Astrometry is the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. The information obtained by astrometric measurements provides information on the kinematics and physical origin of the Solar System and our galaxy, the history of astrometry is linked to the history of star catalogues, which gave astronomers reference points for objects in the sky so they could track their movements. This can be dated back to Hipparchus, who around 190 BC used the catalogue of his predecessors Timocharis, in doing so, he developed the brightness scale still in use today. Hipparchus compiled a catalogue with at least 850 stars and their positions, hipparchuss successor, included a catalogue of 1,022 stars in his work the Almagest, giving their location and brightness. Ibn Yunus observed more than 10,000 entries for the Suns position for years using a large astrolabe with a diameter of nearly 1.4 metres. In the 15th century, the Timurid astronomer Ulugh Beg compiled the Zij-i-Sultani, like the earlier catalogs of Hipparchus and Ptolemy, Ulugh Begs catalogue is estimated to have been precise to within approximately 20 minutes of arc.
In the 16th century, Tycho Brahe used improved instruments, including large mural instruments, to measure star positions more accurately than previously, Taqi al-Din measured the right ascension of the stars at the Istanbul observatory of Taqi al-Din using the observational clock he invented. When telescopes became commonplace, setting circles sped measurements James Bradley first tried to measure stellar parallaxes in 1729, the stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light and the nutation of the Earths axis. His cataloguing of 3222 stars was refined in 1807 by Friedrich Bessel and he made the first measurement of stellar parallax,0.3 arcsec for the binary star 61 Cygni. Being very difficult to measure, only about 60 stellar parallaxes had been obtained by the end of the 19th century, astrographs using astronomical photographic plates sped the process in the early 20th century. Automated plate-measuring machines and more sophisticated technology of the 1960s allowed more efficient compilation of star catalogues.
In the 1980s, charge-coupled devices replaced photographic plates and reduced optical uncertainties to one milliarcsecond and this technology made astrometry less expensive, opening the field to an amateur audience. In 1989, the European Space Agencys Hipparcos satellite took astrometry into orbit, operated from 1989 to 1993, Hipparcos measured large and small angles on the sky with much greater precision than any previous optical telescopes. During its 4-year run, the positions and proper motions of 118,218 stars were determined with a degree of accuracy. A new Tycho catalog drew together a database of 1,058,332 to within 20-30 mas, additional catalogues were compiled for the 23,882 double/multiple stars and 11,597 variable stars analyzed during the Hipparcos mission. Today, the catalogue most often used is USNO-B1.0, during the past 50 years,7,435 Schmidt camera plates were used to complete several sky surveys that make the data in USNO-B1.0 accurate to within 0.2 arcsec. In observational astronomy, astrometric techniques help identify stellar objects by their unique motions and it is instrumental for keeping time, in that UTC is basically the atomic time synchronized to Earths rotation by means of exact observations.
Astrometry is an important step in the distance ladder because it establishes parallax distance estimates for stars in the Milky Way
The components of proper motion in the equatorial coordinate system are measured in seconds of time for right ascension and seconds of arc in declination. Their combined value is computed as the proper motion, which is expressed in seconds of arc per year or per century. Knowledge of the motion and radial velocity allow approximate calculations of a stars true motion in space in respect to the Sun. Proper motion is not entirely proper, because it includes a component due to the motion of the Solar System itself, over the course of centuries, stars appear to maintain nearly fixed positions with respect to each other, so that they form the same constellations over historical time. Ursa Major or Crux, for example, looks nearly the same now as they did hundreds of years ago, precise long-term observations show that the constellations change shape, albeit very slowly, and that each star has an independent motion. This motion is caused by the movement of the relative to the Sun. The proper motion is a vector and is thus defined by two quantities, its position angle and its magnitude.
