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astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the ...
, accretion is the accumulation of particles into a massive object by gravitationally attracting more matter, typically
gas Gas is a state of matter that has neither a fixed volume nor a fixed shape and is a compressible fluid. A ''pure gas'' is made up of individual atoms (e.g. a noble gas like neon) or molecules of either a single type of atom ( elements such as ...
eous matter, into an
accretion disk An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is most frequently a star. Friction, uneven irradiance, magnetohydrodynamic effects, and ...
. Most
astronomical object An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists within the observable universe. In astronomy, the terms ''object'' and ''body'' are of ...
s, such as
galaxies A galaxy is a system of stars, stellar remnants, interstellar gas, dust, and dark matter bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar Sys ...
,
star A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...
s, and
planet A planet is a large, Hydrostatic equilibrium, rounded Astronomical object, astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The Solar System has eight planets b ...
s, are formed by accretion processes.


Overview

The accretion model that Earth and the other
terrestrial planet A terrestrial planet, tellurian planet, telluric planet, or rocky planet, is a planet that is composed primarily of silicate, rocks or metals. Within the Solar System, the terrestrial planets accepted by the IAU are the inner planets closest to ...
s formed from meteoric material was proposed in 1944 by Otto Schmidt, followed by the ''protoplanet theory'' of William McCrea (1960) and finally the ''capture theory'' of Michael Woolfson.
For details of Kant's position, see
In 1978, Andrew Prentice resurrected the initial Laplacian ideas about planet formation and developed the ''modern Laplacian theory''. None of these models proved completely successful, and many of the proposed theories were descriptive. The 1944 accretion model by Otto Schmidt was further developed in a quantitative way in 1969 by Viktor Safronov. He calculated, in detail, the different stages of terrestrial planet formation. Since then, the model has been further developed using intensive numerical simulations to study
planetesimal Planetesimals () are solid objects thought to exist in protoplanetary disks and debris disks. Believed to have formed in the Solar System about 4.6 billion years ago, they aid study of its formation. Formation A widely accepted theory of pla ...
accumulation. It is now accepted that stars form by the gravitational collapse of interstellar gas. Prior to collapse, this gas is mostly in the form of molecular clouds, such as the
Orion Nebula The Orion Nebula (also known as Messier 42, M42, or NGC 1976) is a diffuse nebula in the Milky Way situated south of Orion's Belt in the Orion (constellation), constellation of Orion, and is known as the middle "star" in the "sword" of Orion. It ...
. As the cloud collapses, losing potential energy, it heats up, gaining kinetic energy, and the conservation of
angular momentum Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total ang ...
ensures that the cloud forms a flattened disk—the
accretion disk An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is most frequently a star. Friction, uneven irradiance, magnetohydrodynamic effects, and ...
.


Accretion of galaxies

A few hundred thousand years after the
Big Bang The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including th ...
, the
Universe The universe is all of space and time and their contents. It comprises all of existence, any fundamental interaction, physical process and physical constant, and therefore all forms of matter and energy, and the structures they form, from s ...
cooled to the point where atoms could form. As the Universe continued to expand and cool, the atoms lost enough kinetic energy, and
dark matter In astronomy, dark matter is an invisible and hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravity, gravitational effects that cannot be explained by general relat ...
coalesced sufficiently, to form protogalaxies. As further accretion occurred,
galaxies A galaxy is a system of stars, stellar remnants, interstellar gas, dust, and dark matter bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar Sys ...
formed. Indirect evidence is widespread. Galaxies grow through
mergers Mergers and acquisitions (M&A) are business transactions in which the ownership of a company, business organization, or one of their operating units is transferred to or consolidated with another entity. They may happen through direct absorpt ...
and smooth gas accretion. Accretion also occurs inside galaxies, forming stars.


