# Tidal heating

Last updated

Tidal heating (also known as tidal working or tidal flexing) occurs through the tidal friction processes: orbital and rotational energy is dissipated as heat in either (or both) the surface ocean or interior of a planet or satellite. When an object is in an elliptical orbit, the tidal forces acting on it are stronger near periapsis than near apoapsis. Thus the deformation of the body due to tidal forces (i.e. the tidal bulge) varies over the course of its orbit, generating internal friction which heats its interior. This energy gained by the object comes from its gravitational energy, so over time in a two-body system, the initial elliptical orbit decays into a circular orbit (tidal circularization). Sustained tidal heating occurs when the elliptical orbit is prevented from circularizing due to additional gravitational forces from other bodies that keep tugging the object back into an elliptical orbit. In this more complex system, gravitational energy still is being converted to thermal energy; however, now the orbit's semimajor axis would shrink rather than its eccentricity.

Tidal heating is responsible for the geologic activity of the most volcanically active body in the Solar System: Io, a moon of Jupiter. Io's eccentricity persists as the result of its orbital resonances with the Galilean moons Europa and Ganymede. [1] The same mechanism has provided the energy to melt the lower layers of the ice surrounding the rocky mantle of Jupiter's next-closest large moon, Europa. However, the heating of the latter is weaker, because of reduced flexing—Europa has half Io's orbital frequency and a 14% smaller radius; also, while Europa's orbit is about twice as eccentric as Io's, tidal force falls off with the cube of distance and is only a quarter as strong at Europa. Jupiter maintains the moons' orbits via tides they raise on it and thus its rotational energy ultimately powers the system. [1] Saturn's moon Enceladus is similarly thought to have a liquid water ocean beneath its icy crust, due to tidal heating related to its resonance with Dione. The water vapor geysers which eject material from Enceladus are thought to be powered by friction generated within its interior. [2]

The tidal heating rate, ${\displaystyle {\dot {E}}_{\text{Tidal}}}$, in a satellite that is spin-synchronous, coplanar (${\displaystyle I=0}$), and has an eccentric orbit is given by:

${\displaystyle {\dot {E}}_{\text{Tidal}}=-\operatorname {Im} (k_{2}){\frac {21}{2}}{\frac {GM_{h}^{2}R^{5}ne^{2}}{a^{6}}}}$

where ${\displaystyle R}$, ${\displaystyle n}$, ${\displaystyle a}$, and ${\displaystyle e}$ are respectively the satellite's mean radius, mean orbital motion, orbital distance, and eccentricity. [3] ${\displaystyle M_{h}}$ 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). [4] [5] The rheological parameters' values, in turn, depend upon the temperature and the concentration of partial melt in the body's interior. [6]

The tidally dissipated power in a nonsynchronised rotator is given by a more complex expression. [7]

## Related Research Articles

In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly, this relationship is found between a pair of objects. The physical principle behind orbital resonance is similar in concept to pushing a child on a swing, whereby the orbit and the swing both have a natural frequency, and the body doing the "pushing" will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances greatly enhance the mutual gravitational influence of the bodies. In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be self-correcting and thus stable. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Pluto and Neptune. Unstable resonances with Saturn's inner moons give rise to gaps in the rings of Saturn. The special case of 1:1 resonance between bodies with similar orbital radii causes large solar system bodies to eject most other bodies sharing their orbits; this is part of the much more extensive process of clearing the neighbourhood, an effect that is used in the current definition of a planet.

In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.

Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite and the primary planet that it orbits. The acceleration causes a gradual recession of a satellite in a prograde orbit away from the primary, and a corresponding slowdown of the primary's rotation. The process eventually leads to tidal locking, usually of the smaller body first, and later the larger body. The Earth–Moon system is the best-studied case.

The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient in gravitational field from the other body; it is responsible for diverse phenomena, including tides, tidal locking, breaking apart of celestial bodies and formation of ring systems within the Roche limit, and in extreme cases, spaghettification of objects. It arises because the gravitational field exerted on one body by another is not constant across its parts: the nearest side is attracted more strongly than the farthest side. It is this difference that causes a body to get stretched. Thus, the tidal force is also known as the differential force, as well as a secondary effect of the gravitational field.

A natural satellite is, in the most common usage, an astronomical body that orbits a planet, dwarf planet, or small Solar System body. Natural satellites are often colloquially referred to as moons, a derivation from the Moon of Earth.

