The GENERAL MECHANISM
Tidal heating is the frictional heating of the interior of one planetary body caused by stresses induced from the gravitational pull of another.
Newton’s law of Universal Gravitiation states that
Newton's law of universal gravitation states that any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
i.e
Newton’s law of Universal Gravitiation states that
Newton's law of universal gravitation states that any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
i.e
From the above equation where the gravitational force is inversely proportional to the distance, the side of the satellite closest to the parent body (i.e planet) will experience a greater force than the farther side. The difference in the force of gravity is referred to as Tidal Force and where tidal force is sufficiently great, tidal heating occurs. Tidal force causes the shape of the satellite to be distorted.
The satellite may become tidally locked with the planet. This is a phenomenon where the orbital and rotational periods match i.e one side of the satellite (the distorted side) will always face the planet. The bodies are said to be in synchronous rotation.
Where the system is tidally locked, the orbiting body is distorted such that the side facing the central body is elongated.
The satellite may become tidally locked with the planet. This is a phenomenon where the orbital and rotational periods match i.e one side of the satellite (the distorted side) will always face the planet. The bodies are said to be in synchronous rotation.
Where the system is tidally locked, the orbiting body is distorted such that the side facing the central body is elongated.
In the presence of other satellites, an orbital resonance may be established such that the orbit around which the satellite circles the planet becomes eccentric. It is important to note that in the absence of other satellites, the orbit will undergo circularisation and tidal forces, hence heating, will progressively decrease as is seen in the Earth-Moon system. This eccentricity results in a constant change of the distance between the planet and the satellite. Therefore, a much greater tidal force, hence distortion, will be felt when it is at the periapsis than at the apoapsis. This constant distortion leads to frictional heating as the layers of rock respond to the changes in shape.
Hence, for tidal heating to occur, a smaller body in an eccentric orbit around a larger body is required. This eccentricity is produced and maintained by other satellites orbiting the same planet. It is important to note that tidal heating does not occur where the body is in a circular orbit like in the earth-moon system. Rate of energy dissipation increases with eccentricity[1]. This is why energy generated by tidal heating in the earth is negligible. The total tidal dissiptation on Earth has been estimated at 3TW[2] whereas for Io, which has a higher eccentricity as well as an enormous host planet, the global energy dissipation is 93TW[3].