The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, greater than 1 is a hyperbola; the term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is used for the isolated two-body problem, but extensions exist for objects following a Klemperer rosette orbit through the galaxy. In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit; the eccentricity of this Kepler orbit is a non-negative number. The eccentricity may take the following values: circular orbit: e = 0 elliptic orbit: 0 < e < 1 parabolic trajectory: e = 1 hyperbolic trajectory: e > 1 The eccentricity e is given by e = 1 + 2 E L 2 m red α 2 where E is the total orbital energy, L is the angular momentum, mred is the reduced mass, α the coefficient of the inverse-square law central force such as gravity or electrostatics in classical physics: F = α r 2 or in the case of a gravitational force: e = 1 + 2 ε h 2 μ 2 where ε is the specific orbital energy, μ the standard gravitational parameter based on the total mass, h the specific relative angular momentum.
For values of e from 0 to 1 the orbit's shape is an elongated ellipse. The limit case between an ellipse and a hyperbola, when e equals 1, is parabola. Radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity. Radial orbits hence eccentricity equal to one. Keeping the energy constant and reducing the angular momentum, elliptic and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1. For a repulsive force only the hyperbolic trajectory, including the radial version, is applicable. For elliptical orbits, a simple proof shows that arcsin yields the projection angle of a perfect circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury, one must calculate the inverse sine to find the projection angle of 11.86 degrees. Next, tilt any circular object by that angle and the apparent ellipse projected to your eye will be of that same eccentricity; the word "eccentricity" comes from Medieval Latin eccentricus, derived from Greek ἔκκεντρος ekkentros "out of the center", from ἐκ- ek-, "out of" + κέντρον kentron "center".
"Eccentric" first appeared in English in 1551, with the definition "a circle in which the earth, sun. Etc. deviates from its center". By five years in 1556, an adjectival form of the word had developed; the eccentricity of an orbit can be calculated from the orbital state vectors as the magnitude of the eccentricity vector: e = | e | where: e is the eccentricity vector. For elliptical orbits it can be calculated from the periapsis and apoapsis since rp = a and ra = a, where a is the semimajor axis. E = r a − r p r a + r p = 1 − 2 r a r p + 1 where: ra is the radius at apoapsis. Rp is the radius at periapsis; the eccentricity of an elliptical orbit can be used to obtain the ratio of the periapsis to the apoapsis: r p r a = 1 − e 1 + e For Earth, orbital eccentricity ≈ 0.0167, apoapsis= aphelion and periapsis= perihelion relative to sun. For Earth's annual orbit path, ra/rp ratio = longest_radius / shortest_radius ≈ 1.034 relative to center point of path. The eccentricity of the Earth's orbit is about 0.0167.
ArXiv is a repository of electronic preprints approved for posting after moderation, but not full peer review. It consists of scientific papers in the fields of mathematics, astronomy, electrical engineering, computer science, quantitative biology, mathematical finance and economics, which can be accessed online. In many fields of mathematics and physics all scientific papers are self-archived on the arXiv repository. Begun on August 14, 1991, arXiv.org passed the half-million-article milestone on October 3, 2008, had hit a million by the end of 2014. By October 2016 the submission rate had grown to more than 10,000 per month. ArXiv was made possible by the compact TeX file format, which allowed scientific papers to be transmitted over the Internet and rendered client-side. Around 1990, Joanne Cohn began emailing physics preprints to colleagues as TeX files, but the number of papers being sent soon filled mailboxes to capacity. Paul Ginsparg recognized the need for central storage, in August 1991 he created a central repository mailbox stored at the Los Alamos National Laboratory which could be accessed from any computer.
Additional modes of access were soon added: FTP in 1991, Gopher in 1992, the World Wide Web in 1993. The term e-print was adopted to describe the articles, it began as a physics archive, called the LANL preprint archive, but soon expanded to include astronomy, computer science, quantitative biology and, most statistics. Its original domain name was xxx.lanl.gov. Due to LANL's lack of interest in the expanding technology, in 2001 Ginsparg changed institutions to Cornell University and changed the name of the repository to arXiv.org. It is now hosted principally with eight mirrors around the world, its existence was one of the precipitating factors that led to the current movement in scientific publishing known as open access. Mathematicians and scientists upload their papers to arXiv.org for worldwide access and sometimes for reviews before they are published in peer-reviewed journals. Ginsparg was awarded a MacArthur Fellowship in 2002 for his establishment of arXiv; the annual budget for arXiv is $826,000 for 2013 to 2017, funded jointly by Cornell University Library, the Simons Foundation and annual fee income from member institutions.