The first quantity indicates the direction of the motion on the celestial sphere. Proper motion may alternatively be defined by the changes per year in the stars right ascension and declination. The components of motion by convention are arrived at as follows. Suppose in a year an object moves from coordinates to coordinates, the changes of angle in seconds of arc per year are, The magnitude of the proper motion μ is given by vector addition of its components, where δ is the declination. The factor in cos δ accounts for the fact that the radius from the axis of the sphere to its surface varies as cos δ, for example, zero at the pole. Thus, the component of velocity parallel to the corresponding to a given angular change in α is smaller the further north the objects location. The change μα, which must be multiplied by cos δ to become a component of the motion, is sometimes called the proper motion in right ascension. Hence, the proper motions in right ascension and declination are made equivalent for straightforward calculations of various other stellar motions.
Position angle θ is related to these components by, Motions in equatorial coordinates can be converted to motions in galactic coordinates, for the majority of stars seen in the sky, the observed proper motions are usually small and unremarkable. Such stars are either faint or are significantly distant, have changes of below 10 milliarcseconds per year. A few do have significant motions, and are usually called high-proper motion stars, Motions can be in almost seemingly random directions
A planetary nebula, often abbreviated as PN or plural PNe, is a kind of emission nebula consisting of an expanding, glowing shell of ionized gas ejected from old red giant stars late in their lives. Herschels name for these objects was popularly adopted and has not been changed and they are a relatively short-lived phenomenon, lasting a few tens of thousands of years, compared to a typical stellar lifetime of several billion years. After most of the red giants atmosphere is dissipated, the radiation of the hot luminous core, called a planetary nebula nucleus. Absorbed ultraviolet light energises the shell of gas around the central star. Planetary nebulae likely play a role in the chemical evolution of the Milky Way by expelling elements to the interstellar medium from stars where those elements were created. Planetary nebulae are observed in distant galaxies, yielding useful information about their chemical abundances. Starting from the 1990s, Hubble Space Telescope images have revealed many planetary nebulae to have extremely complex, about one-fifth are roughly spherical, but the majority are not spherically symmetric.
The mechanisms that produce such a variety of shapes and features are not yet well understood. The first planetary nebula discovered was the Dumbbell Nebula in the constellation of Vulpecula and it was observed by Charles Messier in 1764 and listed as M27 in his catalogue of nebulous objects. To early observers with telescopes, M27 and subsequently discovered planetary nebulae resembled the giant planets like Uranus. William Herschel, discoverer of Uranus, eventually coined the term planetary nebula, the nature of planetary nebulae was unknown until the first spectroscopic observations were made in the mid-19th century. Using a prism to disperse their light, William Huggins was one of the earliest astronomers to study the spectra of astronomical objects. On August 29,1864, Huggins was the first to analyze the spectrum of a planetary nebula when he observed Cats Eye Nebula and his observations of stars showed that their spectra consisted of a continuum of radiation with many dark lines superimposed.
He found that many objects such as the Andromeda Nebula had spectra that were quite similar. Those nebulae were shown to be collections of stars now called galaxies, when Huggins looked at the Cats Eye Nebula, he found a very different spectrum. Rather than a strong continuum with absorption lines superimposed, the Cats Eye Nebula, the brightest of these was at a wavelength of 500.7 nanometres, which did not correspond with a line of any known element. At first, it was hypothesized that the line might be due to an unknown element, a similar idea had led to the discovery of helium through analysis of the Suns spectrum in 1868. While helium was isolated on Earth soon after its discovery in the spectrum of the Sun, nebulium was not
The Two Micron All-Sky Survey, or 2MASS, was an astronomical survey of the whole sky in the infrared spectrum and one of the most ambitious projects to do so. It was conducted in the infrared at distinct frequency bands near 2 micrometres. 2MASS produced a catalog with over 300 million observed objects, including minor planets of the Solar System, brown dwarfs, low-mass stars, star clusters. In addition,1 million objects were cataloged in the 2MASS Extended Source Catalog, the cataloged objects are designated with a 2MASS-prefix. The final data release for 2MASS occurred in 2003, and is served by the Infrared Science Archive, the goals of this survey included, Detection of galaxies in the Zone of Avoidance, a strip of sky obscured in visible light by our own galaxy, the Milky Way. 2MASS discovered a total of 173, including 2MASS 0939-2448, 2MASS 0415-0935, 2M1207, an extensive survey of low mass stars, the most common type of star both in our own galaxy and others. Cataloging of all detected stars and galaxies, Infrared measurements from the 2MASS survey have been particularly effective at unveiling previously undiscovered star clusters.
