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.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. 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.
The tidal heating rate, , in a satellite that is spin-synchronous, coplanar (), and has an eccentric orbit is given by:
where , , , and are respectively the satellite's mean radius, mean orbital motion, orbital distance, and eccentricity. is the host (or central) body's mass and 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). The rheological parameters' values, in turn, depend upon the temperature and the concentration of partial melt in the body's interior.
The tidally dissipated power in a nonsynchronised rotator is given by a more complex expression.
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 for a pair of objects. The physical principle behind orbital resonance is similar in concept to pushing a child on a swing, where the orbit and the swing both have a natural frequency, and the other 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 physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet. 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 first, and later the larger body. The Earth–Moon system is the best-studied case.
The tidal force is a force that stretches a body towards and away from 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.
Europa, or Jupiter II, is the smallest of the four Galilean moons orbiting Jupiter, and the sixth-closest to the planet of all the 79 known moons of Jupiter. It is also the sixth-largest moon in the Solar System. Europa was discovered in 1610 by Galileo Galilei and was named after Europa, the Phoenician mother of King Minos of Crete and lover of Zeus.
Ganymede, a satellite of Jupiter, is the largest and most massive of the Solar System's moons. The ninth-largest object in 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% larger than the planet Mercury by volume, although it is only 45% 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, in the best-known case, occurs when an orbiting astronomical body always has the same face toward the object it is orbiting. This is known as synchronous rotation: the tidally locked body 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 due to the first body's tidal forces exceeding 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 astrophysics, dynamical friction or Chandrasekhar friction, sometimes called gravitational drag, is loss of momentum and kinetic energy of moving bodies through gravitational interactions with surrounding matter in space. It was first discussed in detail by Subrahmanyan Chandrasekhar in 1943.
Io, or Jupiter I, is the innermost and third-largest of the four Galilean moons of the planet Jupiter. It is the fourth-largest moon in the Solar System, has the highest density of all of them, and has 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.
The orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a Klemperer rosette orbit through the galaxy.
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: exoplanets with Jovian masses but orbits of only a few days. The generally accepted theory of planet formation from a protoplanetary disk predicts 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.
In celestial mechanics, the Kozai mechanism or Lidov–Kozai mechanism or Kozai–Lidov mechanism, also known as the Kozai, Lidov–Kozai or Kozai–Lidoveffect, oscillations, cycles or resonance, is a dynamical phenomenon affecting the orbit of a binary system perturbed by a distant third body under certain conditions, causing the orbit's argument of pericenter to oscillate about a constant value, which in turn leads to a periodic exchange between its eccentricity and inclination. The process occurs on timescales much longer than the orbital periods. It can drive an initially near-circular orbit to arbitrarily high eccentricity, and flip an initially moderately inclined orbit between a prograde and a retrograde motion.
Gliese 876 d is an exoplanet approximately 15 light-years away in the constellation of Aquarius. The planet was the third planet discovered orbiting the red dwarf Gliese 876. It was the lowest-mass extrasolar planet apart from the pulsar planets orbiting PSR B1257+12 at the time of its discovery. Due to this low mass, it can be categorized as a super-Earth.
The formation and evolution of the Solar System began 4.5 billion years ago with the gravitational collapse of a small part of a giant molecular cloud. Most of the collapsing mass collected in the center, forming the Sun, while the rest flattened into a protoplanetary disk out of which the planets, moons, asteroids, and other small Solar System bodies formed.
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 the potential of natural satellites to have environments hospitable to life. Habitable environments do not necessarily harbor life. Natural satellite habitability is an emerging field which is considered important to astrobiology for several reasons, foremost being that natural satellites are predicted to greatly outnumber planets and it is hypothesized that habitability factors are likely to be similar to those of planets. There are, however, key environmental differences which have a bearing on moons as potential sites for extraterrestrial life.
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 orbiting a common centre of gravity, it may be referred to using the hyphenated names of the primary and major satellite.
An accretion disk is a structure formed by diffuse material in orbital motion around a massive central body. The central body is typically a star. Friction causes orbiting material in the disk to spiral inward towards the central body. Gravitational and frictional forces compress and raise the temperature of the material, causing the emission of electromagnetic radiation. The frequency range of that radiation depends on the central object's mass. Accretion disks of young stars and protostars radiate in the infrared; those around neutron stars and black holes in the X-ray part of the spectrum. The study of oscillation modes in accretion disks is referred to as diskoseismology.