology and self-gravitation. It, therefore, is a function of the body's radius, density, and rheological parameters (the shear modulus, viscosity, and others – dependent upon the rheological model).^[9][10] The rheological parameters' values, in turn, depend upon the temperature and the concentration of partial melt in the body's interior.^[11]

The tidally dissipated power in a nonsynchronised rotator is given by a more complex expression.^[12]

See also

• Cryovolcano
• Tidal acceleration
• Tidal locking
• Io Volcano Observer
• Planetary differentiation

References