Numerical descriptions of point sources and extended sources were cataloged by automated computer programs to a limiting magnitude of about 14. More than 300 million point sources and 1 million extended sources were cataloged, the resulting data and images from the survey are currently in the public domain, and may be accessed online for free by anyone. There is a list of 2MASS science publications with links to free pre-publication copies of the papers, 2MASS is sponsored by the University of Massachusetts Amherst, the Infrared Processing and Analysis Center, NASA, and the National Science Foundation. Category, 2MASS objects 2MASS at IPAC 2MASS at UMass 2MASS Atlas Image Gallery, Miscellaneous Objects Low-Mass Stars and Brown Dwarfs in 2MASS 2MASS All-Sky Release Database
Stellar parallax is parallax on an interstellar scale, the apparent shift of position of any nearby star against the background of distant objects. Stellar parallax is so difficult to detect that its existence was the subject of debate in astronomy for thousands of years. It was first observed by Giuseppe Calandrelli who reported parallax in α-Lyrae in his work Osservazione e riflessione sulla parallasse annua dall’alfa della Lira, in 1838 Friedrich Bessel made the first successful parallax measurement ever, for the star 61 Cygni, using a Fraunhofer heliometer at Königsberg Observatory. Once a stars parallax is known, its distance from Earth can be computed trigonometrically, but the more distant an object is, the smaller its parallax. Even with 21st-century techniques in astrometry, the limits of accurate measurement make distances farther away than about 100 parsecs too approximate to be useful when obtained by this technique. Relatively close on a scale, the applicability of stellar parallax leaves most astronomical distance measurements to be calculated by spectral red-shift or other methods.
Stellar parallax measures are given in the units of arcseconds. The distance unit parsec is defined as the length of the leg of a right triangle adjacent to the angle of one arcsecond at one vertex, because stellar parallaxes and distances all involve such skinny right triangles, a convenient trigonometric approximation can be used to convert parallaxes to distance. The distance is simply the reciprocal of the parallax, d =1 / p, for example, Proxima Centauri, whose parallax is 0.7687, is 1 /0.7687 =1.3009 parsecs distant. Stellar parallax is so small that its apparent absence was used as an argument against heliocentrism during the early modern age. James Bradley first tried to measure stellar parallaxes in 1729, the stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light, the nutation of Earth’s axis, and catalogued 3222 stars. The parsec is defined as the distance for which the annual parallax is 1 arcsecond, annual parallax is normally measured by observing the position of a star at different times of the year as Earth moves through its orbit.
Measurement of annual parallax was the first reliable way to determine the distances to the closest stars, the first successful measurements of stellar parallax were made by Friedrich Bessel in 1838 for the star 61 Cygni using a heliometer. Being very difficult to measure, only about 60 stellar parallaxes had been obtained by the end of the 19th century, astrographs using astronomical photographic plates sped the process in the early 20th century. Automated plate-measuring machines and more sophisticated technology of the 1960s allowed more efficient compilation of star catalogues. In the 1980s, charge-coupled devices replaced photographic plates and reduced optical uncertainties to one milliarcsecond, stellar parallax remains the standard for calibrating other measurement methods. The angles involved in these calculations are very small and thus difficult to measure, the nearest star to the Sun, Proxima Centauri, has a parallax of 0.7687 ±0.0003 arcsec. This angle is approximately that subtended by an object 2 centimeters in diameter located 5.3 kilometers away
The solar mass is a standard unit of mass in astronomy, equal to approximately 1.99 ×1030 kilograms. It is used to indicate the masses of stars, as well as clusters, nebulae. It is equal to the mass of the Sun, about two kilograms, M☉ = ×1030 kg The above mass is about 332946 times the mass of Earth. Because Earth follows an orbit around the Sun, its solar mass can be computed from the equation for the orbital period of a small body orbiting a central mass. The value he obtained differs by only 1% from the modern value, the diurnal parallax of the Sun was accurately measured during the transits of Venus in 1761 and 1769, yielding a value of 9″. From the value of the parallax, one can determine the distance to the Sun from the geometry of Earth. The first person to estimate the mass of the Sun was Isaac Newton, in his work Principia, he estimated that the ratio of the mass of Earth to the Sun was about 1/28700. Later he determined that his value was based upon a faulty value for the solar parallax and he corrected his estimated ratio to 1/169282 in the third edition of the Principia.