This model arose in 2010, when Cornell sought to broaden the financial funding of the project by asking institutions to make annual voluntary contributions based on the amount of download usage by each institution. Each member institution pledges a five-year funding commitment to support arXiv. Based on institutional usage ranking, the annual fees are set in four tiers from $1,000 to $4,400. Cornell's goal is to raise at least $504,000 per year through membership fees generated by 220 institutions. In September 2011, Cornell University Library took overall administrative and financial responsibility for arXiv's operation and development. Ginsparg was quoted in the Chronicle of Higher Education as saying it "was supposed to be a three-hour tour, not a life sentence". However, Ginsparg remains on the arXiv Scientific Advisory Board and on the arXiv Physics Advisory Committee. Although arXiv is not peer reviewed, a collection of moderators for each area review the submissions; the lists of moderators for many sections of arXiv are publicly available, but moderators for most of the physics sections remain unlisted.
Additionally, an "endorsement" system was introduced in 2004 as part of an effort to ensure content is relevant and of interest to current research in the specified disciplines. Under the system, for categories that use it, an author must be endorsed by an established arXiv author before being allowed to submit papers to those categories. Endorsers are not asked to review the paper for errors, but to check whether the paper is appropriate for the intended subject area. New authors from recognized academic institutions receive automatic endorsement, which in practice means that they do not need to deal with the endorsement system at all. However, the endorsement system has attracted criticism for restricting scientific inquiry. A majority of the e-prints are submitted to journals for publication, but some work, including some influential papers, remain purely as e-prints and are never published in a peer-reviewed journal. A well-known example of the latter is an outline of a proof of Thurston's geometrization conjecture, including the Poincaré conjecture as a particular case, uploaded by Grigori Perelman in November 2002.
Perelman appears content to forgo the traditional peer-reviewed journal process, stating: "If anybody is interested in my way of solving the problem, it's all there – let them go and read about it". Despite this non-traditional method of publication, other mathematicians recognized this work by offering the Fields Medal and Clay Mathematics Millennium Prizes to Perelman, both of which he refused. Papers can be submitted in any of several formats, including LaTeX, PDF printed from a word processor other than TeX or LaTeX; the submission is rejected by the arXiv software if generating the final PDF file fails, if any image file is too large, or if the total size of the submission is too large. ArXiv now allows one to store and modify an incomplete submission, only finalize the submission when ready; the time stamp on the article is set. The standard access route is through one of several mirrors. Sev
In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet. Orbit refers to a repeating trajectory, although it may refer to a non-repeating trajectory. To a close approximation and satellites follow elliptic orbits, with the central mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion. For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital motion; the apparent motions of the planets were described by European and Arabic philosophers using the idea of celestial spheres. This model posited the existence of perfect moving spheres or rings to which the stars and planets were attached.
It assumed the heavens were fixed apart from the motion of the spheres, was developed without any understanding of gravity. After the planets' motions were more measured, theoretical mechanisms such as deferent and epicycles were added. Although the model was capable of reasonably predicting the planets' positions in the sky and more epicycles were required as the measurements became more accurate, hence the model became unwieldy. Geocentric it was modified by Copernicus to place the Sun at the centre to help simplify the model; the model was further challenged during the 16th century, as comets were observed traversing the spheres. The basis for the modern understanding of orbits was first formulated by Johannes Kepler whose results are summarised in his three laws of planetary motion. First, he found that the orbits of the planets in our Solar System are elliptical, not circular, as had been believed, that the Sun is not located at the center of the orbits, but rather at one focus. Second, he found that the orbital speed of each planet is not constant, as had been thought, but rather that the speed depends on the planet's distance from the Sun.
Third, Kepler found a universal relationship between the orbital properties of all the planets orbiting the Sun. For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods. Jupiter and Venus, for example, are about 5.2 and 0.723 AU distant from the Sun, their orbital periods about 11.86 and 0.615 years. The proportionality is seen by the fact that the ratio for Jupiter, 5.23/11.862, is equal to that for Venus, 0.7233/0.6152, in accord with the relationship. Idealised orbits meeting these rules are known as Kepler orbits. Isaac Newton demonstrated that Kepler's laws were derivable from his theory of gravitation and that, in general, the orbits of bodies subject to gravity were conic sections. Newton showed that, for a pair of bodies, the orbits' sizes are in inverse proportion to their masses, that those bodies orbit their common center of mass. Where one body is much more massive than the other, it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body.