Accretion of stars

Star A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...
s are thought to form inside giant clouds of cold
molecular hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
giant molecular cloud A molecular cloud—sometimes called a stellar nursery if star formation is occurring within—is a type of interstellar cloud of which the density and size permit absorption nebulae, the formation of molecules (most commonly molecular hydrogen ...
s of roughly and in diameter. Over millions of years, giant molecular clouds are prone to collapse and fragmentation. These fragments then form small, dense cores, which in turn collapse into stars. The cores range in mass from a fraction to several times that of the Sun and are called protostellar (protosolar) nebulae. They possess diameters of and a
particle number density In thermodynamics, the particle number (symbol ) of a thermodynamic system is the number of constituent particles in that system. The particle number is a fundamental thermodynamic property which is conjugate to the chemical potential. Unlike m ...
of roughly . Compare it with the particle number density of the air at the sea level—. The initial collapse of a solar-mass protostellar nebula takes around 100,000 years. Every nebula begins with a certain amount of
angular momentum Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total ang ...
. Gas in the central part of the nebula, with relatively low angular momentum, undergoes fast compression and forms a hot
hydrostatic Hydrostatics is the branch of fluid mechanics that studies fluids at hydrostatic equilibrium and "the pressure in a fluid or exerted by a fluid on an immersed body". The word "hydrostatics" is sometimes used to refer specifically to water and o ...
(non-contracting) core containing a small fraction of the mass of the original nebula. This core forms the seed of what will become a star. As the collapse continues, conservation of angular momentum dictates that the rotation of the infalling envelope accelerates, which eventually forms a disk. As the infall of material from the disk continues, the envelope eventually becomes thin and transparent and the young stellar object (YSO) becomes observable, initially in
far-infrared Far infrared (FIR) or long wave refers to a specific range within the infrared spectrum of electromagnetic radiation. It encompasses radiation with wavelengths ranging from 15 μm ( micrometers) to 1 mm, which corresponds to a freque ...
light and later in the visible. Around this time the protostar begins to fuse
deuterium Deuterium (hydrogen-2, symbol H or D, also known as heavy hydrogen) is one of two stable isotopes of hydrogen; the other is protium, or hydrogen-1, H. The deuterium nucleus (deuteron) contains one proton and one neutron, whereas the far more c ...
. If the protostar is sufficiently massive (above ), hydrogen fusion follows. Otherwise, if its mass is too low, the object becomes a
brown dwarf Brown dwarfs are substellar objects that have more mass than the biggest gas giant planets, but less than the least massive main sequence, main-sequence stars. Their mass is approximately 13 to 80 Jupiter mass, times that of Jupiter ()not big en ...
. This birth of a new star occurs approximately 100,000 years after the collapse begins. Objects at this stage are known as Class I protostars, which are also called young
T Tauri star T Tauri stars (TTS) are a class of variable stars that are less than about ten million years old. This class is named after the prototype, T Tauri, a young star in the Taurus Molecular Cloud, Taurus star-forming region. They are found near mo ...
s, evolved protostars, or young stellar objects. By this time, the forming star has already accreted much of its mass; the total mass of the disk and remaining envelope does not exceed 10–20% of the mass of the central YSO. At the next stage, the envelope completely disappears, having been gathered up by the disk, and the protostar becomes a classical T Tauri star. The latter have accretion disks and continue to accrete hot gas, which manifests itself by strong emission lines in their spectrum. The former do not possess accretion disks. Classical T Tauri stars evolve into weakly lined T Tauri stars. This happens after about 1 million years. The mass of the disk around a classical T Tauri star is about 1–3% of the stellar mass, and it is accreted at a rate of 10−7 to per year. A pair of bipolar jets is usually present as well. The accretion explains all peculiar properties of classical T Tauri stars: strong
flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications in physics. For transport phe ...
in the
emission line A spectral line is a weaker or stronger region in an otherwise uniform and continuous spectrum. It may result from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used ...
s (up to 100% of the intrinsic
luminosity Luminosity is an absolute measure of radiated electromagnetic radiation, electromagnetic energy per unit time, and is synonymous with the radiant power emitted by a light-emitting object. In astronomy, luminosity is the total amount of electroma ...
of the star),
magnetic Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, m ...
activity, photometric variability and jets. The emission lines actually form as the accreted gas hits the "surface" of the star, which happens around its magnetic poles. The jets are byproducts of accretion: they carry away excessive angular momentum. The classical T Tauri stage lasts about 10 million years (there are only a few examples of so-called Peter Pan disks, where the accretion continues to persist for much longer periods, sometimes lasting for more than 40 million years). The disk eventually disappears due to accretion onto the central star, planet formation, ejection by jets, and photoevaporation by
ultraviolet Ultraviolet radiation, also known as simply UV, is electromagnetic radiation of wavelengths of 10–400 nanometers, shorter than that of visible light, but longer than X-rays. UV radiation is present in sunlight and constitutes about 10% of ...
radiation from the central star and nearby stars. As a result, the young star becomes a weakly lined T Tauri star, which, over hundreds of millions of years, evolves into an ordinary Sun-like star, dependent on its initial mass.


