Giant-impact hypothesis

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https://en.wikipedia.org/wiki/Giant-impact_hypothesis 

Artist's depiction of a collision between two planetary bodies. Such an impact between Earth and a Mars-sized object likely formed the Moon.

The giant-impact hypothesis, sometimes called the Big Splash, or the Theia Impact, suggests that the Moon formed from the ejecta of a collision between the proto-Earth and a Mars-sized planetesimal, approximately 4.5 billion years ago, in the Hadean eon (about 20 to 100 million years after the Solar System coalesced). The colliding body is sometimes called Theia, from the name of the mythical Greek Titan who was the mother of Selene, the goddess of the Moon. Analysis of lunar rocks, published in a 2016 report, suggests that the impact may have been a direct hit, causing a thorough mixing of both parent bodies.

The giant-impact hypothesis is currently the favored scientific hypothesis for the formation of the Moon. Supporting evidence includes:

• Earth's spin and the Moon's orbit have similar orientations.
• The Earth-Moon system contains an anomalously high angular momentum. Meaning, the momentum contained in the Earth's rotation, the Moon's rotation, and the Moon revolving around the earth is significantly higher than the other terrestrial planets. A giant impact may have supplied this excess momentum.
• Moon samples indicate that the Moon was once molten down to a substantial, but unknown, depth. This may have required more energy than predicted to be available from the accretion of a body of the Moon's size. An extremely energetic process, such as a giant impact, could provide this energy.
• The Moon has a relatively small iron core. This gives the Moon a lower density than the earth. Computer models of a giant impact of a Mars-sized body with the Earth indicate the impactor's core would likely penetrate the Earth and fuse with its own core. This would leave the Moon with less metallic iron than other planetary bodies.
• The Moon is depleted in volatile elements compared to the earth. Vaporizing at comparably-lower temperatures, they could be lost in a high-energy event, with the Moon's smaller gravity unable to recapture them while the earth did.
• There is evidence in other star systems of similar collisions, resulting in debris disc.
• Giant collisi are consistent with the leading of the formation of the Solar System.
• The stable-isotope ratios of lunar and terrestrial rock are identical, implying a common origin. 

However, there remain several questions concerning the best current models of the giant-impact hypothesis. The energy of such a giant impact is predicted to have heated Earth to produce a global magma ocean, and evidence of the resultant planetary differentiation of the heavier material sinking into Earth's mantle has been documented. However, there is no self-consistent model that starts with the giant-impact event and follows the evolution of the debris into a single moon. Other remaining questions include when the Moon lost its share of volatile elements and why Venus – which experienced giant impacts during its formation – does not host a similar moon.

History

In 1898, George Darwin made the suggestion that the Earth and Moon were once a single body. Darwin's hypothesis was that a molten Moon had been spun from the Earth because of centrifugal forces, and this became the dominant academic explanation. Using Newtonian mechanics, he calculated that the Moon had orbited much more closely in the past and was drifting away from the Earth. This drifting was later confirmed by American and Soviet experiments, using laser ranging targets placed on the Moon.

Nonetheless, Darwin's calculations could not resolve the mechanics required to trace the Moon backward to the surface of the Earth. In 1946, Reginald Aldworth Daly of Harvard University challenged Darwin's explanation, adjusting it to postulate that the creation of the Moon was caused by an impact rather than centrifugal forces. Little attention was paid to Professor Daly's challenge until a conference on satellites in 1974, during which the idea was reintroduced and later published and discussed in Icarus in 1975 by Drs. William K. Hartmann and Donald R. Davis. Their models suggested that, at the end of the planet formation period, several satellite-sized bodies had formed that could collide with the planets or be captured. They proposed that one of these objects may have collided with the Earth, ejecting refractory, volatile-poor dust that could coalesce to form the Moon. This collision could potentially explain the unique geological and geochemical properties of the Moon.

A similar approach was taken by Canadian astronomer Alastair G. W. Cameron and American astronomer William R. Ward, who suggested that the Moon was formed by the tangential impact upon Earth of a body the size of Mars. It is hypothesised that most of the outer silicates of the colliding body would be vaporised, whereas a metallic core would not. Hence, most of the collisional material sent into orbit would consist of silicates, leaving the coalescing Moon deficient in iron. The more volatile materials that were emitted during the collision probably would escape the Solar System, whereas silicates would tend to coalesce.

Theia

The name of the hypothesised protoplanet is derived from the mythical Greek titan Theia /ˈθiːə/, who gave birth to the Moon goddess Selene. This designation was proposed initially by the English geochemist Alex N. Halliday in 2000 and has become accepted in the scientific community. According to modern theories of planet formation, Theia was part of a population of Mars-sized bodies that existed in the Solar System 4.5 billion years ago. One of the attractive features of the giant-impact hypothesis is that the formation of the Moon and Earth align; during the course of its formation, the Earth is thought to have experienced dozens of collisions with planet-sized bodies. The Moon-forming collision would have been only one such "giant impact" but certainly the last significant impactor event. The Late Heavy Bombardment by much smaller asteroids occurred later – approximately 3.9 billion years ago.

Basic model

Simplistic representation of the giant-impact hypothesis.

Astronomers think the collision between Earth and Theia happened at about 4.4 to 4.45 bya; about 0.1 billion years after the Solar System began to form. In astronomical terms, the impact would have been of moderate velocity. Theia is thought to have struck the Earth at an oblique angle when the Earth was nearly fully formed. Computer simulations of this "late-impact" scenario suggest an initial impactor velocity at infinity below 4 km/s, increasing as it fell to over 9.3 km/s at impact, and an impact angle of about 45°. However, oxygen isotope abundance in lunar rock suggests "vigorous mixing" of Theia and Earth, indicating a steep impact angle. Theia's iron core would have sunk into the young Earth's core, and most of Theia's mantle accreted onto the Earth's mantle. However, a significant portion of the mantle material from both Theia and the Earth would have been ejected into orbit around the Earth (if ejected with velocities between orbital velocity and escape velocity) or into individual orbits around the Sun (if ejected at higher velocities). Modelling has hypothesised that material in orbit around the Earth may have accreted to form the Moon in three consecutive phases; accreting first from the bodies initially present outside the Earth's Roche limit, which acted to confine the inner disk material within the Roche limit. The inner disk slowly and viscously spread back out to the Earth's Roche limit, pushing along outer bodies via resonant interactions. After several tens of years, the disk spread beyond the Roche limit, and started producing new objects that continued the growth of the Moon, until the inner disk was depleted in mass after several hundreds of years. Material in stable Kepler orbits was thus likely to hit the earth-moon system sometime later (because the Earth-Moon system's Kepler orbit around the sun also remains stable). Estimates based on computer simulations of such an event suggest that some twenty percent of the original mass of Theia would have ended up as an orbiting ring of debris around the Earth, and about half of this matter coalesced into the Moon. The Earth would have gained significant amounts of angular momentum and mass from such a collision. Regardless of the speed and tilt of the Earth's rotation before the impact, it would have experienced a day some five hours long after the impact, and the Earth's equator and the Moon's orbit would have become coplanar.