The current value for the parallax is smaller still, yielding an estimated mass ratio of 1/332946. As a unit of measurement, the solar mass came into use before the AU, the mass of the Sun has been decreasing since the time it formed. This occurs through two processes in nearly equal amounts, first, in the Suns core, hydrogen is converted into helium through nuclear fusion, in particular the p–p chain, and this reaction converts some mass into energy in the form of gamma ray photons. Most of this energy eventually radiates away from the Sun, high-energy protons and electrons in the atmosphere of the Sun are ejected directly into outer space as a solar wind. The original mass of the Sun at the time it reached the main sequence remains uncertain, the early Sun had much higher mass-loss rates than at present, and it may have lost anywhere from 1–7% of its natal mass over the course of its main-sequence lifetime. The Sun gains a small amount of mass through the impact of asteroids. However, as the Sun already contains 99.
86% of the Solar Systems total mass, M☉ G / c2 ≈1.48 km M☉ G / c3 ≈4.93 μs I. -J. A Bright Young Sun Consistent with Helioseismology and Warm Temperatures on Ancient Earth and Mars
A maser is a device that produces coherent electromagnetic waves through amplification by stimulated emission. The first maser was built by Charles H. Townes, James P. Gordon, Nikolay Basov and Alexander Prokhorov were awarded the 1964 Nobel Prize in Physics for theoretical work leading to the maser. Masers are used as the device in atomic clocks, and as extremely low-noise microwave amplifiers in radio telescopes. Modern masers can be designed to generate electromagnetic waves at not only microwave frequencies but radio, for this reason Charles Townes suggested replacing microwave with the word molecular as the first word in the acronym maser. The laser works by the principle as the maser. The maser was the forerunner of the laser, inspiring theoretical work by Townes, when the coherent optical oscillator was first imagined in 1957, it was originally called the optical maser. This was ultimately changed to laser for Light Amplification by Stimulated Emission of Radiation, Gordon Gould is credited with creating this acronym in 1957.
Independently, Charles Hard Townes, James P. Gordon, and H. J. Zeiger built the first ammonia maser at Columbia University in 1953. This device used stimulated emission in a stream of energized ammonia molecules to produce amplification of microwaves at a frequency of about 24.0 gigahertz. Townes worked with Arthur L. Schawlow to describe the principle of the maser, or laser. For their research in the field of stimulated emission, the maser is based on the principle of stimulated emission proposed by Albert Einstein in 1917. When atoms have been induced into an energy state, they can amplify radiation at a frequency particular to the element or molecule used as the masing medium. By putting such a medium in a resonant cavity, feedback is created that can produce coherent radiation. This development could lead to wide range of new applications for maser technology, including communications, Masers serve as high precision frequency references. These atomic frequency standards are one of the forms of atomic clocks.
They are often used as low-noise microwave amplifiers in radio telescopes, as of 2012, the most important type of maser is the hydrogen maser which is currently used as an atomic frequency standard. Together with other kinds of clocks, these help make up the International Atomic Time standard. This is the time scale coordinated by the International Bureau of Weights
The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is used as an estimate of a bodys surface temperature when the bodys emissivity curve is not known. When the stars or planets net emissivity in the relevant wavelength band is less than unity, the net emissivity may be low due to surface or atmospheric properties, including greenhouse effect. Notice that the luminosity of a star is L =4 π R2 σ T e f f 4. The definition of the radius is obviously not straightforward. More rigorously the effective temperature corresponds to the temperature at the radius that is defined by a value of the Rosseland optical depth within the stellar atmosphere. The effective temperature and the bolometric luminosity are the two fundamental physical parameters needed to place a star on the Hertzsprung–Russell diagram, both effective temperature and bolometric luminosity depend on the chemical composition of a star.
The effective temperature of our Sun is around 5780 kelvin, stars have a decreasing temperature gradient, going from their central core up to the atmosphere. The core temperature of the temperature at the centre of the sun where nuclear reactions take place—is estimated to be 15,000,000 K. The effective temperature of a star indicates the amount of heat that the star radiates per unit of surface area, from the warmest surfaces to the coolest is the sequence of star types known as O, B, A, F, G, K, and M. The effective temperature of a planet can be calculated by equating the power received by the planet with the emitted by a blackbody of temperature T. Take the case of a planet at a distance D from the star and we allow the planet to reflect some of the incoming radiation by incorporating a parameter called the albedo. An albedo of 1 means that all the radiation is reflected, the effective temperature for Jupiter from this calculation is 112 K and 51 Pegasi b is 1258 K. A better estimate of effective temperature for some planets, such as Jupiter, the actual temperature depends on albedo and atmosphere effects.
The actual temperature from spectroscopic analysis for HD209458 b is 1130 K, the internal heating within Jupiter raises the effective temperature to about 152 K. The surface temperature of a planet can be estimated by modifying the effective-temperature calculation to account for emissivity and this area intercepts some of the power which is spread over the surface of a sphere of radius D. We allow the planet to some of the incoming radiation by incorporating a parameter a called the albedo. An albedo of 1 means that all the radiation is reflected, there is a factor ε, which is the emissivity and represents atmospheric effects
A white dwarf, called a degenerate dwarf, is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense, its mass is comparable to that of the Sun, a white dwarfs faint luminosity comes from the emission of stored thermal energy, no fusion takes place in a white dwarf wherein mass is converted to energy. The nearest known white dwarf is Sirius B, at 8.6 light years, there are currently thought to be eight white dwarfs among the hundred star systems nearest the Sun. The unusual faintness of white dwarfs was first recognized in 1910, the name white dwarf was coined by Willem Luyten in 1922. The universe has not existed long enough to experience a white dwarf releasing all of its energy as it will take many billions of years. If a red giant has insufficient mass to generate the temperatures, around 1 billion K, required to fuse carbon. After such a star sheds its outer layers and forms a planetary nebula, it will leave behind a core, white dwarfs are composed of carbon and oxygen.
If the mass of the progenitor is between 8 and 10.5 solar masses, the temperature will be sufficient to fuse carbon but not neon. Stars of very low mass will not be able to fuse helium, the material in a white dwarf no longer undergoes fusion reactions, so the star has no source of energy. As a result, it support itself by the heat generated by fusion against gravitational collapse. A carbon-oxygen white dwarf that approaches this limit, typically by mass transfer from a companion star. A white dwarf is very hot when it forms, but because it has no source of energy, it will gradually radiate its energy and this means that its radiation, which initially has a high color temperature, will lessen and redden with time. Over a very time, a white dwarf will cool. The stars low temperature means it will no longer emit significant heat or light, and it will become a cold black dwarf. Because the length of time it takes for a dwarf to reach this state is calculated to be longer than the current age of the universe.