Advances in Newtonian mechanics were used to explore variations from the simple assumptions behind Kepler orbits, such as the perturbations due to other bodies, or the impact of spheroidal rather than spherical bodies. Lagrange developed a new approach to Newtonian mechanics emphasizing energy more than force, made progress on the three body problem, discovering the Lagrangian points. In a dramatic vindication of classical mechanics, in 1846 Urbain Le Verrier was able to predict the position of Neptune based on unexplained perturbations in the orbit of Uranus. Albert Einstein in his 1916 paper The Foundation of the General Theory of Relativity explained that gravity was due to curvature of space-time and removed Newton's assumption that changes propagate instantaneously; this led astronomers to recognize that Newtonian mechanics did not provide the highest accuracy in understanding orbits. In relativity theory, orbits follow geodesic trajectories which are approximated well by the Newtonian predictions but the differences are measurable.
All the experimental evidence that can distinguish between the theories agrees with relativity theory to within experimental measurement accuracy. The original vindication of general relativity is that it was able to account for the remaining unexplained amount in precession of Mercury's perihelion first noted by Le Verrier. However, Newton's solution is still used for most short term purposes since it is easier to use and sufficiently accurate. Within a planetary system, dwarf planets and other minor planets and space debris orbit the system's barycenter in elliptical orbits. A comet in a parabolic or hyperbolic orbit about a barycenter is not gravitationally bound to the star and therefore is not considered part of the star's planetary system. Bodies which are gravitationally bound to one of the planets in a planetary system, either natural or artificial satellites, follow orbits about a barycenter near or within that planet. Owing to mutual gravitational perturbations, the eccentricities of the planetary orbits vary over time.
Mercury, the smallest planet in the Solar System, has the most eccentric orbit
The parsec is a unit of length used to measure large distances to astronomical objects outside the Solar System. A parsec is defined as the distance at which one astronomical unit subtends an angle of one arcsecond, which corresponds to 648000/π astronomical units. One parsec is equal to 31 trillion kilometres or 19 trillion miles; the nearest star, Proxima Centauri, is about 1.3 parsecs from the Sun. Most of the stars visible to the unaided eye in the night sky are within 500 parsecs of the Sun; the parsec unit was first suggested in 1913 by the British astronomer Herbert Hall Turner. Named as a portmanteau of the parallax of one arcsecond, it was defined to make calculations of astronomical distances from only their raw observational data quick and easy for astronomers. For this reason, it is the unit preferred in astronomy and astrophysics, though the light-year remains prominent in popular science texts and common usage. Although parsecs are used for the shorter distances within the Milky Way, multiples of parsecs are required for the larger scales in the universe, including kiloparsecs for the more distant objects within and around the Milky Way, megaparsecs for mid-distance galaxies, gigaparsecs for many quasars and the most distant galaxies.
In August 2015, the IAU passed Resolution B2, which, as part of the definition of a standardized absolute and apparent bolometric magnitude scale, mentioned an existing explicit definition of the parsec as 648000/π astronomical units, or 3.08567758149137×1016 metres. This corresponds to the small-angle definition of the parsec found in many contemporary astronomical references; the parsec is defined as being equal to the length of the longer leg of an elongated imaginary right triangle in space. The two dimensions on which this triangle is based are its shorter leg, of length one astronomical unit, the subtended angle of the vertex opposite that leg, measuring one arc second. Applying the rules of trigonometry to these two values, the unit length of the other leg of the triangle can be derived. One of the oldest methods used by astronomers to calculate the distance to a star is to record the difference in angle between two measurements of the position of the star in the sky; the first measurement is taken from the Earth on one side of the Sun, the second is taken half a year when the Earth is on the opposite side of the Sun.
The distance between the two positions of the Earth when the two measurements were taken is twice the distance between the Earth and the Sun. The difference in angle between the two measurements is twice the parallax angle, formed by lines from the Sun and Earth to the star at the distant vertex; the distance to the star could be calculated using trigonometry. The first successful published direct measurements of an object at interstellar distances were undertaken by German astronomer Friedrich Wilhelm Bessel in 1838, who used this approach to calculate the 3.5-parsec distance of 61 Cygni. The parallax of a star is defined as half of the angular distance that a star appears to move relative to the celestial sphere as Earth orbits the Sun. Equivalently, it is the subtended angle, from that star's perspective, of the semimajor axis of the Earth's orbit; the star, the Sun and the Earth form the corners of an imaginary right triangle in space: the right angle is the corner at the Sun, the corner at the star is the parallax angle.