Ganymede, a satellite of Jupiter, is the largest and most massive of the Solar System's moons. The ninth-largest object of the Solar System, it is the largest without a substantial atmosphere. It has a diameter of 5,268 km (3,273 mi), making it 26 percent larger than the planet Mercury by volume, although it is only 45 percent as massive. Possessing a metallic core, it has the lowest moment of inertia factor of any solid body in the Solar System and is the only moon known to have a magnetic field. Outward from Jupiter, it is the seventh satellite and the third of the Galilean moons, the first group of objects discovered orbiting another planet. Ganymede orbits Jupiter in roughly seven days and is in a 1:2:4 orbital resonance with the moons Europa and Io, respectively.

Tidal locking between a pair of co-orbiting astronomical bodies occurs when one of the objects reaches a state where there is no longer any net change in its rotation rate over the course of a complete orbit. In the case where a tidally locked body possesses synchronous rotation, the object takes just as long to rotate around its own axis as it does to revolve around its partner. For example, the same side of the Moon always faces the Earth, although there is some variability because the Moon's orbit is not perfectly circular. Usually, only the satellite is tidally locked to the larger body. However, if both the difference in mass between the two bodies and the distance between them are relatively small, each may be tidally locked to the other; this is the case for Pluto and Charon.

In celestial mechanics, the Roche limit, also called Roche radius, is the distance from a celestial body within which a second celestial body, held together only by its own force of gravity, will disintegrate because the first body's tidal forces exceed the second body's gravitational self-attraction. Inside the Roche limit, orbiting material disperses and forms rings, whereas outside the limit, material tends to coalesce. The Roche radius depends on the radius of the first body and on the ratio of the bodies' densities.

In orbital mechanics, orbitaldecay is a gradual decrease of the distance between two orbiting bodies at their closest approach over many orbital periods. These orbiting bodies can be a planet and its satellite, a star and any object orbiting it, or components of any binary system. Orbits do not decay without some friction-like mechanism which transfers energy from the orbital motion. This can be any of a number of mechanical, gravitational, or electromagnetic effects. For bodies in low Earth orbit, the most significant effect is atmospheric drag.

Io, or Jupiter I, is the innermost and third-largest of the four Galilean moons of the planet Jupiter. Slightly larger than Earth’s moon, Io is the fourth-largest moon in the Solar System, has the highest density of any moon, the strongest surface gravity of any moon, and the lowest amount of water of any known astronomical object in the Solar System. It was discovered in 1610 by Galileo Galilei and was named after the mythological character Io, a priestess of Hera who became one of Zeus's lovers.

Planetary migration occurs when a planet or other body in orbit around a star interacts with a disk of gas or planetesimals, resulting in the alteration of its orbital parameters, especially its semi-major axis. Planetary migration is the most likely explanation for hot Jupiters. The generally accepted theory of planet formation from a protoplanetary disk predicts that such planets cannot form so close to their stars, as there is insufficient mass at such small radii and the temperature is too high to allow the formation of rocky or icy planetesimals.

Interacting galaxies are galaxies whose gravitational fields result in a disturbance of one another. An example of a minor interaction is a satellite galaxy disturbing the primary galaxy's spiral arms. An example of a major interaction is a galactic collision, which may lead to a galaxy merger.

Gliese 876 c is an exoplanet orbiting the red dwarf Gliese 876, taking about 30 days to complete an orbit. The planet was discovered in April 2001 and is the second planet in order of increasing distance from its star.

In astronomy, an irregular moon, irregular satellite or irregular natural satellite is a natural satellite following a distant, inclined, and often eccentric and retrograde orbit. They have been captured by their parent planet, unlike regular satellites, which formed in orbit around them. Irregular moons have a stable orbit, unlike temporary satellites which often have similarly irregular orbits but will eventually depart. The term does not refer to shape as Triton is a round moon, but is considered irregular due to its orbit.

Volcanism on Io, a moon of Jupiter, is represented by the presence of volcanoes, volcanic pits and lava flows on the moon's surface. Its volcanic activity was discovered in 1979 by Voyager 1 imaging scientist Linda Morabito. Observations of Io by passing spacecraft and Earth-based astronomers have revealed more than 150 active volcanoes. Up to 400 such volcanoes are predicted to exist based on these observations. Io's volcanism makes the satellite one of only four known currently volcanically active worlds in the Solar System.