Not all of the ring material need have been swept up right away: the thickened crust of the Moon's far side suggests the possibility that a second moon about 1,000  km in diameter formed in a Lagrange point of the Moon. The smaller moon may have remained in orbit for tens of millions of years. As the two moons migrated outward from the Earth, solar tidal effects would have made the Lagrange orbit unstable, resulting in a slow-velocity collision that "pancaked" the smaller moon onto what is now the far side of the Moon, adding material to its crust. Lunar magma cannot pierce through the thick crust of the far side, causing fewer lunar maria, while the near side has a thin crust displaying the large maria visible from Earth.

Composition

In 2001, a team at the Carnegie Institution of Washington reported that the rocks from the Apollo program carried an isotopic signature that was identical with rocks from Earth, and were different from almost all other bodies in the Solar System.

In 2014, a team in Germany reported that the Apollo samples had a slightly different isotopic signature from Earth rocks. The difference was slight, but statistically significant. One possible explanation is that Theia formed near the Earth.

This empirical data showing close similarity of composition can only be explained by the standard giant-impact hypothesis as an extremely unlikely coincidence, where the two bodies prior to collision somehow had a similar composition. However, in science, a very low probability of a situation points toward an error in theory, so effort has been focused on modifying the theory in order to better explain this fact that the Earth and Moon are composed of nearly the same type of rock.

Equilibration hypothesis

In 2007, researchers from the California Institute of Technology showed that the likelihood of Theia having an identical isotopic signature as the Earth was very small (less than 1 percent). They proposed that in the aftermath of the giant impact, while the Earth and the proto-lunar disc were molten and vaporised, the two reservoirs were connected by a common silicate vapor atmosphere and that the Earth–Moon system became homogenised by convective stirring while the system existed in the form of a continuous fluid. Such an "equilibration" between the post-impact Earth and the proto-lunar disc is the only proposed scenario that explains the isotopic similarities of the Apollo rocks with rocks from the Earth's interior. For this scenario to be viable, however, the proto-lunar disc would have to endure for about 100 years. Work is ongoing to determine whether or not this is possible.

Direct collision hypothesis

According to research (2012) to explain similar compositions of Earth and the Moon based on simulations at the University of Bern by physicist Andreas Reufer and his colleagues, Theia collided directly with Earth instead of barely swiping it. The collision speed may have been higher than originally assumed, and this higher velocity may have totally destroyed Theia. According to this modification, the composition of Theia is not so restricted, making a composition of up to 50% water ice possible.

Synestia hypothesis

One effort (2018) to homogenise the products of the collision was to energise the primary body by way of a greater pre-collision rotational speed. This way, more material from the primary body would be spun off to form the moon. Further computer modelling determined that the observed result could be obtained by having the pre-Earth body spinning very rapidly, so much so that it formed a new celestial object which was given the name 'synestia'. This is an unstable state that could have been generated by yet another collision to get the rotation spinning fast enough. Further modelling of this transient structure has shown that the primary body spinning as a doughnut-shaped object (the synestia) existed for about a century (a very short time) before it cooled down and gave birth to the Earth and the Moon.

Terrestrial magma ocean hypothesis

Another model (2019) to explain the similarity of the Earth and Moon's composition posits that shortly after the Earth formed, it was covered by a sea of hot magma, while the impacting object was likely made of solid material. Modelling suggests that this would lead to the impact heating the magma much more than solids from the impacting object, leading to more material being ejected from the proto-Earth, so that about 80% of the Moon-forming debris originated from the proto-Earth. Many prior models had suggested 80% of the Moon coming from the impactor.

Evidence

Indirect evidence for the giant impact scenario comes from rocks collected during the Apollo Moon landings, which show oxygen isotope ratios nearly identical to those of Earth. The highly anorthositic composition of the lunar crust, as well as the existence of KREEP-rich samples, suggest that a large portion of the Moon once was molten; and a giant impact scenario could easily have supplied the energy needed to form such a magma ocean. Several lines of evidence show that if the Moon has an iron-rich core, it must be a small one. In particular, the mean density, moment of inertia, rotational signature, and magnetic induction response of the Moon all suggest that the radius of its core is less than about 25% the radius of the Moon, in contrast to about 50% for most of the other terrestrial bodies. Appropriate impact conditions satisfying the angular momentum constraints of the Earth-Moon system yield a Moon formed mostly from the mantles of the Earth and the impactor, while the core of the impactor accretes to the Earth. It is noteworthy that the Earth has the highest density of all the planets in the Solar System; the absorption of the core of the impactor body explains this observation, given the proposed properties of the early Earth and Theia.

Comparison of the zinc isotopic composition of lunar samples with that of Earth and Mars rocks provides further evidence for the impact hypothesis. Zinc is strongly fractionated when volatilised in planetary rocks, but not during normal igneous processes, so zinc abundance and isotopic composition can distinguish the two geological processes. Moon rocks contain more heavy isotopes of zinc, and overall less zinc, than corresponding igneous Earth or Mars rocks, which is consistent with zinc being depleted from the Moon through evaporation, as expected for the giant impact origin.

Collisions between ejecta escaping Earth's gravity and asteroids would have left impact heating signatures in stony meteorites; analysis based on assuming the existence of this effect has been used to date the impact event to 4.47 billion years ago, in agreement with the date obtained by other means.

Warm silica-rich dust and abundant SiO gas, products of high velocity (> 10  km/s) impacts between rocky bodies, have been detected by the Spitzer Space Telescope around the nearby (29 pc distant) young (~12 My old) star HD172555 in the Beta Pictoris moving group. A belt of warm dust in a zone between 0.25AU and 2AU from the young star HD 23514 in the Pleiades cluster appears similar to the predicted results of Theia's collision with the embryonic Earth, and has been interpreted as the result of planet-sized objects colliding with each other. A similar belt of warm dust was detected around the star BD+20°307 (HIP 8920, SAO 75016).

Difficulties

This lunar origin hypothesis has some difficulties that have yet to be resolved. For example, the giant-impact hypothesis implies that a surface magma ocean would have formed following the impact. Yet there is no evidence that the Earth ever had such a magma ocean and it is likely there exists material that has never been processed in a magma ocean.

Composition

A number of compositional inconsistencies need to be addressed.

• The ratios of the Moon's volatile elements are not explained by the giant-impact hypothesis. If the giant-impact hypothesis is correct, these ratios must be due to some other cause.
• The presence of volatiles such as water trapped in lunar basalts and carbon emissions from the lunar surface is more difficult to explain if the Moon was caused by a high-temperature impact.
• The iron oxide (FeO) content (13%) of the Moon, intermediate between that of Mars (18%) and the terrestrial mantle (8%), rules out most of the source of the proto-lunar material from the Earth's mantle.
• If the bulk of the proto-lunar material had come from an impactor, the Moon should be enriched in siderophilic elements, when, in fact, it is deficient in them.
• The Moon's oxygen isotopic ratios are essentially identical to those of Earth. Oxygen isotopic ratios, which may be measured very precisely, yield a unique and distinct signature for each solar system body. If a separate proto-planet Theia had existed, it probably would have had a different oxygen isotopic signature than Earth, as would the ejected mixed material.
• The Moon's titanium isotope ratio (⁵⁰Ti/⁴⁷Ti) appears so close to the Earth's (within 4 ppm), that little if any of the colliding body's mass could likely have been part of the Moon.

Lack of a Venusian moon

If the Moon was formed by such an impact, it is possible that other inner planets also may have been subjected to comparable impacts. A moon that formed around Venus by this process would have been unlikely to escape. If such a moon-forming event had occurred there, a possible explanation of why the planet does not have such a moon might be that a second collision occurred that countered the angular momentum from the first impact. Another possibility is that the strong tidal forces from the Sun would tend to destabilise the orbits of moons around close-in planets. For this reason, if Venus's slow rotation rate began early in its history, any satellites larger than a few kilometers in diameter would likely have spiraled inwards and collided with Venus.

Simulations of the chaotic period of terrestrial planet formation suggest that impacts like those hypothesised to have formed the Moon were common. For typical terrestrial planets with a mass of 0.5 to 1 Earth masses, such an impact typically results in a single moon containing 4% of the host planet's mass. The inclination of the resulting moon's orbit is random, but this tilt affects the subsequent dynamic evolution of the system. For example, some orbits may cause the moon to spiral back into the planet. Likewise, the proximity of the planet to the star will also affect the orbital evolution. The net effect is that it is more likely for impact-generated moons to survive when they orbit more distant terrestrial planets and are aligned with the planetary orbit.

Possible origin of Theia

One suggested pathway for the Big Splash as viewed from the direction of the south pole (not to scale).

In 2004, Princeton University mathematician Edward Belbruno and astrophysicist J. Richard Gott III proposed that Theia coalesced at the L₄ or L₅ Lagrangian point relative to Earth (in about the same orbit and about 60° ahead or behind), similar to a trojan asteroid. Two-dimensional computer models suggest that the stability of Theia's proposed trojan orbit would have been affected when its growing mass exceeded a threshold of approximately 10% of the Earth's mass (the mass of Mars). In this scenario, gravitational perturbations by planetesimals caused Theia to depart from its stable Lagrangian location, and subsequent interactions with proto-Earth led to a collision between the two bodies.

In 2008, evidence was presented that suggests that the collision may have occurred later than the accepted value of 4.53 Gya, at approximately 4.48 Gya. A 2014 comparison of computer simulations with elemental abundance measurements in the Earth's mantle indicated that the collision occurred approximately 95 My after the formation of the Solar System.

It has been suggested that other significant objects may have been created by the impact, which could have remained in orbit between the Earth and Moon, stuck in Lagrangian points. Such objects may have stayed within the Earth–Moon system for as long as 100 million years, until the gravitational tugs of other planets destabilised the system enough to free the objects. A study published in 2011 suggested that a subsequent collision between the Moon and one of these smaller bodies caused the notable differences in physical characteristics between the two hemispheres of the Moon. This collision, simulations have supported, would have been at a low enough velocity so as not to form a crater; instead, the material from the smaller body would have spread out across the Moon (in what would become its far side), adding a thick layer of highlands crust. The resulting mass irregularities would subsequently produce a gravity gradient that resulted in tidal locking of the Moon so that today, only the near side remains visible from Earth. However, mapping by the GRAIL mission has ruled out this scenario.

In 2019, a team at the University of Münster reported that the molybdenum isotopic composition of Earth's core originates from the outer Solar System, likely bringing water to Earth. One possible explanation is that Theia originated in the outer Solar System.

Alternative hypotheses

Other mechanisms that have been suggested at various times for the Moon's origin are that the Moon was spun off from the Earth's molten surface by centrifugal force; that it was formed elsewhere and was subsequently captured by the Earth's gravitational field; or that the Earth and the Moon formed at the same time and place from the same accretion disk. None of these hypotheses can account for the high angular momentum of the Earth–Moon system.

Another hypothesis attributes the formation of the Moon to the impact of a large asteroid with the Earth much later than previously thought, creating the satellite primarily from debris from Earth. In this hypothesis, the formation of the Moon occurs 60–140 million years after the formation of the Solar System. Previously, the age of the Moon had been thought to be 4.527 ± 0.010 billion years. The impact in this scenario would have created a magma ocean on Earth and the proto-Moon with both bodies sharing a common plasma metal vapor atmosphere. The shared metal vapor bridge would have allowed material from the Earth and proto-Moon to exchange and equilibrate into a more common composition.

Yet another hypothesis proposes that the Moon and the Earth have formed together instead of separately like the giant-impact hypothesis suggests. This model, published in 2012 by Robin M. Canup, suggests that the Moon and the Earth formed from a massive collision of two planetary bodies, each larger than Mars, which then re-collided to form what we now call Earth. After the re-collision, Earth was surrounded by a disk of material, which accreted to form the Moon. This hypothesis could explain evidence that others do not.

History of Solar System formation and evolution hypotheses

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/History_of_Solar_System_formation_and_evolution_hypotheses 

Pierre-Simon Laplace, one of the originators of the nebular hypothesis

The history of scientific thought about the formation and evolution of the Solar System began with the Copernican Revolution. The first recorded use of the term "Solar System" dates from 1704. Since the seventeenth century, philosophers and scientists have been forming theories concerning the origins of our Solar System and the Moon and attempting to predict how the Solar System would change in the future. René Descartes was the first to hypothesize on the beginning of the Solar System; however, more scientists joined the discussion in the eighteenth century, forming the groundwork for later theories on the topic. Later, particularly in the twentieth century, a variety of theories began to build up, including the now-commonly accepted nebular hypothesis.

Meanwhile, theories explaining the evolution of the Sun originated in the nineteenth century, especially as scientists began to understand how stars in general functioned. In contrast, theories attempting to explain the origin of the Moon have been circulating for centuries, although all of the widely accepted hypotheses were proven false by the Apollo missions in the mid-twentieth century. Following Apollo, in 1984, the giant impact hypothesis was composed, replacing the already-disproven binary accretion model as the most common explanation for the formation of the Moon.

Contemporary view

The most widely accepted theory of planetary formation is known as the nebular hypothesis. This theory mentioned that, 4.6 billion years ago, the Solar System was formed by the gravitational collapse of a giant molecular cloud spanning several light-years. Many stars, including the Sun, were formed within this collapsing cloud. The gas that formed the Solar System was slightly more massive than the Sun itself. Most of the mass concentrated in the center, forming the Sun, and the rest of the mass flattened into a protoplanetary disk, out of which all of the current planets, moons, asteroids, and other celestial bodies in the Solar System formed.

Formation hypothesis

French philosopher and mathematician René Descartes was the first to propose a model for the origin of the Solar System in his book The World, written from 1629 to 1633. In his view, the Universe was filled with vortices of swirling particles, and both the Sun and planets had condensed from a large vortex that had contracted, which he thought could explain the circular motion of the planets. However, this was before the knowledge of Newton's theory of gravity, which explains that matter does not behave in this way.

Artist's conception of a protoplanetary disc

The vortex model of 1944, formulated by the German physicist and philosopher Carl Friedrich von Weizsäcker, hearkens back to the Cartesian model by involving a pattern of turbulence-induced eddies in a Laplacian nebular disc. In Weizsäcker's model, a combination of the clockwise rotation of each vortex and the anti-clockwise rotation of the whole system could lead to individual elements moving around the central mass in Keplerian orbits, reducing energy dissipation due to overall motion. However, material would be colliding at a high relative velocity in the inter-vortex boundaries and, in these regions, small roller-bearing eddies would coalesce to give annular condensations. This theory was much criticized, as turbulence is a phenomenon associated with disorder and would not spontaneously produce the highly-ordered structure required by the hypothesis. It also does not provide a solution to the angular momentum problem or explain lunar formation and other very basic characteristics of the Solar System.

This model was modified in 1948 by Dutch theoretical physicist Dirk Ter Haar, who theorized that regular eddies were discarded and replaced by random turbulence, which would lead to a very thick nebula where gravitational instability would not occur. He concluded the planets must have formed by accretion, and explained the compositional difference between the planets as resulting from the temperature difference between the inner and outer regions, the former being hotter and the latter being cooler, so only refractories (non-volatiles) condensed in the inner region. A major difficulty was that, in this supposition, turbulent dissipation took place over the course of a single millennium, which did not give enough time for planets to form.

The nebular hypothesis was first proposed in 1734 by Swedish scientist Emanuel Swedenborg and later expanded upon by Prussian philosopher Immanuel Kant in 1755. A similar theory was independently formulated by the Frenchman Pierre-Simon Laplace in 1796.

In 1749, Georges-Louis Leclerc, Comte de Buffon conceived the idea that the planets were formed when a comet collided with the Sun, sending matter out to form the planets. However, Pierre-Simon Laplace refuted this idea in 1796, stating that any planets formed in such a way would eventually crash into the Sun. Laplace felt that the near-circular orbits of the planets were a necessary consequence of their formation. Today, comets are known to be far too small to have created the Solar System in this way.

In 1755, Immanuel Kant speculated that observed nebulae could be regions of star and planet formation. In 1796, Laplace elaborated by arguing that the nebula collapsed into a star, and, as it did so, the remaining material gradually spun outward into a flat disc, which then formed planets.

Alternative theories

However plausible it may appear at first sight, the nebular hypothesis still faces the obstacle of angular momentum; if the Sun had indeed formed from the collapse of such a cloud, the planets should be rotating far more slowly. The Sun, though it contains almost 99.9 percent of the system's mass, contains just 1 percent of its angular momentum, meaning that the Sun should be spinning much more rapidly.

Tidal theory

Attempts to resolve the angular momentum problem led to the temporary abandonment of the nebular hypothesis in favor of a return to "two-body" theories. For several decades, many astronomers preferred the tidal or near-collision hypothesis put forward by James Jeans in 1917, in which the approach of some other star to the Sun ultimately formed the planets. This near-miss would have drawn large amounts of matter out of the Sun and the other star by their mutual tidal forces, which could have then condensed into planets. In 1929, astronomer Harold Jeffreys countered that such a near-collision was massively unlikely. American astronomer Henry Norris Russell also objected to the hypothesis by showing that it ran into problems with angular momentum for the outer planets, with the planets struggling to avoid being reabsorbed by the Sun.

Chamberlin–Moulton model

In 1900, Forest Moulton showed that the nebular hypothesis was inconsistent with observations because of the angular momentum. Moulton and Chamberlin in 1904 originated the planetesimal hypothesis. Along with many astronomers of the time, they came to believe the pictures of "spiral nebulas" from the Lick Observatory were direct evidence of the formation of planetary systems, which later turned out to be galaxies.

Moulton and Chamberlin suggested that a star had passed close to the Sun early in its life, causing tidal bulges, and that this, along with the internal process that leads to solar prominences, resulted in the ejection of filaments of matter from both stars. While most of the material would have fallen back, part of it would remain in orbit. The filaments cooled into numerous, tiny, solid planetesimals and a few larger protoplanets. This model received favorable support for about 3 decades, but passed out of favor by the late '30s and was discarded in the '40s due to the realization it was incompatible with the angular momentum of Jupiter. A part of the theory, planetesimal accretion, was retained.

Lyttleton's scenario

In 1937 and 1940, Raymond Lyttleton postulated that a companion star to the Sun collided with a passing star. Such a scenario had already been suggested and rejected by Henry Russell in 1935, though it may have been more likely assuming the Sun was born in an open cluster, where stellar collisions are common. Lyttleton showed that terrestrial planets were too small to condense on their own and suggested that one very large proto-planet broke in two because of rotational instability, forming Jupiter and Saturn, with a connecting filament from which the other planets formed. A later model, from 1940 and 1941, involved a triple star system, a binary plus the Sun, in which the binary merged and later split because of rotational instability and escaped from the system, leaving a filament that formed between them to be captured by the Sun. Objections of Lyman Spitzer apply to this model also.

Band-structure model

In 1954, 1975, and 1978, Swedish astrophysicist Hannes Alfvén included electromagnetic effects in equations of particle motions, and angular momentum distribution and compositional differences were explained. In 1954, he first proposed the band structure, in which he distinguished an A-cloud, containing mostly helium with some solid-particle impurities ("meteor rain"), a B-cloud with mostly carbon, a C-cloud having mainly hydrogen, and a D-cloud made mainly of silicon and iron. Impurities in the A-cloud formed Mars and the Moon (later captured by Earth), impurities in the B-cloud collapsed to form the outer planets, the C-cloud condensed into Mercury, Venus, Earth, the asteroid belt, moons of Jupiter, and Saturn's rings, while Pluto, Triton, the outer satellites of Saturn, the moons of Uranus, the Kuiper Belt, and the Oort cloud formed from the D-cloud.

Interstellar cloud theory

In 1943, Soviet astronomer Otto Schmidt proposed that the Sun, in its present form, passed through a dense interstellar cloud and emerged enveloped in a cloud of dust and gas, from which the planets eventually formed. This solved the angular momentum problem by assuming that the Sun's slow rotation was peculiar to it and that the planets did not form at the same time as the Sun. Extensions of the model, together forming the Russian school, include Gurevich and Lebedinsky in 1950, Safronov in 1967 and 1969, Ruskol in 1981 Safronov and Vityazeff in 1985, and Safronov and Ruskol in 1994, among others However, this hypothesis was severely dented by Victor Safronov, who showed that the amount of time required to form the planets from such a diffuse envelope would far exceed the Solar System's determined age.

Ray Lyttleton modified the theory by showing that a third body was not necessary and proposing that a mechanism of line accretion, as described by Bondi and Hoyle in 1944, enabled cloud material to be captured by the star (Williams and Cremin, 1968, loc. cit.).

Hoyle's hypothesis

In Hoyle's model from 1944, the companion went nova with ejected material captured by the Sun and planets forming from this material. In a version a year later it was a supernova. In 1955 he proposed a similar system to Laplace, and again proposed the idea with more mathematical detail in 1960. It differs from Laplace in that a magnetic torque occurred between the disk and the Sun, which came into effect immediately; otherwise, more and more matter would have been ejected, resulting in a massive planetary system exceeding the size of the existing one and comparable to the Sun. The torque caused a magnetic coupling and acted to transfer angular momentum from the Sun to the disk. The magnetic field strength would have to have been 1 gauss. The existence of torque depended on magnetic lines of force being frozen into the disk, a consequence of a well-known magnetohydrodynamic (MHD) theorem on frozen-in lines of force. As the solar condensation temperature when the disk was ejected could not be much more than 1,000 K (730 °C; 1,340 °F), numerous refractories must have been solid, probably as fine smoke particles, which would have grown with condensation and accretion. These particles would have been swept out with the disk only if their diameter at the Earth's orbit was less than 1 meter, so as the disk moved outward, a subsidiary disk consisting of only refractories remained behind, where the terrestrial planets would form. The model agrees with the mass and composition of the planets and angular momentum distribution provided the magnetic coupling. However, it does not explain twinning, the low mass of Mars and Mercury, and the planetoid belts. Alfvén formulated the concept of frozen-in magnetic field lines.

Kuiper's theory

Gerard Kuiper in 1944 argued, like Ter Haar, that regular eddies would be impossible and postulated that large gravitational instabilities might occur in the solar nebula, forming condensations. In this, the solar nebula could be either co-genetic with the Sun or captured by it. Density distribution would determine what could form, a planetary system or a stellar companion. The two types of planets were assumed to have resulted from the Roche limit. No explanation was offered for the Sun's slow rotation, which Kuiper saw as a larger G-star problem.

Whipple's theory

In Fred Whipple's 1948 scenario, a smoke cloud about 60,000 AU in diameter and with 1 solar mass (M_☉) contracted and produced the Sun. It had a negligible angular momentum, thus accounting for the Sun's similar property. This smoke cloud captured a smaller one with a large angular momentum. The collapse time for the large smoke and gas nebula is about 100 million years, and the rate was slow at first, increasing in later stages. The planets condensed from small clouds developed in or captured by the second cloud. The orbits would be nearly circular because accretion would reduce eccentricity due to the influence of the resisting medium, and orbital orientations would be similar because of the size of the small cloud and the common direction of the motions. The protoplanets might have heated up to such high degrees that the more volatile compounds would have been lost, and the orbital velocity decreased with increasing distance so that the terrestrial planets would have been more affected. However, this scenario was weak in that practically all the final regularities are introduced as a prior assumption, and quantitative calculations did not support most of the hypothesizing. For these reasons, it did not gain wide acceptance.

Urey's model

American chemist Harold Urey, who founded cosmochemistry, put forward a scenario in 1951, 1952, 1956, and 1966 based largely on meteorites. His model also used Chandrasekhar's stability equations and obtained density distribution in the gas and dust disk surrounding the primitive Sun. To explain that volatile elements like mercury could be retained by the terrestrial planets, he postulated a moderately thick gas and dust halo shielding the planets from the Sun. To form diamonds, pure carbon crystals, moon-sized objects, and gas spheres that became gravitationally unstable would have to form in the disk, with the gas and dust dissipating at a later stage. Pressure fell as gas was lost and diamonds were converted to graphite, while the gas became illuminated by the Sun. Under these conditions, considerable ionization would be present, and the gas would be accelerated by magnetic fields, hence the angular momentum could be transferred from the Sun. Urey postulated that these lunar-size bodies were destroyed by collisions, with the gas dissipating, leaving behind solids collected at the core, with the resulting smaller fragments pushed far out into space and the larger fragments staying behind and accreting into planets. He suggested the Moon was such a surviving core.

Protoplanet theory

In 1960, 1963, and 1978, W. H. McCrea proposed the protoplanet theory, in which the Sun and planets individually coalesced from matter within the same cloud, with the smaller planets later captured by the Sun's larger gravity. It includes fission in a protoplanetary nebula and excludes a solar nebula. Agglomerations of floccules, which are presumed to compose the supersonic turbulence assumed to occur in the interstellar material from which stars are born, formed the Sun and protoplanets, the latter splitting to form planets. The two portions could not remain gravitationally bound to each other at a mass ratio of at least 8 to 1, and for inner planets, went into independent orbits, while for outer planets, one portion exited the Solar System. The inner protoplanets were Venus-Mercury and Earth-Mars. The moons of the greater planets were formed from "droplets" in the neck connecting the two portions of the dividing protoplanet. These droplets could account for some asteroids. Terrestrial planets would have no major moons, which does not account for Luna. The theory also predicts certain observations, such as the similar angular velocity of Mars and Earth with similar rotation periods and axial tilts. In this scheme, there are six principal planets: two terrestrial, Venus and Earth; two major, Jupiter and Saturn; and two outer, Uranus and Neptune, along with three lesser planets: Mercury, Mars, and Pluto.

This theory has some problems, such as failing to explain the fact that the planets all orbit the Sun in the same direction with relatively low eccentricity, which would appear highly unlikely if they were each individually captured.

Cameron's hypothesis

In American astronomer Alastair G. W. Cameron's hypothesis from 1962 and 1963, the protosun, with a mass of about 1–2 Suns and a diameter of around 100,000 AU, was gravitationally unstable, collapsed, and broke into smaller subunits. The magnetic field was around 1/100,000 gauss. During the collapse, the magnetic lines of force were twisted. The collapse was fast and occurred due to the dissociation of hydrogen molecules, followed by the ionization of hydrogen and the double ionization of helium. Angular momentum led to rotational instability, which produced a Laplacean disk. At this stage, radiation removed excess energy, the disk would cool over a relatively short period of about 1 million years, and the condensation into what Whipple calls cometismals took place. Aggregation of these cometismals produced giant planets, which in turn produced disks during their formation, which evolved into lunar systems. The formation of terrestrial planets, comets, and asteroids involved disintegration, heating, melting, and solidification. Cameron also formulated the giant-impact hypothesis for the origin of the Moon.

Capture theory

The capture theory, proposed by Michael Mark Woolfson in 1964, posits that the Solar System formed from tidal interactions between the Sun and a low-density protostar. The Sun's gravity would have drawn material from the diffuse atmosphere of the protostar, which would then have collapsed to form the planets. However, the capture theory predicts a different age for the Sun than for the planets, whereas the similar ages of the Sun and the rest of the Solar System indicate that they formed at roughly the same time.

As captured planets would have initially eccentric orbits, Dormand and Woolfson in 1974 and 1977 and Woolfson proposed the possibility of a collision. They theorized that a filament was thrown out by a passing proto-star and was captured by the Sun, resulting in the formation of planets. In this idea, there were 6 original planets, corresponding to 6 point-masses in the filament, with planets "Enyo" and "Bellona", the two innermost, colliding. Enyo, at twice the mass of Neptune, was ejected out of the Solar System, while Bellona, estimated to be one-third the mass of Uranus, split into two to form Earth and Venus. In a version of the hypothesis revised in 2017, Bellona and Enyo were both determined to be gas giants more massive than Jupiter, and their collision briefly caused deuterium-deuterium chain reactions, shattering both planets. Sediments from Enyo's interior formed Venus, while sediments from Bellona's interior formed Earth. According to this theory, Mars, the Moon, Haumea, Makemake, Eris, and V774104 are former moons of Enyo, while Mercury is either a fragment of Bellona or an escaped moon of Enyo. The Enyo-Bellona collision also formed the asteroid belt, Kuiper belt, Oort cloud, and comets. Pluto, either a fragment or moon of one of the planets, passed close to Neptune's satellite Triton, causing it to assume its retrograde orbit.

American astronomer T.J.J. See developed a model while at the USNO's Mare Island, California station which he called capture theory. Published in 1910, in his "Researches on the Evolution of the Stellar Systems: v. 2. The capture theory of cosmical evolution, founded on dynamical principles and illustrated by phenomena observed in the spiral nebulae, the planetary system, the double and multiple stars and clusters and the star-clouds of the Milky Way", the theory proposed that the planets formed in the outer Solar System and were captured by the Sun, while the moons were formed in this manner and were captured by the planets. This caused a feud with Forest Moulton, who co-developed the planetesimal hypothesis. A preview was presented in 1909 at a meeting of the Astronomical Society of the Pacific (ASP) at the Chabot Observatory in Oakland, California. The current knowledge of dynamics makes capture most unlikely, as it requires special conditions.

Solar fission

In 1951, 1962, and 1981, Swiss astronomer Louis Jacot, like Weisacker and Ter Haar, continued the Cartesian idea of vortices but proposed a hierarchy of vortices, or vortices within vortices, i.e. a lunar system vortex, a Solar System vortex, and a galactic vortex. He put forward the notion that planetary orbits are spirals, not circles or ellipses. Jacot also proposed the expansion of galaxies in that stars move away from the hub and moons move away from their planets.

He also maintained that planets were expelled, one at a time, from the Sun, specifically from an equatorial bulge caused by rotation, and that one hypothetical planet shattered in this expulsion, leaving the asteroid belt. The Kuiper Belt was unknown at the time, but presumably it, too, would have resulted from the same kind of shattering. The moons, like the planets, originated as equatorial expulsions from their parent planets, with some shattering, leaving the rings, and the Earth was supposed to eventually expel another moon.

In this model, there were 4 phases to the planets: no rotation and keeping the same side to the Sun, very slow, accelerated, and daily rotation.

Jacot explained the differences between inner and outer planets and inner and outer moons through vortex behavior. Mercury's eccentric orbit was explained by its recent expulsion from the Sun and Venus' slow rotation as its being in the "slow rotation phase", having been expelled second to last.

The Tom Van Flandern model was first proposed in 1993 in the first edition of his book. In the revised version from 1999 and later, the original Solar System had six pairs of twin planets, and each fissioned off from the equatorial bulges of an overspinning Sun, where outward centrifugal forces exceeded the inward gravitational force, at different times, giving them different temperatures, sizes, and compositions, and having condensed thereafter with the nebular disk dissipating after some 100 million years, with six planets exploding. Four of these were helium-dominated, fluid, and unstable. These were V (Maldek, V standing for the fifth planet, the first four including Mercury and Mars), K (Krypton), T (transneptunian), and Planet X. In these cases, the smaller moons exploded because of tidal stresses, leaving the four component belts of the two major planetoid zones. Planet LHB-A, the explosion for which is postulated to have caused the Late Heavy Bombardment (LHB) about 4 eons ago, was twinned with Jupiter, and LHB-B, the explosion for which is postulated to have caused another LHB, was twinned with Saturn. In planets LHB-A, Jupiter, LHB-B, and Saturn, the inner and smaller partner in each pair was subjected to enormous tidal stresses, causing it to blow up. The explosions took place before they were able to fission off moons. As the six were fluid, they left no trace. Solid planets fissioned off only one moon, and Mercury was a moon of Venus but drifted away as a result of the Sun's gravitational influence. Mars was a moon of Maldek.

One major argument against exploding planets and moons is that there would not be an energy source powerful enough to cause such explosions.

Herndon's model

In J. Marvin Herndon's model, inner, large-core planets formed by condensation and raining-out from within giant gaseous protoplanets at high pressures and high temperatures. Earth's complete condensation included a roughly 300 M_⊕ gas/ice shell that compressed the rocky kernel to about 66 percent of Earth's present diameter. T Tauri eruptions of the Sun stripped the gases away from the inner planets. Mercury was incompletely condensed, and a portion of its gases was stripped away and transported to the region between Mars and Jupiter, where it fused with in-falling oxidized condensate from the outer reaches of the Solar System and formed the parent material for ordinary chondrite meteorites, the Main-Belt asteroids, and veneer for the inner planets, especially Mars. The differences between the inner planets are primarily the consequence of different degrees of protoplanetary compression. There are two types of responses to decompression-driven planetary volume increases: cracks, which were formed to increase surface area, and folding, which created mountain ranges to accommodate changes in curvature.

This planetary formation theory represents an extension of the Whole-Earth Decompression Dynamics (WEDD) model, which includes natural nuclear-fission reactors in planetary cores; Herndon expounds upon it in eleven articles in Current Science from 2005 to 2013 and five books published from 2008 to 2012. He refers to his model as "indivisible" – meaning that the fundamental aspects of Earth are connected logically and causally and can be deduced from its early formation as a Jupiter-like giant.

In 1944, German chemist and physicist Arnold Eucken considered the thermodynamics of Earth condensing and raining-out within a giant protoplanet at pressures of 100–1000 atm. In the 1950s and early 1960s, discussion of planetary formation at such pressures took place, but Cameron's 1963 low-pressure (c. 4–10 atm.) model largely supplanted the idea.

Classification of the theories

Jeans, in 1931, divided the various models into two groups: those where the material for planet formation came from the Sun, and those where it did not and may be concurrent or consecutive.

In 1963, William McCrea divided them into another two groups: those that relate the formation of the planets to the formation of the Sun and those where it is independent of the formation of the Sun, where the planets form after the Sun becomes a normal star.

Ter Haar and Cameron distinguished between those theories that consider a closed system, which is a development of the Sun and possibly a solar envelope, that starts with a protosun rather than the Sun itself, and state that Belot calls these theories monistic; and those that consider an open system, which is where there is an interaction between the Sun and some foreign body that is supposed to have been the first step in the developments leading to the planetary system, and state that Belot calls these theories dualistic.

Hervé Reeves' classification also categorized them as co-genetic with the Sun or not, but also considered their formation from altered or unaltered stellar and interstellar material. He also recognized four groups: models based on the solar nebula, originated by Swedenborg, Kant, and Laplace in the 1700s; theories proposing a cloud captured from interstellar space, major proponents being Alfvén and Gustaf Arrhenius in 1978; the binary hypotheses which propose that a sister star somehow disintegrated and a portion of its dissipating material was captured by the Sun, with the principal hypothesizer being Lyttleton in the 1940s; and the close-approach filament ideas of Jeans, Jeffreys, and Woolfson and Dormand.

Williams and Cremin created the categories of models that regard the origin and formation of the planets as being essentially related to the Sun, with the two formation processes taking place concurrently or consecutively, and models that regard the formation of the planets as being independent of the formation process of the Sun, the planets forming after the Sun becomes a normal star. The latter classification has 2 subcategories: models where the material for the formation of the planets is extracted either from the Sun or another star, and models where the material is acquired from interstellar space. They conclude that the best models are Hoyle's magnetic coupling and McCrea's floccules.

Woolfson recognized monistic models, which included Laplace, Descartes, Kant, and Weisacker, and dualistic models, which included Buffon, Chamberlin-Moulton, Jeans, Jeffreys, and Schmidt-Lyttleton.

Reemergence of the nebular hypothesis

Beta Pictoris as seen by the Hubble Space Telescope

In 1978, astronomer A. J. R. Prentice revived the Laplacian nebular model in his Modern Laplacian Theory by suggesting that the angular momentum problem could be resolved by drag created by dust grains in the original disc, which slowed down rotation in the centre. Prentice also suggested that the young Sun transferred some angular momentum to the protoplanetary disc and planetesimals through supersonic ejections understood to occur in T Tauri stars. However, his contention that such formation would occur in toruses or rings has been questioned, as any such rings would disperse before collapsing into planets.

The birth of the modern, widely accepted theory of planetary formation, the Solar Nebular Disk Model (SNDM), can be traced to the works of Soviet astronomer Victor Safronov. His book Evolution of the protoplanetary cloud and formation of the Earth and the planets, which was translated to English in 1972, had a long-lasting effect on how scientists thought about the formation of the planets. In this book, almost all major problems of the planetary formation process were formulated, and some of them were solved. Safronov's ideas were further developed in the works of George Wetherill, who discovered runaway accretion. By the early 1980s, the nebular hypothesis in the form of SNDM had come back into favor, led by two major discoveries in astronomy. First, several young stars, such as Beta Pictoris, were found to be surrounded by discs of cool dust, much as was predicted by the nebular hypothesis. Second, the Infrared Astronomical Satellite, launched in 1983, observed that many stars had an excess of infrared radiation that could be explained if they were orbited by discs of cooler material.

Outstanding issues

While the broad picture of the nebular hypothesis is widely accepted, many of the details are not well understood and continue to be refined.

The refined nebular model was developed entirely on observations of the Solar System because it was the only one known until the mid-1990s. It was not confidently assumed to be widely applicable to other planetary systems, although scientists were anxious to test the nebular model by finding protoplanetary discs or even planets around other stars. As of August 30, 2013, the discovery of 941 extrasolar planets has turned up many surprises, and the nebular model must be revised to account for these discovered planetary systems, or new models considered.

Among the extrasolar planets discovered to date are planets the size of Jupiter or larger, but that possess very short orbital periods of only a few hours. Such planets would have to orbit very closely to their stars, so closely that their atmospheres would be gradually stripped away by solar radiation.There is no consensus on how to explain these so-called hot Jupiters, but one leading idea is that of planetary migration, similar to the process which is thought to have moved Uranus and Neptune to their current, distant orbit. Possible processes that cause the migration include orbital friction while the protoplanetary disk is still full of hydrogen and helium gas and exchange of angular momentum between giant planets and the particles in the protoplanetary disc.

One other problem is the detailed features of the planets. The solar nebula hypothesis predicts that all planets will form exactly in the ecliptic plane. Instead, the orbits of the classical planets have various small inclinations with respect to the ecliptic. Furthermore, for the gas giants, it is predicted that their rotations and moon systems will not be inclined with respect to the ecliptic plane. However, most gas giants have substantial axial tilts with respect to the ecliptic, with Uranus having a 98° tilt. The Moon being relatively large with respect to the Earth and other moons in irregular orbits with respect to their planet is yet another issue. It is now believed these observations are explained by events that happened after the initial formation of the Solar System.

Solar evolution hypotheses

Attempts to isolate the physical source of the Sun's energy, and thus determine when and how it might ultimately run out, began in the 19th century.

Kelvin–Helmholtz contraction

In the 19th century, the prevailing scientific view on the source of the Sun's heat was that it was generated by gravitational contraction. In the 1840s, astronomers J. R. Mayer and J. J. Waterson first proposed that the Sun's massive weight would cause it to collapse in on itself, generating heat. Both Hermann von Helmholtz and Lord Kelvin expounded upon this idea in 1854, suggesting that heat may also be produced by the impact of meteors on the Sun's surface. Theories at the time suggested that stars evolved moving down the main sequence of the Hertzsprung-Russell diagram, starting as diffuse red supergiants before contracting and heating to become blue main-sequence stars, then even further down to red dwarfs before finally ending up as cool, dense black dwarfs. However, the Sun only has enough gravitational potential energy to power its luminosity by this mechanism for about 30 million years—far less than the age of the Earth. (This collapse time is known as the Kelvin–Helmholtz timescale.)

Albert Einstein's development of the theory of relativity in 1905 led to the understanding that nuclear reactions could create new elements from smaller precursors with the loss of energy. In his treatise Stars and Atoms, Arthur Eddington suggested that pressures and temperatures within stars were great enough for hydrogen nuclei to fuse into helium, a process which could produce the massive amounts of energy required to power the Sun. In 1935, Eddington went further and suggested that other elements might also form within stars. Spectral evidence collected after 1945 showed that the distribution of the commonest chemical elements, such as carbon, hydrogen, oxygen, nitrogen, neon, and iron, was fairly uniform across the galaxy, suggesting that these elements had a common origin. Numerous anomalies in the proportions hinted at an underlying mechanism for creation. For example, lead has a higher atomic weight than gold, but is far more common; besides, hydrogen and helium (elements 1 and 2) are virtually ubiquitous, yet lithium and beryllium (elements 3 and 4) are extremely rare.

Red giants

While the unusual spectra of red giant stars had been known since the 19th century, it was George Gamow who, in the 1940s, first understood that they were stars of roughly solar mass that had run out of hydrogen in their cores and had resorted to burning the hydrogen in their outer shells. This allowed Martin Schwarzschild to draw the connection between red giants and the finite lifespans of stars. It is now understood that red giants are stars in the last stages of their life cycles.

Fred Hoyle noted that, even while the distribution of elements was fairly uniform, different stars had varying amounts of each element. To Hoyle, this indicated that they must have originated within the stars themselves. The abundance of elements peaked around the atomic number for iron, an element that could only have been formed under intense pressures and temperatures. Hoyle concluded that iron must have formed within giant stars. From this, in 1945 and 1946, Hoyle constructed the final stages of a star's life cycle. As the star dies, it collapses under its weight, leading to a stratified chain of fusion reactions: carbon-12 fuses with helium to form oxygen-16, oxygen-16 fuses with helium to produce neon-20, and so on up to iron. There was, however, no known method by which carbon-12 could be produced. Isotopes of beryllium produced via fusion were too unstable to form carbon, and for three helium atoms to form carbon-12 was so unlikely as to have been impossible over the age of the Universe. However, in 1952, physicist Ed Salpeter showed that a short enough time existed between the formation and the decay of the beryllium isotope that another helium had a small chance to form carbon, but only if their combined mass/energy amounts were equal to that of carbon-12. Hoyle, employing the anthropic principle, showed that it must be so, since he himself was made of carbon, and he existed. When the matter/energy level of carbon-12 was finally determined, it was found to be within a few percent of Hoyle's prediction.

White dwarfs

The first white dwarf discovered was in the triple star system of 40 Eridani, which contains the relatively bright main sequence star 40 Eridani A, orbited at a distance by the closer binary system of the white dwarf 40 Eridani B and the main sequence red dwarf 40 Eridani C. The pair 40 Eridani B/C was discovered by William Herschel on January 31, 1783; it was again observed by Friedrich Georg Wilhelm Struve in 1825 and by Otto Wilhelm von Struve in 1851. In 1910, Henry Norris Russell, Edward Charles Pickering, and Williamina Fleming discovered that, despite being a dim star, 40 Eridani B was of spectral type A, or white.

White dwarfs were found to be extremely dense soon after their discovery. If a star is in a binary system, as is the case for Sirius B and 40 Eridani B, it is possible to estimate its mass from observations of the binary orbit. This was done for Sirius B by 1910, yielding a mass estimate of 0.94 M_☉ (a more modern estimate being 1.00 M_☉). Since hotter bodies radiate more than colder ones, a star's surface brightness can be estimated from its effective surface temperature, and hence from its spectrum. If the star's distance is known, its overall luminosity can also be estimated. A comparison of the two figures yields the star's radius. Reasoning of this sort led to the realization, puzzling to astronomers at the time, that Sirius B and 40 Eridani B must be very dense. For example, when Ernst Öpik estimated the density of some visual binary stars in 1916, he found that 40 Eridani B had a density of over 25,000 times the Sun's, which was so high that he called it "impossible".

Such densities are possible because white dwarf material is not composed of atoms bound by chemical bonds, but rather consists of a plasma of unbound nuclei and electrons. There is therefore no obstacle to placing nuclei closer to each other than electron orbitals—the regions occupied by electrons bound to an atom—would normally allow. Eddington, however, wondered what would happen when this plasma cooled and the energy which kept the atoms ionized was no longer present. This paradox was resolved by R. H. Fowler in 1926 by an application of newly devised quantum mechanics. Since electrons obey the Pauli exclusion principle, no two electrons can occupy the same state, and they must obey Fermi–Dirac statistics, also introduced in 1926 to determine the statistical distribution of particles that satisfies the Pauli exclusion principle. At zero temperature, therefore, electrons could not all occupy the lowest-energy, or ground, state; some of them had to occupy higher-energy states, forming a band of lowest-available energy states, the Fermi sea. This state of the electrons, called degenerate, meant that a white dwarf could cool to zero temperature and still possess high energy.

Planetary nebulae

Planetary nebulae are generally faint objects, and none are visible to the naked eye. The first planetary nebula discovered was the Dumbbell Nebula in the constellation of Vulpecula, observed by Charles Messier in 1764 and listed as M27 in his catalogue of nebulous objects. To early observers with low-resolution telescopes, M27 and subsequently discovered planetary nebulae somewhat resembled the gas giants, and William Herschel, the discoverer of Uranus, eventually coined the term 'planetary nebula' for them, although, as we now know, they are very different from planets.

The central stars of planetary nebulae are very hot. Their luminosity, though, is very low, implying that they must be very small. A star can collapse to such a small size only once it has exhausted all its nuclear fuel, so planetary nebulae came to be understood as a final stage of stellar evolution. Spectroscopic observations show that all planetary nebulae are expanding, and so the idea arose that planetary nebulae were caused by a star's outer layers being thrown into space at the end of its life.

Lunar origins hypotheses

George Darwin

Over the centuries, many scientific hypotheses have been put forward concerning the origin of Earth's Moon. One of the earliest was the so-called binary accretion model, which concluded that the Moon accreted from material in orbit around the Earth leftover from its formation. Another, the fission model, was developed by George Darwin (son of Charles Darwin), who noted that, as the Moon is gradually receding from the Earth at a rate of about 4 cm per year, so at one point in the distant past, it must have been part of the Earth but was flung outward by the momentum of Earth's then–much faster rotation. This hypothesis is also supported by the fact that the Moon's density, while less than Earth's, is about equal to that of Earth's rocky mantle, suggesting that, unlike the Earth, it lacks a dense iron core. A third hypothesis, known as the capture model, suggested that the Moon was an independently orbiting body that had been snared into orbit by Earth's gravity.

Apollo missions

The existing hypotheses were all refuted by the Apollo lunar missions in the late 1960s and early 1970s, which introduced a stream of new scientific evidence, specifically concerning the Moon's composition, age, and history. These lines of evidence contradict many predictions made by these earlier models. The rocks brought back from the Moon showed a marked decrease in water relative to rocks elsewhere in the Solar System and evidence of an ocean of magma early in its history, indicating that its formation must have produced a great deal of energy. Also, oxygen isotopes in lunar rocks showed a marked similarity to those on Earth, suggesting that they formed at a similar location in the solar nebula. The capture model fails to explain the similarity in these isotopes (if the Moon had originated in another part of the Solar System, those isotopes would have been different), while the co-accretion model cannot adequately explain the loss of water (if the Moon formed similarly to the Earth, the amount of water trapped in its mineral structure would also be roughly similar). Conversely, the fission model, while it can account for the similarity in chemical composition and the lack of iron in the Moon, cannot adequately explain its high orbital inclination and, in particular, the large amount of angular momentum in the Earth–Moon system, more than any other planet–satellite pair in the Solar System.

Giant impact hypothesis

For many years after Apollo, the binary accretion model was settled on as the best hypothesis for explaining the Moon's origins, even though it was known to be flawed. Then, at a conference in Kona, Hawaii in 1984, a compromise model was composed that accounted for all of the observed discrepancies. Originally formulated by two independent research groups in 1976, the giant impact model supposed that a massive planetary object the size of Mars had collided with Earth early in its history. The impact would have melted Earth's crust, and the other planet's heavy core would have sunk inward and merged with Earth's. The superheated vapor produced by the impact would have risen into orbit around the planet, coalescing into the Moon. This explained the lack of water, as the vapor cloud was too hot for water to condense; the similarity in composition, since the Moon had formed from part of the Earth; the lower density, since the Moon had formed from the Earth's crust and mantle, rather than its core; and the Moon's unusual orbit, since an oblique strike would have imparted a massive amount of angular momentum to the Earth–Moon system.

Outstanding issues

The giant impact model has been criticized for being too explanatory, since it can be expanded to explain any future discoveries and, as such, is unfalsifiable. Many also claim that much of the material from the impactor would have ended up in the Moon, meaning that the isotope levels would be different, but they are not. In addition, while some volatile compounds such as water are absent from the Moon's crust, many others, such as manganese, are not.

Other natural satellites

While the co-accretion and capture models are not currently accepted as valid explanations for the existence of the Moon, they have been employed to explain the formation of other natural satellites in the Solar System. Jupiter's Galilean satellites are believed to have formed via co-accretion, while the Solar System's irregular satellites, such as Triton, are all believed to have been captured.