The length of the opposite side to the parallax angle is the distance from the Earth to the Sun (defined as one astronomical unit, the length of the adjacent side gives the distance from the sun to the star. Therefore, given a measurement of the parallax angle, along with the rules of trigonometry, the distance from the Sun to the star can be found. A parsec is defined as the length of the side adjacent to the vertex occupied by a star whose parallax angle is one arcsecond; the use of the parsec as a unit of distance follows from Bessel's method, because the distance in parsecs can be computed as the reciprocal of the parallax angle in arcseconds. No trigonometric functions are required in this relationship because the small angles involved mean that the approximate solution of the skinny triangle can be applied. Though it may have been used before, the term parsec was first mentioned in an astronomical publication in 1913. Astronomer Royal Frank Watson Dyson expressed his concern for the need of a name for that unit of distance.
He proposed the name astron, but mentioned that Carl Charlier had suggested siriometer and Herbert Hall Turner had proposed parsec. It was Turner's proposal. In the diagram above, S represents the Sun, E the Earth at one point in its orbit, thus the distance ES is one astronomical unit. The angle SDE is one arcsecond so by definition D is a point in space at a distance of one parsec from the Sun. Through trigonometry, the distance SD is calculated as follows: S D = E S tan 1 ″ S D ≈ E S 1 ″ = 1 au 1 60 × 60 × π
A binary star is a star system consisting of two stars orbiting around their common barycenter. Systems of two or more stars are called multiple star systems; these systems when more distant appear to the unaided eye as a single point of light, are revealed as multiple by other means. Research over the last two centuries suggests that half or more of visible stars are part of multiple star systems; the term double star is used synonymously with binary star. Optical doubles are so called because the two stars appear close together in the sky as seen from the Earth, their "doubleness" depends only on this optical effect. A double star can be revealed as optical by means of differences in their parallax measurements, proper motions, or radial velocities. Most known double stars have not been studied adequately to determine whether they are optical doubles or doubles physically bound through gravitation into a multiple star system. Binary star systems are important in astrophysics because calculations of their orbits allow the masses of their component stars to be directly determined, which in turn allows other stellar parameters, such as radius and density, to be indirectly estimated.
This determines an empirical mass-luminosity relationship from which the masses of single stars can be estimated. Binary stars are detected optically, in which case they are called visual binaries. Many visual binaries have long orbital periods of several centuries or millennia and therefore have orbits which are uncertain or poorly known, they may be detected by indirect techniques, such as spectroscopy or astrometry. If a binary star happens to orbit in a plane along our line of sight, its components will eclipse and transit each other. If components in binary star systems are close enough they can gravitationally distort their mutual outer stellar atmospheres. In some cases, these close binary systems can exchange mass, which may bring their evolution to stages that single stars cannot attain. Examples of binaries are Sirius, Cygnus X-1. Binary stars are common as the nuclei of many planetary nebulae, are the progenitors of both novae and type Ia supernovae; the term binary was first used in this context by Sir William Herschel in 1802, when he wrote: If, on the contrary, two stars should be situated near each other, at the same time so far insulated as not to be materially affected by the attractions of neighbouring stars, they will compose a separate system, remain united by the bond of their own mutual gravitation towards each other.
This should be called a real double star. By the modern definition, the term binary star is restricted to pairs of stars which revolve around a common center of mass. Binary stars which can be resolved with a telescope or interferometric methods are known as visual binaries. For most of the known visual binary stars one whole revolution has not been observed yet, they are observed to have travelled along a curved path or a partial arc; the more general term double star is used for pairs of stars which are seen to be close together in the sky. This distinction is made in languages other than English. Double stars may be binary systems or may be two stars that appear to be close together in the sky but have vastly different true distances from the Sun; the latter are termed optical optical pairs. Since the invention of the telescope, many pairs of double stars have been found. Early examples include Acrux. Mizar, in the Big Dipper, was observed to be double by Giovanni Battista Riccioli in 1650; the bright southern star Acrux, in the Southern Cross, was discovered to be double by Father Fontenay in 1685.