The habitability of natural satellites is a measure of their potential to sustain life in favorable circumstances. Habitable environments do not necessarily harbor life. Natural satellite habitability is a new area that is significant to astrobiology for various reasons, the most important of which being that natural satellites are expected to outnumber planets by a large margin, and it is projected that habitability parameters will be comparable to those of planets. There are, nevertheless, significant environmental variables that affect moons as prospective alien life locations. The strongest candidates for natural satellite habitability are currently icy satellites such as those of Jupiter and Saturn—Europa and Enceladus respectively, although if life exists in either place, it would probably be confined to subsurface habitats. Historically, life on Earth was thought to be strictly a surface phenomenon, but recent studies have shown that up to half of Earth's biomass could live below the surface. Europa and Enceladus exist outside the circumstellar habitable zone which has historically defined the limits of life within the Solar System as the zone in which water can exist as liquid at the surface. In the Solar System's habitable zone, there are only three natural satellites—the Moon, and Mars's moons Phobos and Deimos —none of which sustain an atmosphere or water in liquid form. Tidal forces are likely to play as significant a role providing heat as stellar radiation in the potential habitability of natural satellites.

A lava planet is a type of terrestrial planet, with a surface mostly or entirely covered by molten lava. Situations where such planets could exist include a young terrestrial planet just after its formation, a planet that has recently suffered a large collision event, or a planet orbiting very close to its star, causing intense irradiation and tidal forces.

Tidal circularization is an effect of the tidal forces between an orbiting body and the primary object that it orbits, whereby the eccentricity of the orbit is reduced over time so that the orbit becomes less and less elliptical.

Tidal heating of Io occurs through the tidal friction processes between Jupiter and its moon. Orbital and rotational energy are dissipated as heat in the crust of the moon. Io has a similar mass and size as the Moon, but Io is the most geologically active body in the Solar System. This is caused by the heating mechanism of Io. The major heating source of Earth and its moon is radioactive heating, but the heating source on Io is tidal heating. As Jupiter is very massive, the side of Io nearest to Jupiter has a slightly larger gravitational pull than the opposite side. This difference in gravitational forces cause distortion of Io’s shape. Differently from the Earth’s only moon, Jupiter has two other large moons that are in an orbital resonance with it. Io is the innermost of this set of resonant moons, and their interactions maintain its orbit in an eccentric (elliptical) state. The varying distance between Jupiter and Io continually changes the degree of distortion of Io's shape and flexes its interior, frictionally heating it. The friction-induced heating drives strong volcanic activities on the surface of Io.

A satellite system is a set of gravitationally bound objects in orbit around a planetary mass object or minor planet, or its barycenter. Generally speaking, it is a set of natural satellites (moons), although such systems may also consist of bodies such as circumplanetary disks, ring systems, moonlets, minor-planet moons and artificial satellites any of which may themselves have satellite systems of their own. Some bodies also possess quasi-satellites that have orbits gravitationally influenced by their primary, but are generally not considered to be part of a satellite system. Satellite systems can have complex interactions including magnetic, tidal, atmospheric and orbital interactions such as orbital resonances and libration. Individually major satellite objects are designated in Roman numerals. Satellite systems are referred to either by the possessive adjectives of their primary, or less commonly by the name of their primary. Where only one satellite is known, or it is a binary with a common centre of gravity, it may be referred to using the hyphenated names of the primary and major satellite.

## 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, JSTOR   1747884, PMID   17771724
2. Peale, S.J. (2003). "Tidally induced volcanism". Celestial Mechanics and Dynamical Astronomy 87, 129–155.
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. Henning, Wade G. (2009), "Tidally Heated Terrestrial Exoplanets: Viscoelastic Response Models", The Astrophysical Journal , 707 (2): 1000–1015, arXiv:, Bibcode:2009ApJ...707.1000H, doi:10.1088/0004-637X/707/2/1000
5. Renaud, Joe P.; Henning, Wade G. (2018), "Increased Tidal Dissipation Using Advanced Rheological Models: Implications for Io and Tidally Active Exoplanets", The Astrophysical Journal, 857 (2): 98, arXiv:, Bibcode:2018ApJ...857...98R, doi:
6. Efroimsky, Michael (2012), "Tidal Dissipation Compared to Seismic Dissipation: In Small Bodies, in Earths, and in Superearths", The Astrophysical Journal, 746: 150, doi:
7. Efroimsky, Michael; Makarov, Valeri V. (2014), "Tidal Dissipation in a Homogeneous Spherical Body. I. Methods", The Astrophysical Journal, 795 (1): 6, arXiv:, Bibcode:2014ApJ...795....6E, doi: