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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 the Sun which clumped up together to form the planets. The theory was developed by Immanuel Kant and published in his Universal Natural History and Theory of the Heavens (1755) and then modified in 1796 by Pierre Laplace. Originally applied to the Solar System, the process of planetary system formation is now thought to be at work throughout the universe. The widely accepted modern variant of the nebular theory is the solar nebular disk model (SNDM) or solar nebular model.[1] It offered explanations for a variety of properties of the Solar System, including the nearly circular and coplanar orbits of the planets, and their motion in the same direction as the Sun's rotation. Some elements of the original nebular theory are echoed in modern theories of planetary formation, but most elements have been superseded.

According to the nebular theory, stars form in massive and dense clouds of molecular hydrogen—giant molecular clouds (GMC). These clouds are gravitationally unstable, and matter coalesces within them to smaller denser clumps, which then rotate, collapse, and form stars. Star formation is a complex process, which always produces a gaseous protoplanetary disk (proplyd) around the young star. This may give birth to planets in certain circumstances, which are not well known. Thus the formation of planetary systems is thought to be a natural result of star formation. A Sun-like star usually takes approximately 1 million years to form, with the protoplanetary disk evolving into a planetary system over the next 10–100 million years.[2]

The protoplanetary disk is an accretion disk that feeds the central star.[3] Initially very hot, the disk later cools in what is known as the T Tauri star stage; here, formation of small dust grains made of rocks and ice is possible. The grains eventually may coagulate into kilometer-sized planetesimals. If the disk is massive enough, the runaway accretions begin, resulting in the rapid—100,000 to 300,000 years—formation of Moon- to Mars-sized planetary embryos. Near the star, the planetary embryos go through a stage of violent mergers, producing a few terrestrial planets. The last stage takes approximately 100 million to a billion years.[2]

The formation of giant planets is a more complicated process. It is thought to occur beyond the frost line, where planetary embryos mainly are made of various types of ice. As a result, they are several times more massive than in the inner part of the protoplanetary disk. What follows after the embryo formation is not completely clear. Some embryos appear to continue to grow and eventually reach 5–10 Earth masses—the threshold value, which is necessary to begin accretion of the hydrogen–helium gas from the disk.[4] The accumulation of gas by the core is initially a slow process, which continues for several million years, but after the forming protoplanet reaches about 30 Earth masses (M🜨) it accelerates and proceeds in a runaway manner. Jupiter- and Saturn-like planets are thought to accumulate the bulk of their mass during only 10,000 years. The accretion stops when the gas is exhausted. The formed planets can migrate over long distances during or after their formation. Ice giants such as Uranus and Neptune are thought to be failed cores, which formed too late when the disk had almost disappeared.[2]

History

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Main article: History of Solar System formation and evolution hypotheses

There is evidence that Emanuel Swedenborg first proposed parts of the nebular theory in 1734.[5][6] Immanuel Kant, familiar with Swedenborg's work, developed the theory further in 1755, publishing his own Universal Natural History and Theory of the Heavens, wherein he argued that gaseous clouds (nebulae) slowly rotate, gradually collapse and flatten due to gravity, eventually forming stars and planets.[1][7]

Pierre-Simon Laplace independently developed and proposed a similar model in 1796[1] in his Exposition du systeme du monde. He envisioned that the Sun originally had an extended hot atmosphere throughout the volume of the Solar System. His theory featured a contracting and cooling protosolar cloud—the protosolar nebula. As this cooled and contracted, it flattened and spun more rapidly, throwing off (or shedding) a series of gaseous rings of material; and according to him, the planets condensed from this material. His model was similar to Kant's, except more detailed and on a smaller scale.[1] While the Laplacian nebular model dominated in the 19th century, it encountered a number of difficulties. The main problem involved angular momentum distribution between the Sun and planets. The planets have 99% of the angular momentum, and this fact could not be explained by the nebular model.[1] As a result, astronomers largely abandoned this theory of planet formation at the beginning of the 20th century.

According to some, a major critique came during the 19th century from James Clerk Maxwell (1831–1879), who in some sources is claimed to have maintained that different rotation between the inner and outer parts of a ring could not allow condensation of material.[8] However, both the critique and the attribution to Maxwell have been deemed to be incorrect upon further investigation, with the original error being made by George Gamow in some popular publications and propagated continually ever since.[9] Astronomer Sir David Brewster also rejected Laplace, writing in 1876 that "those who believe in the Nebular Theory consider it as certain that our Earth derived its solid matter and its atmosphere from a ring thrown from the Solar atmosphere, which afterwards contracted into a solid terraqueous sphere, from which the Moon was thrown off by the same process". He argued that under such view, "the Moon must necessarily have carried off water and air from the watery and aerial parts of the Earth and must have an atmosphere".[10]: 153  Brewster claimed that Sir Isaac Newton's religious beliefs had previously considered nebular ideas as tending to atheism, and quoted him as saying that "the growth of new systems out of old ones, without the mediation of a Divine power, seemed to him apparently absurd".[10]: 233 

The perceived deficiencies of the Laplacian model stimulated scientists to find a replacement for it. During the 20th century many theories addressed the issue, including the planetesimal theory of Thomas Chamberlin and Forest Moulton (1901), the tidal model of James Jeans (1917), the accretion model of Otto Schmidt (1944), the protoplanet theory of William McCrea (1960) and finally the capture theory of Michael Woolfson.[1] In 1978 Andrew Prentice resurrected the initial Laplacian ideas about planet formation and developed the modern Laplacian theory.[1] None of these attempts proved completely successful, and many of the proposed theories were descriptive.

The birth of the modern widely accepted theory of planetary formation—the solar nebular disk model (SNDM)—can be traced to the Soviet astronomer Victor Safronov.[11] His 1969 book Evolution of the protoplanetary cloud and formation of the Earth and the planets,[12] which was translated to English in 1972, had a long-lasting effect on the way scientists think about the formation of the planets.[13] In this book almost all major problems of the planetary formation process were formulated and some of them solved. Safronov's ideas were further developed in the works of George Wetherill, who discovered runaway accretion.[1] While originally applied only to the Solar System, the SNDM was subsequently thought by theorists to be at work throughout the Universe; as of 23 April 2026 astronomers have discovered 6,416 extrasolar planets in our galaxy.[14]

Solar nebular model: achievements and problems

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Achievements

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Dusty disks surrounding nearby young stars in greater detail.[15]

The star formation process naturally results in the appearance of accretion disks around young stellar objects.[16] At the age of about 1 million years, 100% of stars may have such disks.[17] This conclusion is supported by the discovery of the gaseous and dusty disks around protostars and T Tauri stars as well as by theoretical considerations.[18] Observations of these disks show that the dust grains inside them grow in size on short (thousand-year) time scales, producing 1 centimeter sized particles.[19]

The accretion process, by which 1 km planetesimals grow into 1,000 km sized bodies, is well understood now.[20] This process develops inside any disk where the number density of planetesimals is sufficiently high, and proceeds in a runaway manner. Growth later slows and continues as oligarchic accretion. The end result is formation of planetary embryos of varying sizes, which depend on the distance from the star.[20] Various simulations have demonstrated that the merger of embryos in the inner part of the protoplanetary disk leads to the formation of a few Earth-sized bodies. Thus the origin of terrestrial planets is now considered to be an almost solved problem.[21]

Current issues

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The physics of accretion disks encounters some problems.[22] The most important one is how the material, which is accreted by the protostar, loses its angular momentum. One possible explanation suggested by Hannes Alfvén was that angular momentum was shed by the solar wind during its T Tauri star phase. The momentum is transported to the outer parts of the disk by viscous stresses.[23] Viscosity is generated by macroscopic turbulence, but the precise mechanism that produces this turbulence is not well understood. Another possible process for shedding angular momentum is magnetic braking, where the spin of the star is transferred into the surrounding disk via that star's magnetic field.[24] The main processes responsible for the disappearance of the gas in disks are viscous diffusion and photo-evaporation.[25][26]

Multiple star system AS 205.[27]

The formation of planetesimals is the biggest unsolved problem in the nebular disk model. How 1 cm sized particles coalesce into 1 km planetesimals is a mystery. This mechanism appears to be the key to the question as to why some stars have planets, while others have nothing around them, not even dust belts.[28]

The formation timescale of giant planets is also an important problem. Old theories were unable to explain how their cores could form fast enough to accumulate significant amounts of gas from the quickly disappearing protoplanetary disk.[20][29] The mean lifetime of the disks, which is less than ten million (107) years, appeared to be shorter than the time necessary for the core formation.[17] Much progress has been done to solve this problem and current models of giant planet formation are now capable of forming Jupiter (or more massive planets) in about 4 million years or less, well within the average lifetime of gaseous disks.[30][31][32]

Another potential problem of giant planet formation is their orbital migration. Some calculations show that interaction with the disk can cause rapid inward migration, which, if not stopped, results in the planet reaching the "central regions still as a sub-Jovian object."[33] More recent calculations indicate that disk evolution during migration can mitigate this problem.[34]

Formation of stars and protoplanetary disks

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Protostars

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Main article: Protostar
The visible-light (left) and infrared (right) views of the Trifid Nebula—a giant star-forming cloud of gas and dust located 5,400 light-years away in the constellation Sagittarius

Stars are thought to form inside giant clouds of cold molecular hydrogen—giant molecular clouds roughly 300,000 times the mass of the Sun (M☉) and 20 parsecs in diameter.[2][35] Over millions of years, giant molecular clouds are prone to collapse and fragmentation.[36] These fragments then form small, dense cores, which in turn collapse into stars.[35] The cores range in mass from a fraction to several times that of the Sun and are called protostellar (protosolar) nebulae.[2] They possess diameters of 0.01–0.1 pc (2,000–20,000 AU) and a particle number density of roughly 10,000 to 100,000 cm−3.[a][35][37]

The initial collapse of a solar-mass protostellar nebula takes around 100,000 years.[2][35] Every nebula begins with a certain amount of angular momentum. Gas in the central part of the nebula, with relatively low angular momentum, undergoes fast compression and forms a hot hydrostatic (not contracting) core containing a small fraction of the mass of the original nebula.[38] This core forms the seed of what will become a star.[2][38] As the collapse continues, conservation of angular momentum means that the rotation of the infalling envelope accelerates,[39][40] which largely prevents the gas from directly accreting onto the central core. The gas is instead forced to spread outwards near its equatorial plane, forming a disk, which in turn accretes onto the core.[2][39][40] The core gradually grows in mass until it becomes a young hot protostar.[38] At this stage, the protostar and its disk are heavily obscured by the infalling envelope and are not directly observable.[16] In fact the remaining envelope's opacity is so high that even millimeter-wave radiation has trouble escaping from inside it.[2][16] Such objects are observed as very bright condensations, which emit mainly millimeter-wave and submillimeter-wave radiation.[37] They are classified as spectral Class 0 protostars.[16] The collapse is often accompanied by bipolar outflows—jets—that emanate along the rotational axis of the inferred disk. The jets are frequently observed in star-forming regions (see Herbig–Haro (HH) objects).[41] The luminosity of the Class 0 protostars is high — a solar-mass protostar may radiate at up to 100 solar luminosities.[16] The source of this energy is gravitational collapse, as their cores are not yet hot enough to begin nuclear fusion.[38][42]

Infrared image of the molecular outflow from an otherwise hidden newborn star HH 46/47

As the infall of its material onto the disk continues, the envelope eventually becomes thin and transparent and the young stellar object (YSO) becomes observable, initially in far-infrared light and later in the visible.[37] Around this time the protostar begins to fuse deuterium. If the protostar is sufficiently massive (above 80 Jupiter masses (MJ)), hydrogen fusion follows. Otherwise, if its mass is too low, the object becomes a brown dwarf.[42] This birth of a new star occurs approximately 100,000 years after the collapse begins.[2] Objects at this stage are known as Class I protostars,[16] which are also called young T Tauri stars, evolved protostars, or young stellar objects.[16] 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.[37]

At the next stage the envelope completely disappears, having been gathered up by the disk, and the protostar becomes a classical T Tauri star.[b] This happens after about 1 million years.[2] 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 10−9 M☉ per year.[45] A pair of bipolar jets is usually present as well.[46] The accretion explains all peculiar properties of classical T Tauri stars: strong flux in the emission lines (up to 100% of the intrinsic luminosity of the star), magnetic activity, photometric variability and jets.[47] The emission lines actually form as the accreted gas hits the "surface" of the star, which happens around its magnetic poles.[47] The jets are byproducts of accretion: they carry away excessive angular momentum. The classical T Tauri stage lasts about 10 million years.[2] The disk eventually disappears due to accretion onto the central star, planet formation, ejection by jets and photoevaporation by UV-radiation from the central star and nearby stars.[48] As a result, the young star becomes a weakly lined T Tauri star, which slowly, over hundreds of millions of years, evolves into an ordinary Sun-like star.[38]

Protoplanetary disks

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See also: Protoplanetary disk and planetesimal
Debris disks detected in HST archival images of young stars, HD 141943 and HD 191089, using improved imaging processes (24 April 2014).[49]

Under certain circumstances the disk, which can now be called protoplanetary, may give birth to a planetary system.[2] Protoplanetary disks have been observed around a very high fraction of stars in young star clusters.[17][50] They exist from the beginning of a star's formation, but at the earliest stages are unobservable due to the opacity of the surrounding envelope.[16] The disk of a Class 0 protostar is thought to be massive and hot. It is an accretion disk, which feeds the central protostar.[39][40] The temperature can easily exceed 400 K inside 5 AU and 1,000 K inside 1 AU.[51] The heating of the disk is primarily caused by the viscous dissipation of turbulence in it and by the infall of the gas from the nebula.[39][40] The high temperature in the inner disk causes most of the volatile material—water, organics, and some rocks—to evaporate, leaving only the most refractory elements like iron. The ice can survive only in the outer part of the disk.[51]

A protoplanetary disk forming in the Orion Nebula

The main problem in the physics of accretion disks is the generation of turbulence and the mechanism responsible for the high effective viscosity.[2] The turbulent viscosity is thought to be responsible for the transport of the mass to the central protostar and momentum to the periphery of the disk. This is vital for accretion, because the gas can be accreted by the central protostar only if it loses most of its angular momentum, which must be carried away by the small part of the gas drifting outwards.[39][52] The result of this process is the growth of both the protostar and of the disk radius, which can reach 1,000 AU if the initial angular momentum of the nebula is large enough.[40] Large disks are routinely observed in many star-forming regions such as the Orion Nebula.[18]

Artist's impression of the disc and gas streams around young star HD 142527.[53]

The lifespan of the accretion disks is about 10 million years.[17] By the time the star reaches the classical T-Tauri stage, the disk becomes thinner and cools.[45] Less volatile materials start to condense close to its center, forming 0.1–1 μm dust grains that contain crystalline silicates.[19] The transport of the material from the outer disk can mix these newly formed dust grains with primordial ones, which contain organic matter and other volatiles. This mixing can explain some peculiarities in the composition of Solar System bodies such as the presence of interstellar grains in primitive meteorites and refractory inclusions in comets.[51]

Various planet formation processes, including exocomets and other planetesimals, around Beta Pictoris, a very young type A V star (NASA artist's conception).

Dust particles tend to stick to each other in the dense disk environment, leading to the formation of larger particles up to several centimeters in size.[54] The signatures of the dust processing and coagulation are observed in the infrared spectra of the young disks.[19] Further aggregation can lead to the formation of planetesimals measuring 1 km across or larger, which are the building blocks of planets.[2][54] Planetesimal formation is another unsolved problem of disk physics, as simple sticking becomes ineffective as dust particles grow larger.[28]

One hypothesis is formation by gravitational instability. Particles several centimeters in size or larger slowly settle near the middle plane of the disk, forming a very thin—less than 100 km—and dense layer. This layer is gravitationally unstable and may fragment into numerous clumps, which in turn collapse into planetesimals.[2][28] However, the differing velocities of the gas disk and the solids near the mid-plane can generate turbulence which prevents the layer from becoming thin enough to fragment due to gravitational instability.[55] This may limit the formation of planetesimals via gravitational instabilities to specific locations in the disk where the concentration of solids is enhanced.[56]

Another possible mechanism for the formation of planetesimals is the streaming instability in which the drag felt by particles orbiting through gas creates a feedback effect causing the growth of local concentrations. These local concentrations push back on the gas creating a region where the headwind felt by the particles is smaller. The concentration is thus able to orbit faster and undergoes less radial drift. Isolated particles join these concentrations as they are overtaken or as they drift inward causing it to grow in mass. Eventually these concentrations form massive filaments which fragment and undergo gravitational collapse forming planetesimals the size of the larger asteroids.[57]

Planetary formation can also be triggered by gravitational instability within the disk itself, which leads to its fragmentation into clumps. Some of them, if they are dense enough, will collapse,[52] which can lead to rapid formation of gas giant planets and even brown dwarfs on the timescale of 1,000 years.[58] If these clumps migrate inward as the collapse proceeds tidal forces from the star can result in a significant mass loss leaving behind a smaller body.[59] However it is only possible in massive disks—more massive than 0.3 M☉. In comparison, typical disk masses are 0.01–0.03 M☉. Because the massive disks are rare, this mechanism of planet formation is thought to be infrequent.[2][22] On the other hand, it may play a major role in the formation of brown dwarfs.[60]

Asteroid collision—building planets (artist concept).

The ultimate dissipation of protoplanetary disks is triggered by a number of different mechanisms. The inner part of the disk is either accreted by the star or ejected by the bipolar jets,[45][46] whereas the outer part can evaporate under the star's powerful UV radiation during the T Tauri stage[61] or by nearby stars.[48] The gas in the central part can either be accreted or ejected by the growing planets, while the small dust particles are ejected by the radiation pressure of the central star. What is finally left is either a planetary system, a remnant disk of dust without planets, or nothing, if planetesimals failed to form.[2]

Because planetesimals are so numerous, and spread throughout the protoplanetary disk, some survive the formation of a planetary system. Asteroids are understood to be left-over planetesimals, gradually grinding each other down into smaller and smaller bits, while comets are typically planetesimals from the farther reaches of a planetary system. Meteorites are samples of planetesimals that reach a planetary surface, and provide a great deal of information about the formation of the Solar System. Primitive-type meteorites are chunks of shattered low-mass planetesimals, where no thermal differentiation took place, while processed-type meteorites are chunks from shattered massive planetesimals.[62] Interstellar objects could have been captured, and become part of the young Solar system.[63]

Formation of planets

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Rocky planets

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According to the solar nebular disk model, rocky planets form in the inner part of the protoplanetary disk, within the frost line, where the temperature is high enough to prevent condensation of water ice and other substances into grains.[64] This results in coagulation of purely rocky grains and later in the formation of rocky planetesimals.[c][64] Such conditions are thought to exist in the inner 3–4 AU part of the disk of a Sun-like star.[2]

After small planetesimals—about 1 km in diameter—have formed by one way or another, runaway accretion begins.[20] It is called runaway because the mass growth rate is proportional to R4~M4/3, where R and M are the radius and mass of the growing body, respectively.[65] The specific (divided by mass) growth accelerates as the mass increases. This leads to the preferential growth of larger bodies at the expense of smaller ones.[20] The runaway accretion lasts between 10,000 and 100,000 years and ends when the largest bodies exceed approximately 1,000 km in diameter.[20] Slowing of the accretion is caused by gravitational perturbations by large bodies on the remaining planetesimals.[20][65] In addition, the influence of larger bodies stops further growth of smaller bodies.[20]

The next stage is called oligarchic accretion.[20] It is characterized by the dominance of several hundred of the largest bodies—oligarchs, which continue to slowly accrete planetesimals.[20] No body other than the oligarchs can grow.[65] At this stage the rate of accretion is proportional to R2, which is derived from the geometrical cross-section of an oligarch.[65] The specific accretion rate is proportional to M−1/3; and it declines with the mass of the body. This allows smaller oligarchs to catch up to larger ones. The oligarchs are kept at the distance of about 10·Hr (Hr=a(1-e)(M/3Ms)1/3 is the Hill radius, where a is the semimajor axis, e is the orbital eccentricity, and Ms is the mass of the central star) from each other by the influence of the remaining planetesimals.[20] Their orbital eccentricities and inclinations remain small. The oligarchs continue to accrete until planetesimals are exhausted in the disk around them.[20] Sometimes nearby oligarchs merge. The final mass of an oligarch depends on the distance from the star and surface density of planetesimals and is called the isolation mass.[65] For the rocky planets it is up to 0.1 M🜨, or one Mars mass.[2] The final result of the oligarchic stage is the formation of about 100 Moon- to Mars-sized planetary embryos uniformly spaced at about 10·Hr.[21] They are thought to reside inside gaps in the disk and to be separated by rings of remaining planetesimals. This stage is thought to last a few hundred thousand years.[2][20]

The last stage of rocky planet formation is the merger stage.[2] It begins when only a small number of planetesimals remains and embryos become massive enough to perturb each other, which causes their orbits to become chaotic.[21] During this stage embryos expel remaining planetesimals, and collide with each other. The result of this process, which lasts for 10 to 100 million years, is the formation of a limited number of Earth-sized bodies. Simulations show that the number of surviving planets is on average from 2 to 5.[2][21][62][66] In the Solar System they may be represented by Earth and Venus.[21] Formation of both planets required merging of approximately 10–20 embryos, while an equal number of them were thrown out of the Solar System.[62] Some of the embryos, which originated in the asteroid belt, are thought to have brought water to Earth.[64] Mars and Mercury may be regarded as remaining embryos that survived that rivalry.[62] Rocky planets which have managed to coalesce settle eventually into more or less stable orbits, explaining why planetary systems are generally packed to the limit; or, in other words, why they always appear to be at the brink of instability.[21]

Giant planets

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The dust disk around Fomalhaut—the brightest star in Piscis Austrinus constellation. Asymmetry of the disk may be caused by a giant planet (or planets) orbiting the star.

The formation of giant planets is an outstanding problem in the planetary sciences.[22] In the framework of the solar nebular model two theories for their formation exist. The first one is the disk instability model, where giant planets form in the massive protoplanetary disks as a result of its gravitational fragmentation (see above).[58] The second possibility is the core accretion model, which is also known as the nucleated instability model.[22][34] The latter scenario is thought to be the most promising one, because it can explain the formation of the giant planets in relatively low-mass disks (less than 0.1 M☉).[34] In this model giant planet formation is divided into two stages: a) accretion of a core of approximately 10 M🜨 and b) accretion of gas from the protoplanetary disk.[2][22][67] Either method may also lead to the creation of brown dwarfs.[31][68] Searches as of 2011 have found that core accretion is likely the dominant formation mechanism.[68]

Giant planet core formation is thought to proceed roughly along the lines of the terrestrial planet formation.[20] It starts with planetesimals that undergo runaway growth, followed by the slower oligarchic stage.[65] Hypotheses do not predict a merger stage, due to the low probability of collisions between planetary embryos in the outer part of planetary systems.[65] An additional difference is the composition of the planetesimals, which in the case of giant planets form beyond the so-called frost line and consist mainly of ice—the ice to rock ratio is about 4 to 1.[29] This enhances the mass of planetesimals fourfold. However, the minimum mass nebula capable of terrestrial planet formation can only form 1–2 M🜨 cores at the distance of Jupiter (5 AU) within 10 million years.[65] The latter number represents the average lifetime of gaseous disks around Sun-like stars.[17] The proposed solutions include enhanced mass of the disk—a tenfold increase would suffice;[65] protoplanet migration, which allows the embryo to accrete more planetesimals;[29] and finally accretion enhancement due to gas drag in the gaseous envelopes of the embryos.[29][32][69] Some combination of the above-mentioned ideas may explain the formation of the cores of gas giant planets such as Jupiter and perhaps even Saturn.[22] The formation of planets like Uranus and Neptune is more problematic, since no theory has been capable of providing for the in situ formation of their cores at the distance of 20–30 AU from the central star.[2] One hypothesis is that they initially accreted in the Jupiter-Saturn region, then were scattered and migrated to their present location.[70] Another possible solution is the growth of the cores of the giant planets via pebble accretion. In pebble accretion objects between a cm and a meter in diameter falling toward a massive body are slowed enough by gas drag for them to spiral toward it and be accreted. Growth via pebble accretion may be as much as 1000 times faster than by the accretion of planetesimals.[71]

Once the cores are of sufficient mass (5–10 M🜨), they begin to gather gas from the surrounding disk.[2] Initially it is a slow process, increasing the core masses up to 30 M🜨 in a few million years.[29][69] After that, the accretion rates increase dramatically and the remaining 90% of the mass is accumulated in approximately 10,000 years.[69] The accretion of gas stops when the supply from the disk is exhausted.[67] This happens gradually, due to the formation of a density gap in the protoplanetary disk and to disk dispersal.[34][72] In this model ice giants—Uranus and Neptune—are failed cores that began gas accretion too late, when almost all gas had already disappeared. The post-runaway-gas-accretion stage is characterized by migration of the newly formed giant planets and continued slow gas accretion.[72] Migration is caused by the interaction of the planet sitting in the gap with the remaining disk. It stops when the protoplanetary disk disappears or when the end of the disk is attained. The latter case corresponds to the so-called hot Jupiters, which are likely to have stopped their migration when they reached the inner hole in the protoplanetary disk.[72]

During the accretion of gas via streams, a giant planet can be surrounded by a circumplanetary disk. This circumplanetary disk also carries solids and can form satellites. The Galilean moons are thought to have formed in such a circumplanetary disk.[67]

In this artist's conception, a planet spins through a clearing (gap) in a nearby star's dusty, planet-forming disc.

Giant planets can significantly influence terrestrial planet formation. The presence of giants tends to increase eccentricities and inclinations (see Kozai mechanism) of planetesimals and embryos in the terrestrial planet region (inside 4 AU in the Solar System).[62][66] If giant planets form too early, they can slow or prevent inner planet accretion. If they form near the end of the oligarchic stage, as is thought to have happened in the Solar System, they will influence the merges of planetary embryos, making them more violent.[62] As a result, the number of terrestrial planets will decrease and they will be more massive.[73] In addition, the size of the system will shrink, because terrestrial planets will form closer to the central star. The influence of giant planets in the Solar System, particularly that of Jupiter, is thought to have been limited because they are relatively remote from the terrestrial planets.[73]

The region of a planetary system adjacent to the giant planets will be influenced in a different way.[66] In such a region, eccentricities of embryos may become so large that the embryos pass close to a giant planet, which may cause them to be ejected from the system.[d][62][66] If all embryos are removed, then no planets will form in this region.[66] An additional consequence is that a huge number of small planetesimals will remain, because giant planets are incapable of clearing them all out without the help of embryos. The total mass of remaining planetesimals will be small, because cumulative action of the embryos before their ejection and giant planets is still strong enough to remove 99% of the small bodies.[62] Such a region will eventually evolve into an asteroid belt, which is a full analog of the asteroid belt in the Solar System, located from 2 to 4 AU from the Sun.[62][66]

Exoplanets

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Thousands of exoplanets have been identified in the last twenty years, with, at the very least, billions more, within our observable universe, yet to be discovered.[74] The orbits of many of these planets and systems of planets differ significantly from the planets in the Solar System. The exoplanets discovered include hot-Jupiters, warm-Jupiters, super-Earths, and systems of tightly packed inner planets.

The hot-Jupiters and warm-Jupiters are thought to have migrated to their current orbits during or following their formation. A number of possible mechanisms for this migration have been proposed. Type I or Type II migration could smoothly decrease the semimajor axis of the planet's orbit resulting in a warm- or hot-Jupiter. Gravitational scattering by other planets onto eccentric orbits with a perihelion near the star followed by the circularization of its orbit due to tidal interactions with the star can leave a planet on a close orbit. If a massive companion planet or star on an inclined orbit was present an exchange of inclination for eccentricity via the Kozai mechanism raising eccentricities and lowering perihelion followed by circularization can also result in a close orbit. Many of the Jupiter-sized planets have eccentric orbits which may indicate that gravitational encounters occurred between the planets, although migration while in resonance can also excite eccentricities.[75] The in situ growth of hot Jupiters from closely orbiting super Earths has also been proposed. The cores in this hypothesis could have formed locally or at a greater distance and migrated close to the star.[76]

Super-Earths and other closely orbiting planets are thought to have either formed in situ or ex situ, that is, to have migrated inward from their initial locations.[77] The in situ formation of closely orbiting super-Earths would require a massive disk, the migration of planetary embryos followed by collisions and mergers, or the radial drift of small solids from farther out in the disk. The migration of the super-Earths, or the embryos that collided to form them, is likely to have been Type I due to their smaller mass. The resonant orbits of some of the exoplanet systems indicates that some migration occurred in these systems, while the spacing of the orbits in many of the other systems not in resonance indicates that an instability likely occurred in those systems after the dissipation of the gas disk. The absence of Super-Earths and closely orbiting planets in the Solar System may be due to the previous formation of Jupiter blocking their inward migration.[78]

The amount of gas a super-Earth that formed in situ acquires may depend on when the planetary embryos merged due to giant impacts relative to the dissipation of the gas disk. If the mergers happen after the gas disk dissipates terrestrial planets can form, if in a transition disk a super-Earth with a gas envelope containing a few percent of its mass may form. If the mergers happen too early runaway gas accretion may occur leading to the formation of a gas giant. The mergers begin when the dynamical friction due to the gas disk becomes insufficient to prevent collisions, a process that will begin earlier in a higher metallicity disk.[79] Alternatively gas accretion may be limited due to the envelopes not being in hydrostatic equilibrium, instead gas may flow through the envelope slowing its growth and delaying the onset of runaway gas accretion until the mass of the core reaches 15 Earth masses.[80]

Meaning of accretion

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Use of the term "accretion disk" for the protoplanetary disk leads to confusion over the planetary accretion process. The protoplanetary disk is sometimes referred to as an accretion disk, because while the young T Tauri-like protostar is still contracting, gaseous material may still be falling onto it, accreting on its surface from the disk's inner edge.[40] In an accretion disk, there is a net flux of mass from larger radii toward smaller radii.[23]

However, that meaning should not be confused with the process of accretion forming the planets. In this context, accretion refers to the process of cooled, solidified grains of dust and ice orbiting the protostar in the protoplanetary disk, colliding and sticking together and gradually growing, up to and including the high-energy collisions between sizable planetesimals.[20]

In addition, the giant planets probably had accretion disks of their own, in the first meaning of the word.[81] The clouds of captured hydrogen and helium gas contracted, spun up, flattened, and deposited gas onto the surface of each giant protoplanet, while solid bodies within that disk accreted into the giant planet's regular moons.[82]

See also

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Notes

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References

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Nebular hypothesis

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The nebular hypothesis is a scientific model explaining the origin of the Solar System as the result of gravitational collapse within a giant molecular cloud composed primarily of hydrogen and helium gas along with dust, which flattened into a rotating protoplanetary disk from which the Sun formed at the center and the planets accreted through the aggregation of particles.[1] This process, occurring approximately 4.6 billion years ago, accounts for the coplanar orbits of the planets, their counterclockwise rotation around the Sun when viewed from above the north pole, and the distinction between inner rocky planets and outer gas giants due to temperature gradients in the disk.[2] The hypothesis posits that conservation of angular momentum during the collapse caused the cloud to spin faster and flatten, with residual material beyond Neptune forming structures like the Kuiper Belt.[3] The idea was first proposed by the German philosopher and astronomer Immanuel Kant in his 1755 work Universal Natural History and Theory of the Heavens, where he described the Solar System emerging from a rotating primordial nebula that condensed under gravity.[4] Kant's model drew on Newtonian mechanics to suggest that solar systems could form similarly across the universe, including the Milky Way as a flattened disk of stars.[5] Independently, French mathematician and astronomer Pierre-Simon Laplace refined and popularized the concept in 1796 in his book Exposition du Système du Monde, proposing that the Sun initially formed as a hot gaseous mass that cooled and shed rings of material, each condensing into a planet.[6] Laplace's version emphasized the role of successive ejections from the contracting Sun, though it faced challenges in explaining the distribution of angular momentum, with about 99% of the system's mass in the Sun but 99% of its angular momentum in the planets.[2] Modern refinements to the nebular hypothesis, often termed the solar nebular disk model, incorporate advances in astrophysics and observations of star-forming regions, addressing early limitations by invoking turbulence, magnetic fields, and pebble-sized accretion to explain rapid planet formation within the disk's lifetime of a few million years.[1] Evidence supporting the model includes isotopic similarities between meteorites and the Sun, indicating a common origin, as well as direct imaging of protoplanetary disks around young stars like HL Tauri.[7] The hypothesis has successfully predicted features such as the existence of the Kuiper Belt decades before its discovery in the 1990s, reinforcing its explanatory power for both our Solar System and exoplanetary systems.[3]

Historical Development

Early Concepts

The origins of the nebular hypothesis trace back to the early 18th century, when Swedish philosopher and scientist Emanuel Swedenborg proposed in his 1734 work Principia rerum naturalium that the solar system formed from a cosmic vortex of elementary particles. In this model, vortical motion caused particles to aggregate into a crust surrounding a central solar mass, which then expanded due to centrifugal force, thinned, and burst, ejecting material that coalesced into spherical planets and satellites in spiral orbits that eventually stabilized.[8] Swedenborg's ideas anticipated later formulations by emphasizing a dynamic, whirling process of planetary birth from solar material, though they were framed within a non-Newtonian, qualitative cosmology.[9] Building on such concepts, Immanuel Kant elaborated the hypothesis in his 1755 treatise Allgemeine Naturgeschichte und Theorie des Himmels (Universal Natural History and Theory of the Heavens). Kant envisioned the solar system emerging from a vast, rotating primordial nebula of diffuse gas and dust particles, which, under the influence of mutual attraction, gradually contracted and cooled. As the nebula rotated faster to conserve angular momentum, it flattened into a disk-like structure, with denser regions condensing into the central Sun and surrounding planets that inherited the nebula's rotational direction and plane.[10] This mechanical explanation integrated Newtonian gravity with a naturalistic origin for the ordered solar system, positing that similar processes could form other stellar systems from interstellar matter.[11] Independently, French mathematician Pierre-Simon Laplace refined the idea in the first edition of his 1796 Exposition du système du monde, presenting a more mathematically grounded version without direct reference to Kant. Laplace described a hot, gaseous nebula slowly cooling and contracting under gravity, leading to accelerated rotation and equatorial bulging that flattened it into a protoplanetary disk. Successive rings detached from the disk's outer edges due to centrifugal forces, condensing into planets that orbited in the same direction and plane as the Sun's rotation, thus accounting for the observed coplanarity and co-rotation of planetary orbits.[12] Laplace's formulation emphasized the hypothesis's explanatory power for the solar system's architecture while assuming initial conditions aligned with empirical observations. Despite its appeal, the nebular hypothesis faced early criticisms, particularly the angular momentum paradox identified in the 19th century. Observers noted that the Sun, comprising over 99% of the solar system's mass, possesses only about 2% of its total angular momentum, while the planets hold the majority through their orbital motion; this distribution contradicted expectations from a collapsing nebula, where the central body should retain most rotational energy to conserve angular momentum.[13] Critics argued that the model failed to explain how the Sun's slow rotation could result from material predominantly derived from the rotating nebula, prompting calls for mechanisms like external torques or alternative formation scenarios.[14] In response to these issues, American geologist Thomas Chamberlin and astronomer Forest Moulton introduced the planetesimal hypothesis in 1905 as a variant that retained nebular elements but addressed angular momentum concerns. Their model proposed that a near-collision between the Sun and another star tidally disrupted solar material, ejecting it into a disk of small, solid planetesimals—icy and rocky fragments—that gravitationally accreted over time to form planets and moons. By attributing high angular momentum to the ejected, cooler outer material rather than the hot central Sun, the hypothesis mitigated the paradox while explaining the presence of comets and asteroids as remnants.[15] This elaboration shifted emphasis from gaseous condensation to discrete particle aggregation, influencing subsequent refinements into the 20th century.[16]

20th-Century Refinements

In the early 20th century, the nebular hypothesis faced significant challenges regarding the gravitational collapse of interstellar clouds, addressed through James Jeans' analysis of instability criteria in 1929, which demonstrated that clouds exceeding a critical mass would collapse under their own gravity, forming denser structures suitable for star and planet formation.[17] However, persistent issues with angular momentum conservation complicated the transition from a collapsing spherical cloud to a flattened disk, as excessive rotation could prevent full collapse or lead to unrealistic ejection of material.[18] A major refinement came in 1944 with Otto Schmidt's accretion disk model, which proposed that the proto-Sun captured diffuse material from the interstellar medium, gradually accreting it into a rotating disk where planetesimals could form through gradual aggregation rather than catastrophic events.[19] Building on this in the 1950s, Gerard Kuiper advanced disk models by estimating the solar nebula's mass at approximately 0.1 solar masses and deriving a density distribution that increased outward, explaining planetary spacing through gravitational instabilities in turbulent eddies that condensed into proto-planets at the Roche density limit.[20] Viktor Safronov's 1969 book, Evolution of the Protoplanetary Cloud and Formation of the Earth and Planets, provided a quantitative framework for planetesimal accretion, incorporating gravitational instabilities to model the growth of solid bodies from dust particles in the disk, emphasizing pairwise collisions enhanced by gravitational focusing.[21] Central to this was the Safronov number, defined as
Θ=GMRσ2, \Theta = \frac{GM}{R \sigma^2},
where MM is the planetesimal mass, RR its radius, and σ\sigma the velocity dispersion; this dimensionless parameter quantifies the enhancement of collision cross-sections due to gravitational attraction relative to random motions. During the 1960s and 1970s, integrations of nuclear astrophysics with meteorite analyses further supported these disk models, revealing extinct radionuclides like aluminum-26 that implied rapid heating and differentiation within 3-5 million years of solar system formation, while overall disk accretion timelines extended to 10-100 million years based on chondrite cooling sequences and core formation indicators.[22] These studies confirmed the protoplanetary disk's short-lived nature, aligning with the refined nebular hypothesis's predictions for efficient planet assembly.[22]

Core Principles of the Model

Nebula Collapse and Disk Formation

The formation of the solar system according to the nebular hypothesis begins within giant molecular clouds (GMCs), expansive regions of cold, dense interstellar gas and dust that serve as the birthplaces of stars and planetary systems. These GMCs typically have masses ranging from 10410^4 to 10610^6 solar masses and average number densities of approximately 10210^2 cm−3^{-3}, consisting primarily of molecular hydrogen with traces of heavier elements.[23][24] The collapse initiating the solar nebula occurs in dense subregions of these clouds, often triggered by external perturbations such as shock waves from nearby supernovae or spiral density waves in the galaxy, which compress the gas and create local overdensities.[25] This compression leads to the Jeans instability when the cloud's size exceeds the critical Jeans length, allowing gravitational forces to overcome internal pressure support and drive collapse. The Jeans length is defined as
λJ=πcs2Gρ, \lambda_J = \sqrt{\frac{\pi c_s^2}{G \rho}},
where csc_s is the isothermal sound speed, GG is the gravitational constant, and ρ\rho is the cloud density; perturbations on scales larger than λJ\lambda_J become gravitationally unstable, fragmenting the cloud and funneling material toward the center.[26] As the collapsing fragment contracts, conservation of angular momentum—arising from the initial slow rotation of the GMC core—causes the material to spin faster, flattening the infalling gas and dust into a rotationally supported protoplanetary disk with a typical radius of around 100 AU.[27] This disk forms rapidly during the early stages of collapse, with magnetic fields and outflows helping to regulate angular momentum transport and prevent excessive outward spreading.[27] Within the disk, a radial temperature gradient emerges due to viscous heating near the protosun and radiative cooling farther out, resulting in inner regions reaching temperatures of about 1000 K and outer regions dropping to around 10 K. This gradient establishes the snow line at approximately 2.7 AU, beyond which volatile ices can condense onto dust grains.[28] The disk maintains a dust-to-gas mass ratio of roughly 1:100, inherited from the interstellar medium, with the presence of metals (heavier elements) facilitating the initial growth of dust grains through coagulation and settling toward the midplane.[29]

Angular Momentum and Rotation

A central challenge in the nebular hypothesis, known as the angular momentum paradox, arises from the observed distribution in the Solar System, where the Sun accounts for approximately 2% of the total angular momentum despite comprising over 99% of the system's mass, with the remaining 98% residing primarily in the orbital angular momentum of the planets.[https://pages.uoregon.edu/jschombe/ast121/lectures/lec23.html] This discrepancy implies that mechanisms must have transferred most of the initial angular momentum from the central protostar outward during the nebula's collapse and disk formation.[https://arxiv.org/pdf/1709.07294.pdf] The paradox is resolved through processes that redistribute angular momentum, beginning with magnetic braking in the early protostellar phase, where magnetic fields couple the rotating protosun to the surrounding envelope, torquing material outward and slowing the central spin.[https://ui.adsabs.harvard.edu/abs/1980M%26P....22...31M/abstract] As the protoplanetary disk forms, turbulent viscosity dominates the transport, parameterized by the Shakura-Sunyaev α model, where the effective viscosity ν ≈ α c_s H (with c_s the sound speed and H the disk scale height) enables outward angular momentum flux, allowing inner material to accrete while outer regions expand.[https://ui.adsabs.harvard.edu/abs/1973A&A....24..337S/abstract] Typical values of α in protoplanetary disks range from 10^{-3} to 10^{-2}, consistent with observed disk evolution timescales of a few million years.[https://arxiv.org/abs/1305.3416] In a Keplerian protoplanetary disk, the specific angular momentum l of gas at radius r increases with distance as
l=GMr, l = \sqrt{G M r},
where G is the gravitational constant and M is the central stellar mass; this radial gradient drives the viscous spreading, with angular momentum transported outward to larger r, facilitating the concentration of mass near the star while preserving overall conservation.[https://iopscience.iop.org/article/10.3847/1538-4357/aa6249] The magneto-rotational instability (MRI) provides the underlying turbulence for this viscosity, as weak magnetic fields in the differentially rotating disk amplify perturbations, generating stresses that efficiently move angular momentum outward at rates matching α ≈ 0.01.[https://ui.adsabs.harvard.edu/abs/1991ApJ...376..214B/abstract] Observational support comes from T Tauri stars, analogs to the young Sun, which exhibit protoplanetary disks with masses typically 0.01–0.1 M_⊙ and rotation periods of 1–12 days, indicating rapid spin-up from inherited nebula rotation and ongoing angular momentum redistribution.[https://iopscience.iop.org/article/10.3847/0004-6256/152/6/198][https://www.sciencedirect.com/topics/earth-and-planetary-sciences/t-tauri-stars] These disks, observed via infrared and millimeter interferometry, show extended structures consistent with viscous evolution, where MRI-driven turbulence maintains the necessary transport efficiency.[https://arxiv.org/abs/1305.3416]

Achievements and Observational Evidence

Explanatory Successes

The nebular hypothesis provides a compelling explanation for the architectural regularities observed in the solar system, particularly the near-coplanarity of planetary orbits and their predominantly prograde rotation directions, which are direct consequences of angular momentum conservation during the collapse of the protoplanetary disk.[30] This disk inheritance ensures that planets form in a flattened, rotating structure, aligning their orbital planes with the disk's equatorial plane and imparting the same rotational sense to both orbital motion and planetary spin.[30] A key success of the model lies in accounting for the radial zoning of planetary compositions, where inner solar system bodies are predominantly rocky due to high temperatures that vaporized volatile ices, restricting accretion to refractory silicates and metals, while outer planets incorporated abundant ices and gases in the cooler disk regions beyond the snow line.[30] This temperature-dependent condensation sequence naturally delineates the terrestrial from the giant planets, with the latter growing massive enough to capture extensive nebular envelopes.[30] The asteroid belt between Mars and Jupiter is interpreted as a region of failed planet formation, where dynamical resonances with the massive planet Jupiter—such as the 3:1 and 2:1 mean-motion resonances—excited eccentricities and prevented efficient planetesimal accretion into a coherent planetary body.[31] These resonances depleted much of the original material, leaving a sparse population of remnants that trace the disk's compositional transition zone.[31] In the outer solar system, the Kuiper belt and Oort cloud represent surviving planetesimals from the primordial disk, with the former comprising a disk-like structure of icy bodies scattered by Neptune's migration and the latter forming a spherical reservoir of comets ejected to large distances by giant planet perturbations during the early dynamical instability.[32] These structures preserve the outer disk's volatile-rich composition and provide evidence of the nebular material's extent beyond the giant planets.[32] Supporting a common origin from a single nebula, meteorites exhibit remarkably similar isotopic ratios across diverse parent bodies, consistent with mixing and processing within the protoplanetary disk, while calcium-aluminum-rich inclusions (CAIs)—the oldest dated solids—yield a precise formation age of 4567.30 ± 0.16 million years, anchoring the timeline of nebular condensation. This isotopic homogeneity, punctuated by minor variations attributable to disk processes like evaporation and recondensation, reinforces the hypothesis's framework for solar system genesis.[30]

Modern Observations

Modern astronomical observations have provided compelling visual evidence for protoplanetary disks, key structures in the nebular hypothesis. The Hubble Space Telescope has imaged numerous protoplanetary disks, or proplyds, surrounding young stars in regions like the Orion Nebula, revealing flattened, rotating disks of gas and dust that align with expectations of early solar system formation. Complementing this, the Atacama Large Millimeter/submillimeter Array (ALMA) captured a groundbreaking image of the disk around the young star HL Tauri in 2014, displaying concentric rings and gaps indicative of planet-forming processes within a collapsing nebula.[33][34] The James Webb Space Telescope (JWST), operational since 2022, has further illuminated these processes through high-resolution infrared observations. In the PDS 70 system, JWST data from 2022 to 2025 have directly imaged two forming gas giant planets embedded in a protoplanetary disk, with gaps and circumplanetary disks suggesting ongoing accretion and potential disk instabilities that drive planet formation. Similarly, JWST's 2025 observations of the Flame Nebula, a star-forming region in Orion approximately 1,400 light-years away, reveal intricate details of nascent disks and young stellar objects, highlighting the dynamic collapse and fragmentation predicted by the nebular model.[35][36] Sample return missions have offered direct chemical evidence from solar system remnants. The Hayabusa2 mission returned samples from asteroid Ryugu in 2020, containing organic matter and minerals consistent with condensation processes in the early solar nebula, such as hydrated silicates formed under nebular conditions. The OSIRIS-REx mission followed in 2023 with samples from Bennu, which include microscopic grains preserving signatures of a solar nebula magnetic field, supporting the role of magnetized disk accretion in transporting angular momentum and materials during planet formation.[37][38] By November 2025, over 6,000 exoplanets have been confirmed, with architectures that mirror nebular disk formation, such as the compact, coplanar multi-planet system TRAPPIST-1, where seven Earth-sized worlds orbit in resonance, indicative of shared disk origins. Additionally, data from the Parker Solar Probe, launched in 2018 and continuing operations through 2025, have measured solar wind structures and magnetic switchbacks originating near the Sun.[39][40][41]

Challenges and Ongoing Issues

Planetesimal Formation Problems

One of the primary challenges in planetesimal formation within the protoplanetary disk is the meter-size barrier, where dust aggregates stall in growth at approximately 1 meter in size due to collisions resulting in bouncing or fragmentation rather than sticking. This barrier arises because relative velocities between particles reach about 1 m/s at these sizes, exceeding the threshold for efficient coagulation and instead leading to erosion or rebound.[42] Experimental and numerical studies confirm that without mechanisms to reduce these velocities, further growth beyond meter scales becomes inefficient. Compounding this issue is the rapid radial drift of intermediate-sized particles, which migrate inward toward the star before they can grow larger. Simulations demonstrate that particles around 1 meter experience peak inward velocities of $ v_r \approx \eta v_K $, where $ v_K $ is the Keplerian velocity and $ \eta \approx 0.005 $ parameterizes the sub-Keplerian gas rotation due to pressure support. This drift, driven by aerodynamic drag, limits the time available for growth to mere decades at 1 AU, depleting solids from the midplane before planetesimals can form. To address these barriers, the streaming instability has been proposed as a mechanism to concentrate centimeter- to meter-sized "pebbles" into dense clumps via differential drag between solids and gas, potentially enabling gravitational collapse into kilometer-sized planetesimals. However, this process requires overcoming the timescale constraints, as forming 1 km planetesimals through such clumping would take approximately 100,000 years, while typical protoplanetary disks dissipate within 1–10 million years. Turbulence in the disk, particularly driven by the magnetorotational instability (MRI), introduces further complications by diffusing particle concentrations and increasing relative velocities, which can hinder clumping and exacerbate fragmentation.[43] Yet, MRI turbulence may also aid formation in localized regions, such as near the snow line, by settling larger particles to the midplane and creating pressure maxima that trap drifting solids.[43] Overall, these dynamics underscore the delicate balance required for efficient planetesimal formation amid competing physical processes.

Planetary Migration and Timescales

In the nebular hypothesis, planetary migration refers to the radial drift of forming planets within the protoplanetary disk due to gravitational interactions with the gas, which can significantly alter orbital configurations. For low-mass planets (typically below a few Earth masses), Type I migration dominates, where the planet does not open a gap in the disk, and the migration arises from asymmetric torques caused by density waves excited in the disk. The timescale for Type I migration is given by
τmig∼(M⋆Mp)(hr)2Porb, \tau_{\rm mig} \sim \left( \frac{M_\star}{M_p} \right) \left( \frac{h}{r} \right)^2 P_{\rm orb},
where M⋆M_\star is the stellar mass, MpM_p the planet mass, h/rh/r the disk aspect ratio (typically ∼0.05\sim 0.05), and PorbP_{\rm orb} the orbital period; this yields rapid inward migration on timescales of 10410^4 to 10510^5 years for Earth-mass planets at 1 AU. For more massive planets (above ∼10M⊕\sim 10 M_\oplus), Type II migration occurs once a gap forms, slowing the drift to match the disk's viscous evolution rate, typically 10510^5 to 10610^6 years, preventing excessive inward spiraling. These processes assume prior formation of planetesimal cores as a prerequisite for planet growth. A key application in the Solar System is the Grand Tack hypothesis, which posits that Jupiter initially migrated inward to ∼1.5\sim 1.5 AU due to Type II torques before reversing direction outward to its current orbit, driven by resonant interactions with Saturn and disk properties. This inward-then-outward ("tacking") motion truncated the inner disk, reducing material available for Mars' growth (explaining its low mass) and dynamically exciting the asteroid belt by scattering planetesimals.[44] The hypothesis aligns with compositional and dynamical evidence, such as the depletion of inner disk solids. The aftermath of such migrations is linked to the Late Heavy Bombardment (LHB), a spike in impacts on the inner Solar System from approximately 4.1 to 3.8 billion years ago, triggered by giant planet instabilities in the Nice model, where delayed resonant scattering destabilized planetesimal populations. However, timescale mismatches persist: core accretion models suggest giant planets like Jupiter form in ∼10\sim 10 Myr, consistent with disk lifetimes, yet classical variants predict longer durations (up to 100 Myr) due to insufficient solid material beyond the snow line, challenging rapid gas envelope accretion.[45] Exoplanet observations, particularly hot Jupiters at ∼0.05\sim 0.05 AU, require even faster migration (within 1-5 Myr post-formation) to explain their proximity without in-situ formation.[46] Recent James Webb Space Telescope (JWST) observations of young protoplanetary disks in 2024-2025 have revealed nested disk winds that drive accretion and torque planets more efficiently than previously modeled, suggesting migration rates potentially faster than Type I/II predictions in turbulent environments. These insights from systems aged 1-10 Myr highlight ongoing refinements to nebular models, emphasizing wind-driven angular momentum transport.

Star Formation Processes

Protostellar Evolution

The protostellar evolution within the nebular hypothesis begins following the initial gravitational collapse of a molecular cloud core, marking the transition from a prestellar phase to the formation of a central star. This process unfolds over several distinct stages, driven by accretion and contraction, ultimately leading to a pre-main-sequence star capable of initiating hydrogen fusion. For low-mass stars like the Sun, these stages span from approximately 10^5 years to 10 million years, with key physical properties such as temperature, radius, and luminosity evolving predictably based on theoretical models and observations.[47] The first phase involves the isothermal collapse of the core, where the gas maintains a near-constant temperature of about 10 K due to efficient radiative cooling, allowing unchecked gravitational contraction. This stage lasts roughly 10^5 years, the characteristic free-fall timescale for a dense core of density ~10^{-18} g cm^{-3}, culminating in the formation of a protostar with an initial radius of around 100 AU. The collapse follows self-similar dynamics, as described in models where an expansion wave propagates outward from the center, enabling inside-out accretion onto the growing central object. During this phase, the central density reaches ~10^{-13} g cm^{-3}, forming the first hydrostatic core, though the object remains deeply embedded and invisible at optical wavelengths.[48][49][47] In the subsequent accretion phase, lasting up to ~0.5 million years, the protostar grows by accreting material from the surrounding envelope at a rate of approximately 10^{-6} M_\sun yr^{-1}, powered by gravitational potential energy release that contributes to the object's luminosity of around 100 L_\sun. Bipolar outflows, collimated jets of gas ejected along the rotation axis, emerge during this stage to regulate angular momentum and prevent excessive spin-up, with velocities reaching hundreds of km s^{-1} and extending several thousand AU. These outflows, often molecular in nature, are driven by magneto-centrifugal processes at the base of an accretion disk and help clear the envelope, transitioning the source from Class 0 (deeply embedded, envelope-dominated) to Class I (less embedded, disk-dominated). The Kelvin-Helmholtz contraction mechanism begins to play a role here, as gravitational energy release during slow contraction heats the core, supplementing accretion luminosity and establishing a thermal equilibrium.[50][47] As accretion wanes and the envelope dissipates after ~1-10 million years, the protostar enters the pre-main-sequence contraction phase, following the Hayashi track on the Hertzsprung-Russell diagram. This fully convective stage involves radial contraction at nearly constant effective temperature of ~4000 K, with the radius shrinking from several solar radii to about 3 R_\sun, and luminosity decreasing to ~1-10 L_\sun for a solar-mass object. The Hayashi track reflects the protostar's descent toward the main sequence as T Tauri stars, where surface activity like spots and winds is prominent, but core heating via Kelvin-Helmholtz contraction—releasing gravitational energy over the thermal timescale of ~10^7 years—prepares the interior for fusion without significant mass gain. This phase ends when the central temperature reaches ~10^7 K, marking the onset of hydrogen burning and the fully formed star.[51][47] Observational evidence for these embedded phases comes from infrared surveys, classifying sources as Class 0 (protostars with massive, cold envelopes) or Class I (more evolved with warmer disks) based on spectral energy distributions and bolometric temperatures below 70 K. Spitzer Space Telescope surveys, such as the c2d legacy program, identified hundreds of such objects in nearby star-forming regions like Taurus and Ophiuchus, revealing typical luminosities of 1-10 L_\sun and confirming short Class 0 lifetimes of ~0.15 million years. Recent JWST observations, including the JOYS program and MIRI spectroscopy of sources like IRAS 15398-3359, have resolved finer details of outflows and envelopes at mid-infrared wavelengths, validating the rapid evolution and accretion-driven heating predicted by models. As of 2025, additional JWST studies have advanced understanding of protostellar outflows and early planet formation, revealing jets with wiggly structures indicative of hidden binaries and evidence that Class 0/I disks may hide forming planets under dense envelopes.[52][53][54][55]

Protoplanetary Disk Dynamics

Protoplanetary disks exhibit a characteristic vertical structure determined by hydrostatic equilibrium, where the scale height $ H $ is given by $ H = \frac{c_s}{\Omega} $, with $ c_s $ representing the isothermal sound speed and $ \Omega = \sqrt{\frac{GM_}{r^3}} $ the Keplerian orbital frequency for a central star of mass $ M_ $ at radial distance $ r $. This structure results in a flared geometry, with the disk becoming relatively thicker at larger radii, influencing the temperature profile and dust settling. The pressure scale height typically ranges from a few astronomical units near the star to tens of AU in the outer regions, supporting the conditions for grain settling and radial drift.[56] The radial evolution of protoplanetary disks is primarily driven by viscous spreading, a process where internal turbulence transports angular momentum outward, causing the inner disk to accrete onto the central star while the outer disk expands. This dynamics follows the standard α\alpha-disk model, with kinematic viscosity parameterized as $ \nu = \alpha c_s H $, where α\alpha (typically 10−210^{-2} to 10−410^{-4}) quantifies the efficiency of turbulent stresses relative to thermal pressure. The characteristic viscous timescale is approximated as $ t_\text{visc} \approx \frac{r^2}{\nu} $, yielding disk lifetimes of 1–10 Myr for typical parameters, consistent with observed dispersal rates around young stars. Viscous evolution thus regulates the disk's mass accretion rate, typically 10−810^{-8} to 10−9M⊙10^{-9} M_\odot yr−1^{-1}, and shapes the surface density profile over time. In addition to viscous processes, photoevaporation plays a crucial role in disk dissipation, particularly in later stages. High-energy stellar radiation, including ultraviolet (UV) and X-ray photons, ionizes and heats the disk's upper layers, driving thermal winds that remove gas at rates up to 10−8M⊙10^{-8} M_\odot yr−1^{-1}. This mass loss can carve inner gaps and truncate the disk beyond ~10–20 AU, accelerating dispersal and limiting the planet-formation window. Models incorporating both EUV and X-ray photoevaporation predict rapid clearing once the viscous accretion rate drops below the wind mass-loss rate, explaining the observed scarcity of transitional disks. Recent studies as of 2025 have highlighted nested morphologies in disk winds, providing new constraints on accretion and planet migration.[57][58] Dust dynamics within the disk involve grain growth through inelastic collisions and sticking, enabling particles to reach millimeter to centimeter sizes within the first million years. This growth is inferred from the spectral energy distribution and resolved sub-millimeter emissions, where ALMA observations reveal compact dust distributions with opacities consistent with porous aggregates up to ~1 cm in radius. Such growth enhances dust-to-gas coupling and sets the stage for further concentration mechanisms, though fragmentation limits sizes in turbulent regions. Representative examples include disks around T Tauri stars, where mm-sized grains dominate the outer disk emission.[59] Recent James Webb Space Telescope (JWST) observations from 2024 have provided unprecedented mid-infrared imaging of protoplanetary disk structures, highlighting dynamic features such as spirals in systems like SAO 206462. These spirals, detected in filters tracing warm dust, suggest warping or twisting induced by embedded companions or misalignments, with pattern speeds indicating perturbers at ~100–300 AU. Such findings reveal non-axisymmetric dynamics, where warps propagate as bending waves, altering the disk's vertical alignment and potentially influencing migration pathways. Building on this, 2025 JWST observations have revealed longer-than-expected disk lifetimes around some young stars and detailed structures in edge-on and inclined disks, such as HH 30 and d216-0939, further elucidating dissipation mechanisms and planet-forming environments.[60][61][62][63] Overall, protoplanetary disks typically harbor masses of 0.01–0.1 $ M_* $ (1–10% of the stellar mass), dominated by gas with a dust fraction of ~1%, as measured from sub-millimeter continuum fluxes in nearby star-forming regions. As disks evolve viscously and photoevaporatively, their gas content dissipates, transitioning into gas-poor debris disks characterized by collisional cascades of km-sized planetesimals, observable as infrared excesses around main-sequence stars. This evolution underscores the finite timescale for planet formation, with disk masses declining by orders of magnitude over 5–10 Myr.[64]

Planet Formation Mechanisms

Terrestrial Planet Accretion

Terrestrial planet accretion occurs primarily in the inner regions of the protoplanetary disk, where temperatures exceed approximately 150-200 K, preventing the condensation of water ice and favoring the accumulation of refractory materials such as silicates and metals. This environment leads to the formation of dry, rocky bodies through hierarchical processes, beginning with small particles and culminating in the assembly of Earth-like planets. The process is divided into distinct stages, each characterized by increasing gravitational influence and collision rates, ultimately resulting in differentiated planets with metallic cores and silicate mantles.[65][66] The initial stage involves pebble accretion, where millimeter- to centimeter-sized particles in the disk are efficiently captured by growing dust aggregates, leading to the rapid formation of 1-10 km planetesimals within about 0.1 million years. These pebbles, aerodynamically coupled to the gas, drift inward and are accreted onto proto-planetesimals via mechanisms like streaming instability, enhancing growth rates by orders of magnitude compared to pure dust coagulation. This phase transitions smoothly into planetesimal formation, setting the stage for subsequent gravitational instabilities, though challenges in initial dust clumping remain a topic of ongoing research.[67][66] In the second stage, runaway growth dominates, with the largest planetesimals rapidly accreting surrounding material to form Moon- to Mars-sized planetary embryos over approximately 1 million years. Gravitational cross-sections of these bodies expand due to their enhanced Hill spheres, allowing them to capture planetesimals at rates proportional to their mass, creating a bimodal size distribution where embryos outpace smaller remnants. This acceleration, driven by dynamical excitation and reduced relative velocities, occurs preferentially in the inner disk's denser regions.[68][69] The third stage features giant impacts and mergers among these embryos, consolidating them into full-sized terrestrial planets over 10-100 million years. During this oligarchic phase, embryos are spaced at intervals of about 10 Hill radii, where the Hill radius $ R_H $ is defined as $ R_H = a \left( \frac{M_p}{3 M_\star} \right)^{1/3} $, with $ a $ as the semimajor axis, $ M_p $ the embryo mass, and $ M_\star $ the stellar mass; this spacing maintains relative stability while permitting occasional high-velocity collisions. A prominent example is the Moon-forming giant impact on proto-Earth approximately 4.5 billion years ago, involving a Mars-sized body and reshaping the planet's composition and rotation.[70][71] High temperatures in the inner disk, often exceeding 1000 K near 1 AU, inhibit volatile ices and promote the condensation of metal and silicate grains, facilitating early differentiation as molten embryos segregate iron cores from silicate mantles during accretion. This thermal structure ensures terrestrial planets are iron-rich and volatile-poor compared to outer bodies.[72] Radiometric evidence from hafnium-tungsten (Hf-W) dating of meteorites and lunar samples indicates that core formation in terrestrial planets, including Earth, completed within about 30 million years, aligning with the giant impact phase and providing a chronological anchor for the accretion timeline.

Giant Planet Formation

The formation of giant planets like Jupiter and Saturn in the solar system proceeds primarily through two competing mechanisms within the protoplanetary disk: core accretion and disk instability. In the core accretion model, a solid core composed of ice and rock accumulates mass over several million years before rapidly accreting a massive hydrogen-helium envelope. Numerical simulations demonstrate that a core of approximately 10-15 Earth masses (M⊕_\oplus) forms in 3-10 million years (Myr) under typical disk conditions near 5 AU, after which the envelope undergoes runaway collapse as the core's gravity binds gas effectively.[73] This process requires the core to reach a critical mass of about 10 M⊕_\oplus, at which point the planet's Hill sphere expands sufficiently to gravitationally capture and retain ambient hydrogen and helium gas from the disk.[74] The efficiency of core growth is strongly influenced by the snow line, located at approximately 2.7 AU in the minimum-mass solar nebula, beyond which volatile ices such as water (H2_2O) and ammonia (NH3_3) condense onto dust grains, increasing the solid surface density by a factor of 2-4 and enabling faster accretion rates. Gas capture onto the growing core is governed by the Bondi accretion radius, defined as
RB=2GMcs2, R_B = \frac{2 G M}{c_s^2},
where GG is the gravitational constant, MM is the core mass, and csc_s is the sound speed in the disk gas; this radius delineates the region where gravitational infall dominates thermal motion, facilitating envelope buildup.[75] An alternative pathway is disk instability, in which gravitational fragmentation occurs in the outer regions of a massive protoplanetary disk with total mass exceeding 0.1 solar masses (M\sun_\sun), leading to the direct formation of gas clumps that contract into giant planets on timescales of about 1000 years.[76] This rapid process favors formation at large orbital distances (>10 AU) where cooling times are shorter, producing planets with modest solid cores embedded in extensive gaseous envelopes. The ice giants Uranus and Neptune likely represent outcomes of incomplete core accretion, where cores failed to reach the critical mass for full runaway gas capture, or alternatively, as scattered remnants of larger giants perturbed outward during early disk evolution.[77]

Exoplanet System Insights

The discovery of hot Jupiters, such as 51 Pegasi b in 1995, challenged the nebular hypothesis by revealing gas giants in orbits far closer to their stars than expected, necessitating models of rapid inward migration during the protoplanetary disk phase. This planet, with an orbital period of just 4.2 days, is interpreted as having formed farther out and migrated inward via Type II disk migration, where the planet opens a gap in the disk and exchanges angular momentum with the gas, supporting the universality of disk-driven dynamics in the nebular model.[78] Such migrations align with theoretical predictions from the nebular framework, extended beyond the solar system to explain the prevalence of close-in giants in about 1% of Sun-like star systems.[79] Super-Earths and mini-Neptunes, which dominate exoplanet populations, provide further tests of the nebular model, comprising approximately 50% of systems detected by the Kepler mission through their frequent occurrence at intermediate orbital distances.[80] These planets are thought to form via inward pebble accretion, where centimeter-sized particles drift toward pressure maxima and accrete onto growing cores, followed by atmospheric photoevaporation that strips hydrogen envelopes to leave rocky or volatile-rich remnants.[81] This process enhances core growth rates, with the pebble accretion efficiency given by
M˙peb∼ρdust vdrift Σ, \dot{M}_{\rm peb} \sim \rho_{\rm dust} \, v_{\rm drift} \, \Sigma,
where ρdust\rho_{\rm dust} is the dust density, vdriftv_{\rm drift} the radial drift speed, and Σ\Sigma the surface density, allowing cores of 5–10 Earth masses to assemble within a few million years.[82] Unlike solar system giants, these compact worlds highlight variations in disk conditions that favor efficient solid accretion over gas runaway. Multi-planet systems exhibiting mean-motion resonances, such as the TRAPPIST-1 system with its seven Earth-sized planets in a chain of 8:5, 5:3, 3:2, and 4:3 ratios, suggest in-situ formation with minimal large-scale migration, as the compact architecture preserves resonant configurations from the disk phase.[83] In this scenario, planets accrete from a narrow annular region near the water ice line, capturing pebbles and planetesimals locally before disk dissipation locks them into resonances, contrasting with migratory hot Jupiters and underscoring the nebular model's flexibility for low-mass stars.[84] Recent observations from the James Webb Space Telescope (JWST) in 2025 have provided spectroscopic insights into the HR 8799 system, detecting carbon dioxide in the atmospheres of its young giant planets and revealing compositions consistent with disk instability formation, where gravitational collapse in the outer disk rapidly assembles massive bodies without requiring core accretion.[85] These findings, combined with the catalog of over 6,000 confirmed exoplanets as of November 2025, validate diverse disk architectures predicted by the nebular hypothesis, from core accretion in inner regions to instability in outer zones.[39] However, high-eccentricity exoplanets, such as those with e>0.5e > 0.5, pose challenges, often requiring post-formation planet-planet scattering to excite orbits after disk dispersal, as instabilities among multiple giants can eject or perturb survivors into eccentric paths.[86] This dynamical phase refines the nebular model by incorporating late-stage interactions that diversify system outcomes.

References

  1. 1.2. How did our Solar System form? - NASA Astrobiology
  2. Origin of the Solar System - University of Oregon
  3. [PDF] Nebular Theory: Summary
  4. immanuel_kant.html - UNLV Physics
  5. ASTR 5630/40, Whittle Images Window - Mark Whittle
  6. Pierre Simon de Laplace (1749–1827) | High Altitude Observatory
  7. The Solar Nebula Formation of the Earth Origin of the Atmosphere ...
  8. Swedenborg and the Plurality of Worlds: Astrotheology in the ...
  9. Emanuel Swedenborg-An 18th century cosmologist - ResearchGate
  10. Universal natural history and theory of the heavens - Internet Archive
  11. Matter and cosmogenesis in Kant's Theory of the Heavens - arXiv
  12. Pierre-Simon Laplace - Linda Hall Library
  13. Theories of the origin of the solar system 1956- 1985 | Rev. Mod. Phys.
  14. Meteorites and the origin of the solar system - GeoScienceWorld
  15. The origin of the planetesimal theory. - NASA ADS
  16. The origin of the planetesimal theory | Discover Life
  17. Jeans' formula for gravitational instability - Astrophysics Data System
  18. Jeans\' gravitational instability and nonextensive kinetic theory
  19. The origin and evolution of the solar system - Oxford Academic
  20. On the Origin of the Solar System - PNAS
  21. Evolution of the protoplanetary cloud and formation of the earth and ...
  22. [PDF] METEORITES AND THE EARLY SOLAR SYSTEM Edward Anders
  23. [PDF] 1.1 Gravitational Collapse: Jeans Criterion - Rice University
  24. [PDF] Lecture 2: Molecular Clouds: Galactic Context and Observational ...
  25. What triggers star formation in galaxies? - Bruce G. Elmegreen
  26. The Jeans Collapse Criterion
  27. Formation and evolution of a protoplanetary disk
  28. DISK TEMPERATURE VARIATIONS AND EFFECTS ON THE SNOW ...
  29. The Dust and Gas in Protoplanetary Disks | Center for Astrophysics
  30. [1501.03101] The formation of the solar system - arXiv
  31. [PDF] The Dynamical Evolution of the Asteroid Belt - SwRI Boulder Office
  32. [PDF] The evolution of comets in the Oort cloud and Kuiper belt
  33. Hubble Confirms Abundance of Protoplanetary Disks around ...
  34. Revolutionary ALMA Image Reveals Planetary Genesis - Eso.org
  35. Webb telescope provides unprecedented view into PDS 70 system
  36. NASA's Webb Peers Deeper into Mysterious Flame Nebula
  37. JAXA | The dark Macromolecular organic matter of asteroid Ryugu
  38. [PDF] POTENTIAL EVIDENCE OF A SOLAR NEBULA MAGNETIC FIELD ...
  39. NASA Exoplanet Archive
  40. Largest Batch of Earth-size Habitable Zone Planets Found Orbiting ...
  41. Parker Solar Probe flies into the fast solar wind and finds its source
  42. Planetesimal formation by sweep-up: how the bouncing barrier can ...
  43. Planetesimal formation near the snow line in MRI-driven turbulent ...
  44. A low mass for Mars from Jupiter's early gas-driven migration - Nature
  45. On the Formation Timescale and Core Masses of Gas Giant Planets
  46. [1804.10578] Planetary Migration in Protoplanetary Disks - arXiv
  47. [PDF] The Evolution of Protostars - arXiv
  48. https://ui.adsabs.harvard.edu/abs/1977ApJ...214..488S/abstract
  49. [PDF] N91-22962
  50. https://ui.adsabs.harvard.edu/abs/1996ARA&A..34..111B/abstract
  51. [PDF] Protostars & pre-main-sequence evolution
  52. CORINOS. I. JWST/MIRI Spectroscopy and Imaging of a Class 0 ...
  53. JWST Observations of Young protoStars (JOYS)
  54. [PDF] Theoretical Models of the Structure of Protoplanetary Disks Les ...
  55. https://ui.adsabs.harvard.edu/abs/2014prpl.conf..475A/abstract
  56. [1402.1354] Dust Evolution in Protoplanetary Disks - arXiv
  57. [2401.02834] JWST/NIRCam Imaging of Young Stellar Objects. II ...
  58. THE MASS DEPENDENCE BETWEEN PROTOPLANETARY DISKS ...
  59. The Outer Planets: How Planets Form
  60. Forming Planets via Pebble Accretion - Annual Reviews
  61. A pebble accretion model for the formation of the terrestrial planets ...
  62. On Runaway Growth of Planetesimals - ScienceDirect.com
  63. The Growth of Planetary Embryos: Orderly, Runaway, or Oligarchic?
  64. Oligarchic Growth of Protoplanets - ScienceDirect.com
  65. The Energy Budgets of Giant Impacts - Carter - AGU Journals - Wiley
  66. [PDF] Chemical Fractionation in the Solar Nebula
  67. Formation of the Giant Planets by Concurrent Accretion of Solids ...
  68. MINIMUM CORE MASSES FOR GIANT PLANET FORMATION WITH ...
  69. On Spherically Symmetrical Accretion - Oxford Academic
  70. Giant Planet Formation by Gravitational Instability
  71. THE FORMATION OF URANUS AND NEPTUNE - IOP Science
  72. Orbital migration of the planetary companion of 51 Pegasi to its ...
  73. Giant Planet Formation and Migration | Space Science Reviews
  74. Formation of Super-Earths and Mini-Neptunes from Rings of ...
  75. Most super-Earths formed by dry pebble accretion are less massive ...
  76. [PDF] Rapid growth of gas-giant cores by pebble accretion
  77. Formation of TRAPPIST-1 and other compact systems
  78. On the Local Formation of the TRAPPIST-1 Exoplanets - IOPscience
  79. NASA's Webb Images Young, Giant Exoplanets, Detects Carbon ...
  80. Planet–planet scattering as the source of the highest eccentricity ...
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