John Michell was the first to suggest that double stars might be physically attached to each other when he argued in 1767 that the probability that a double star was due to a chance alignment was small. William Herschel began observing double stars in 1779 and soon thereafter published catalogs of about 700 double stars. By 1803, he had observed changes in the relative positions in a number of double stars over the course of 25 years, concluded that they must be binary systems. Since this time, many more double stars have been measured; the Washington Double Star Catalog, a database of visual double stars compiled by the United States Naval Observatory, contains over 100,000 pairs of double stars, including optical doubles as well as binary stars. Orbits are known for only a few thousand of these double stars, most have not been ascertained to be either true binaries or optical double stars; this can be determined by observing the relative motion of the pairs. If the motion is part of an orbit, or if the stars have similar radial velocities and the difference in their proper motions is small compared to their common proper motion, the pair is physical.
One of the tasks that remains for visual observers of double stars is to obtain sufficient observations to prove or disprove gravitational connection. Binary stars are classified into four types accordi
The Kelvin scale is an absolute thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The kelvin is the base unit of temperature in the International System of Units; until 2018, the kelvin was defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. In other words, it was defined such that the triple point of water is 273.16 K. On 16 November 2018, a new definition was adopted, in terms of a fixed value of the Boltzmann constant. For legal metrology purposes, the new definition will come into force on 20 May 2019; the Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Thomson, 1st Baron Kelvin, who wrote of the need for an "absolute thermometric scale". Unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or written as a degree; the kelvin is the primary unit of temperature measurement in the physical sciences, but is used in conjunction with the degree Celsius, which has the same magnitude.
The definition implies that absolute zero is equivalent to −273.15 °C. In 1848, William Thomson, made Lord Kelvin, wrote in his paper, On an Absolute Thermometric Scale, of the need for a scale whereby "infinite cold" was the scale's null point, which used the degree Celsius for its unit increment. Kelvin calculated; this absolute scale is known today as the Kelvin thermodynamic temperature scale. Kelvin's value of "−273" was the negative reciprocal of 0.00366—the accepted expansion coefficient of gas per degree Celsius relative to the ice point, giving a remarkable consistency to the accepted value. In 1954, Resolution 3 of the 10th General Conference on Weights and Measures gave the Kelvin scale its modern definition by designating the triple point of water as its second defining point and assigned its temperature to 273.16 kelvins. In 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol °K. Furthermore, feeling it useful to more explicitly define the magnitude of the unit increment, the 13th CGPM held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction 1/273.16 of the thermodynamic temperature of the triple point of water."In 2005, the Comité International des Poids et Mesures, a committee of the CGPM, affirmed that for the purposes of delineating the temperature of the triple point of water, the definition of the Kelvin thermodynamic temperature scale would refer to water having an isotopic composition specified as Vienna Standard Mean Ocean Water.
In 2018, Resolution A of the 26th CGPM adopted a significant redefinition of SI base units which included redefining the Kelvin in terms of a fixed value for the Boltzmann constant of 1.380649×10−23 J/K. When spelled out or spoken, the unit is pluralised using the same grammatical rules as for other SI units such as the volt or ohm; when reference is made to the "Kelvin scale", the word "kelvin"—which is a noun—functions adjectivally to modify the noun "scale" and is capitalized. As with most other SI unit symbols there is a space between the kelvin symbol. Before the 13th CGPM in 1967–1968, the unit kelvin was called a "degree", the same as with the other temperature scales at the time, it was distinguished from the other scales with either the adjective suffix "Kelvin" or with "absolute" and its symbol was °K. The latter term, the unit's official name from 1948 until 1954, was ambiguous since it could be interpreted as referring to the Rankine scale. Before the 13th CGPM, the plural form was "degrees absolute".
The 13th CGPM changed the unit name to "kelvin". The omission of "degree" indicates that it is not relative to an arbitrary reference point like the Celsius and Fahrenheit scales, but rather an absolute unit of measure which can be manipulated algebraically. In science and engineering, degrees Celsius and kelvins are used in the same article, where absolute temperatures are given in degrees Celsius, but temperature intervals are given in kelvins. E.g. "its measured value was 0.01028 °C with an uncertainty of 60 µK." This practice is permissible because the degree Celsius is a special name for the kelvin for use in expressing relative temperatures, the magnitude of the degree Celsius is equal to that of the kelvin. Notwithstanding that the official endorsement provided by Resolution 3 of the 13th CGPM states "a temperature interval may be expressed in degrees Celsius", the practice of using both °C and K is widespread throughout the scientific world; the use of SI prefixed forms of the degree Celsius to express a temperature interval has not been adopted.