Accretion of planets

Self-accretion of
cosmic dust Cosmic dustalso called extraterrestrial dust, space dust, or star dustis dust that occurs in outer space or has fallen onto Earth. Most cosmic dust particles measure between a few molecules and , such as micrometeoroids (30 μm). Cosmic dust can ...
accelerates the growth of the particles into boulder-sized
planetesimal Planetesimals () are solid objects thought to exist in protoplanetary disks and debris disks. Believed to have formed in the Solar System about 4.6 billion years ago, they aid study of its formation. Formation A widely accepted theory of pla ...
s. The more massive planetesimals accrete some smaller ones, while others shatter in collisions. Accretion disks are common around smaller stars, stellar remnants in a close binary, or
black hole A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...
s surrounded by material (such as those at the centers of
galaxies A galaxy is a system of stars, stellar remnants, interstellar gas, dust, and dark matter bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar Sys ...
). Some dynamics in the disk, such as dynamical friction, are necessary to allow orbiting gas to lose
angular momentum Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total ang ...
and fall onto the central massive object. Occasionally, this can result in stellar surface fusion (see Bondi accretion). In the formation of terrestrial planets or
planetary core A planetary core consists of the innermost layers of a planet. Cores may be entirely liquid, or a mixture of solid and liquid layers as is the case in the Earth. In the Solar System, core sizes range from about 20% (the Moon) to 85% of a plan ...
s, several stages can be considered. First, when gas and dust grains collide, they agglomerate by microphysical processes like
van der Waals force In molecular physics and chemistry, the van der Waals force (sometimes van der Waals' force) is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical elec ...
s and electromagnetic forces, forming micrometer-sized particles. During this stage, accumulation mechanisms are largely non-gravitational in nature. However, planetesimal formation in the centimeter-to-meter range is not well understood, and no convincing explanation is offered as to why such grains would accumulate rather than simply rebound. In particular, it is still not clear how these objects grow to become sized planetesimals; this problem is known as the "meter size barrier": As dust particles grow by coagulation, they acquire increasingly large relative velocities with respect to other particles in their vicinity, as well as a systematic inward drift velocity, that leads to destructive collisions, and thereby limit the growth of the aggregates to some maximum size. Ward (1996) suggests that when slow moving grains collide, the very low, yet non-zero, gravity of colliding grains impedes their escape. It is also thought that grain fragmentation plays an important role replenishing small grains and keeping the disk thick, but also in maintaining a relatively high abundance of solids of all sizes. A number of mechanisms have been proposed for crossing the 'meter-sized' barrier. Local concentrations of pebbles may form, which then gravitationally collapse into planetesimals the size of large asteroids. These concentrations can occur passively due to the structure of the gas disk, for example, between eddies, at pressure bumps, at the edge of a gap created by a giant planet, or at the boundaries of turbulent regions of the disk. Or, the particles may take an active role in their concentration via a feedback mechanism referred to as a
streaming instability In planetary science a streaming instability is a hypothetical mechanism for the formation of planetesimals in which the drag felt by solid particles orbiting in a gas disk leads to their spontaneous concentration into clumps which can gravitational ...
. In a streaming instability the interaction between the solids and the gas in the protoplanetary disk results in the growth of local concentrations, as new particles accumulate in the wake of small concentrations, causing them to grow into massive filaments. Alternatively, if the grains that form due to the agglomeration of dust are highly porous their growth may continue until they become large enough to collapse due to their own gravity. The low density of these objects allows them to remain strongly coupled with the gas, thereby avoiding high velocity collisions which could result in their erosion or fragmentation. Grains eventually stick together to form mountain-size (or larger) bodies called planetesimals. Collisions and gravitational interactions between planetesimals combine to produce Moon-size planetary embryos (
protoplanet A protoplanet is a large planetary embryo that originated within a protoplanetary disk and has undergone internal melting to produce a differentiated interior. Protoplanets are thought to form out of kilometer-sized planetesimals that gravitatio ...
s) over roughly 0.1–1 million years. Finally, the planetary embryos collide to form planets over 10–100 million years. The planetesimals are massive enough that mutual gravitational interactions are significant enough to be taken into account when computing their evolution. Growth is aided by orbital decay of smaller bodies due to gas drag, which prevents them from being stranded between orbits of the embryos. Further collisions and accumulation lead to terrestrial planets or the core of giant planets. If the planetesimals formed via the gravitational collapse of local concentrations of pebbles, their growth into planetary embryos and the cores of giant planets is dominated by the further accretions of pebbles. Pebble accretion is aided by the gas drag felt by objects as they accelerate toward a massive body. Gas drag slows the pebbles below the escape velocity of the massive body causing them to spiral toward and to be accreted by it. Pebble accretion may accelerate the formation of planets by a factor of 1000 compared to the accretion of planetesimals, allowing giant planets to form before the dissipation of the gas disk. However, core growth via pebble accretion appears incompatible with the final masses and compositions of
Uranus Uranus is the seventh planet from the Sun. It is a gaseous cyan-coloured ice giant. Most of the planet is made of water, ammonia, and methane in a Supercritical fluid, supercritical phase of matter, which astronomy calls "ice" or Volatile ( ...
and
Neptune Neptune is the eighth and farthest known planet from the Sun. It is the List of Solar System objects by size, fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the densest giant planet. It is 17 t ...
. Direct calculations indicate that, in a typical
protoplanetary disk A protoplanetary disk is a rotating circumstellar disc of dense gas and dust surrounding a young newly formed star, a T Tauri star, or Herbig Ae/Be star. The protoplanetary disk may not be considered an accretion disk; while the two are sim ...
, the formation time of a giant planet via pebble accretion is comparable to the formation times resulting from planetesimal accretion. The formation of
terrestrial planet A terrestrial planet, tellurian planet, telluric planet, or rocky planet, is a planet that is composed primarily of silicate, rocks or metals. Within the Solar System, the terrestrial planets accepted by the IAU are the inner planets closest to ...
s differs from that of giant gas planets, also called
Jovian planet Jovian is the adjectival form of Jupiter and may refer to: * Jovian (emperor) (Flavius Iovianus Augustus), Roman emperor (363–364 AD) * Jovians and Herculians, Roman imperial guard corps * Jovian (lemur), a Coquerel's sifaka known for ''Zoboom ...
s. The particles that make up the terrestrial planets are made from metal and rock that condensed in the inner
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...
. However, Jovian planets began as large, icy planetesimals, which then captured hydrogen and helium gas from the
solar nebula There is evidence that the formation of the Solar System began about 4.6 bya, 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, whil ...
. Differentiation between these two classes of planetesimals arise due to the frost line of the solar nebula.