In 2005 the CIPM embarked on a programme to redefine the kelvin using a more experimentally rigorous methodology. In particular, the committee proposed redefining the kelvin such that Boltzmann's constant takes the exact value 1.3806505×10−23 J/K. The committee had hoped tha
Stellar evolution is the process by which a star changes over the course of time. Depending on the mass of the star, its lifetime can range from a few million years for the most massive to trillions of years for the least massive, longer than the age of the universe; the table shows the lifetimes of stars as a function of their masses. All stars are born from collapsing clouds of gas and dust called nebulae or molecular clouds. Over the course of millions of years, these protostars settle down into a state of equilibrium, becoming what is known as a main-sequence star. Nuclear fusion powers a star for most of its life; the energy is generated by the fusion of hydrogen atoms at the core of the main-sequence star. As the preponderance of atoms at the core becomes helium, stars like the Sun begin to fuse hydrogen along a spherical shell surrounding the core; this process causes the star to grow in size, passing through the subgiant stage until it reaches the red giant phase. Stars with at least half the mass of the Sun can begin to generate energy through the fusion of helium at their core, whereas more-massive stars can fuse heavier elements along a series of concentric shells.
Once a star like the Sun has exhausted its nuclear fuel, its core collapses into a dense white dwarf and the outer layers are expelled as a planetary nebula. Stars with around ten or more times the mass of the Sun can explode in a supernova as their inert iron cores collapse into an dense neutron star or black hole. Although the universe is not old enough for any of the smallest red dwarfs to have reached the end of their lives, stellar models suggest they will become brighter and hotter before running out of hydrogen fuel and becoming low-mass white dwarfs. Stellar evolution is not studied by observing the life of a single star, as most stellar changes occur too to be detected over many centuries. Instead, astrophysicists come to understand how stars evolve by observing numerous stars at various points in their lifetime, by simulating stellar structure using computer models. Stellar evolution starts with the gravitational collapse of a giant molecular cloud. Typical giant molecular clouds are 100 light-years across and contain up to 6,000,000 solar masses.
As it collapses, a giant molecular cloud breaks into smaller pieces. In each of these fragments, the collapsing gas releases gravitational potential energy as heat; as its temperature and pressure increase, a fragment condenses into a rotating sphere of superhot gas known as a protostar. A protostar continues to grow by accretion of gas and dust from the molecular cloud, becoming a pre-main-sequence star as it reaches its final mass. Further development is determined by its mass. Mass is compared to the mass of the Sun: 1.0 M☉ means 1 solar mass. Protostars are encompassed in dust, are thus more visible at infrared wavelengths. Observations from the Wide-field Infrared Survey Explorer have been important for unveiling numerous Galactic protostars and their parent star clusters. Protostars with masses less than 0.08 M☉ never reach temperatures high enough for nuclear fusion of hydrogen to begin. These are known as brown dwarfs; the International Astronomical Union defines brown dwarfs as stars massive enough to fuse deuterium at some point in their lives.
Objects smaller than 13 MJ are classified as sub-brown dwarfs. Both types, deuterium-burning and not, shine dimly and die away cooling over hundreds of millions of years. For a more-massive protostar, the core temperature will reach 10 million kelvin, initiating the proton–proton chain reaction and allowing hydrogen to fuse, first to deuterium and to helium. In stars of over 1 M☉, the carbon–nitrogen–oxygen fusion reaction contributes a large portion of the energy generation; the onset of nuclear fusion leads quickly to a hydrostatic equilibrium in which energy released by the core maintains a high gas pressure, balancing the weight of the star's matter and preventing further gravitational collapse. The star thus evolves to a stable state, beginning the main-sequence phase of its evolution. A new star will sit at a specific point on the main sequence of the Hertzsprung–Russell diagram, with the main-sequence spectral type depending upon the mass of the star. Small cold, low-mass red dwarfs fuse hydrogen and will remain on the main sequence for hundreds of billions of years or longer, whereas massive, hot O-type stars will leave the main sequence after just a few million years.
A mid-sized yellow dwarf star, like the Sun, will remain on the main sequence for about 10 billion years. The Sun is thought to be in the middle of its main sequence lifespan; the core exhausts its supply of hydrogen and the star begins to evolve off of the main sequence. Without the outward pressure generated by the fusion of hydrogen to counteract the force of gravity the core contracts until either electron degeneracy pressure becomes sufficient to oppose gravity or the core becomes hot enough for helium fusion to begin. Which of these happens first depends upon the star's mass. What happens after a low-mass star ceases to produce energy through fusion has not been directly observed. Recent astrophysical models suggest that red dwarfs of 0.1 M☉ may stay on the main sequence for some six to twelve tril