Accretion of asteroids

Meteorite A meteorite is a rock (geology), rock that originated in outer space and has fallen to the surface of a planet or Natural satellite, moon. When the original object enters the atmosphere, various factors such as friction, pressure, and chemical ...
s contain a record of accretion and impacts during all stages of
asteroid An asteroid is a minor planet—an object larger than a meteoroid that is neither a planet nor an identified comet—that orbits within the Solar System#Inner Solar System, inner Solar System or is co-orbital with Jupiter (Trojan asteroids). As ...
origin and evolution; however, the mechanism of asteroid accretion and growth is not well understood. Evidence suggests the main growth of asteroids can result from gas-assisted accretion of
chondrule A chondrule (from Ancient Greek χόνδρος ''chondros'', grain) is a round grain found in a chondrite. Chondrules form as molten or partially molten droplets in space before being Accretion (astrophysics), accreted to their parent asteroids ...
s, which are millimeter-sized spherules that form as molten (or partially molten) droplets in space before being accreted to their parent asteroids. In the inner Solar System, chondrules appear to have been crucial for initiating accretion. The tiny mass of asteroids may be partly due to inefficient chondrule formation beyond 2 AU, or less-efficient delivery of chondrules from near the protostar. Also, impacts controlled the formation and destruction of asteroids, and are thought to be a major factor in their geological evolution. Chondrules, metal grains, and other components likely formed in the
solar nebula There is evidence that the formation of the Solar System began about 4.6 bya, 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, whil ...
. These accreted together to form parent asteroids. Some of these bodies subsequently melted, forming metallic cores and
olivine The mineral olivine () is a magnesium iron Silicate minerals, silicate with the chemical formula . It is a type of Nesosilicates, nesosilicate or orthosilicate. The primary component of the Earth's upper mantle (Earth), upper mantle, it is a com ...
-rich mantles; others were aqueously altered. After the asteroids had cooled, they were eroded by impacts for 4.5 billion years, or disrupted. For accretion to occur, impact velocities must be less than about twice the escape velocity, which is about for a radius asteroid. Simple models for accretion in the
asteroid belt The asteroid belt is a torus-shaped region in the Solar System, centered on the Sun and roughly spanning the space between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies called asteroids ...
generally assume micrometer-sized dust grains sticking together and settling to the midplane of the nebula to form a dense layer of dust, which, because of gravitational forces, was converted into a disk of kilometer-sized planetesimals. But, several arguments suggest that asteroids may not have accreted this way.


Accretion of comets

Comet A comet is an icy, small Solar System body that warms and begins to release gases when passing close to the Sun, a process called outgassing. This produces an extended, gravitationally unbound atmosphere or Coma (cometary), coma surrounding ...
s, or their precursors, formed in the outer Solar System, possibly millions of years before planet formation. How and when comets formed is debated, with distinct implications for Solar System formation, dynamics, and geology. Three-dimensional computer simulations indicate the major structural features observed on cometary nuclei can be explained by pairwise low velocity accretion of weak cometesimals. The currently favored formation mechanism is that of the
nebular hypothesis The nebular hypothesis is the most widely accepted model in the field of cosmogony to explain the formation and evolution of the Solar System (as well as other planetary systems). It suggests the Solar System is formed from gas and dust orbiting t ...
, which states that comets are probably a remnant of the original planetesimal "building blocks" from which the planets grew. Astronomers think that comets originate in both the
Oort cloud The Oort cloud (pronounced or ), sometimes called the Öpik–Oort cloud, is scientific theory, theorized to be a cloud of billions of Volatile (astrogeology), icy planetesimals surrounding the Sun at distances ranging from 2,000 to 200,000 A ...
and the scattered disk. The scattered disk was created when
Neptune Neptune is the eighth and farthest known planet from the Sun. It is the List of Solar System objects by size, fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the densest giant planet. It is 17 t ...
migrated outward into the proto-Kuiper belt, which at the time was much closer to the Sun, and left in its wake a population of dynamically stable objects that could never be affected by its orbit (the
Kuiper belt The Kuiper belt ( ) is a circumstellar disc in the outer Solar System, extending from the orbit of Neptune at 30 astronomical units (AU) to approximately 50 AU from the Sun. It is similar to the asteroid belt, but is far larger—20 times ...
proper), and a population whose perihelia are close enough that Neptune can still disturb them as it travels around the Sun (the scattered disk). Because the scattered disk is dynamically active and the Kuiper belt relatively dynamically stable, the scattered disk is now seen as the most likely point of origin for periodic comets. The classic Oort cloud theory states that the Oort cloud, a sphere measuring about in radius, formed at the same time as the solar nebula and occasionally releases comets into the inner Solar System as a giant planet or star passes nearby and causes gravitational disruptions. Examples of such comet clouds may already have been seen in the Helix Nebula. The ''Rosetta'' mission to comet
67P/Churyumov–Gerasimenko 67P/Churyumov–Gerasimenko (abbreviated as 67P or 67P/C–G) is a Jupiter-family comet. It is originally from the Kuiper belt and has an orbital period of 6.45 years as of 2012, a rotation period of approximately 12.4 hours, and a maximum velo ...
determined in 2015 that when Sun's heat penetrates the surface, it triggers evaporation (sublimation) of buried ice. While some of the resulting water vapour may escape from the nucleus, 80% of it recondenses in layers beneath the surface. This observation implies that the thin ice-rich layers exposed close to the surface may be a consequence of cometary activity and evolution, and that global layering does not necessarily occur early in the comet's formation history. While most scientists thought that all the evidence indicated that the structure of nuclei of comets is processed
rubble pile In astronomy, a rubble pile is a celestial body that consists of numerous pieces of debris that have coalesced under the influence of gravity. Rubble piles have low density because there are large cavities between the various chunks that make the ...
s of smaller ice planetesimals of a previous generation, the ''Rosetta'' mission confirmed the idea that comets are "rubble piles" of disparate material. Comets appear to have formed as ~100-km bodies, then overwhelmingly ground/recontacted into their present states.


See also

* * * * * * * * *
Quasi-star A quasi-star (also called black hole star) is a hypothetical star, hypothetical type of extremely large and luminosity, luminous star that may have existed early in the history of the Universe. They are thought to have existed for around 7� ...
* * *


References

{{DEFAULTSORT:Accretion (Astrophysics) Concepts in astrophysics Celestial mechanics Solar System dynamic theories