The oldest white dwarfs still radiate at temperatures of a few thousand kelvins, the pair 40 Eridani B/C was discovered by William Herschel on 31 January 1783, p.73 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. In 1939, Russell looked back on the discovery, p.1 I was visiting my friend and generous benefactor and this piece of apparently routine work proved very fruitful—it led to the discovery that all the stars of very faint absolute magnitude were of spectral class M
A star catalogue or star catalog, is an astronomical catalogue that lists stars. In astronomy, many stars are referred to simply by catalogue numbers, there are a great many different star catalogues which have been produced for different purposes over the years, and this article covers only some of the more frequently quoted ones. Star catalogues were compiled by many different ancient peoples, including the Babylonians, Chinese, most modern catalogues are available in electronic format and can be freely downloaded from space agencies data center. Completeness and accuracy is described by the weakest apparent magnitude V, from their existing records, it is known that the ancient Egyptians recorded the names of only a few identifiable constellations and a list of thirty-six decans that were used as a star clock. They are better known by their Assyrian-era name Three Stars Each and these star catalogues, written on clay tablets, listed thirty-six stars, twelve for Anu along the celestial equator, twelve for Ea south of that, and twelve for Enlil to the north.
In Ancient Greece, the astronomer and mathematician Eudoxus laid down a set of the classical constellations around 370 BC. His catalogue Phaenomena, rewritten by Aratus of Soli between 275 and 250 BC as a poem, became one of the most consulted astronomical texts in antiquity. It contains descriptions of the positions of the stars, the shapes of the constellations, approximately in the 3rd century BC, the Greek astronomers Timocharis of Alexandria and Aristillus created another star catalogue. Hipparchus completed his star catalogue in 129 BC, which he compared to Timocharis and this led him to determine the first value of the precession of the equinoxes. In the 2nd century, Ptolemy of Roman Egypt published a star catalogue as part of his Almagest, ptolemys catalogue was based almost entirely on an earlier one by Hipparchus. It remained the star catalogue in the Western and Arab worlds for over eight centuries. The earliest known inscriptions for Chinese star names were written on oracle bones, sources dating from the Zhou Dynasty which provide star names include the Zuo Zhuan, the Shi Jing, and the Canon of Yao in the Book of Documents.
The Lüshi Chunqiu written by the Qin statesman Lü Buwei provides most of the names for the twenty-eight mansions, an earlier lacquerware chest found in the Tomb of Marquis Yi of Zeng contains a complete list of the names of the twenty-eight mansions. Star catalogues are traditionally attributed to Shi Shen and Gan De, the Shi Shen astronomy is attributed to Shi Shen, and the Astronomic star observation to Gan De. It was not until the Han Dynasty that astronomers started to observe and record names for all the stars that were apparent in the night sky, not just those around the ecliptic. A star catalogue is featured in one of the chapters of the late 2nd-century-BC history work Records of the Grand Historian by Sima Qian and contains the schools of Shi Shen and Gan Des work. For his Spiritual Constitution of the Universe of 120 AD, the astronomer Zhang Heng compiled a star catalogue comprising 124 constellations, Chinese constellation names were adopted by the Koreans and Japanese. A large number of star catalogues were published by Muslim astronomers in the medieval Islamic world and these were mainly Zij treatises, including Arzachels Tables of Toledo, the Maragheh observatorys Zij-i Ilkhani and Ulugh Begs Zij-i-Sultani
Stellar evolution is the process by which a star changes over the course of time. The table shows the lifetimes of stars as a function of their masses, all stars are born from collapsing clouds of gas and dust, often called nebulae or molecular clouds. Over the course of millions of years, these protostars settle down into a state of equilibrium, nuclear fusion powers a star for most of its life. Initially the energy is generated by the fusion of hydrogen atoms at the core of the main-sequence star, later, 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 gradually grow in size, passing through the subgiant stage until it reaches the red giant phase. Once a star like the Sun has exhausted its fuel, its core collapses into a dense white dwarf. Stars with around ten or more times the mass of the Sun can explode in a supernova as their inert iron cores collapse into a dense neutron star or black hole.
Stellar evolution is not studied by observing the life of a star, as most stellar changes occur too slowly to be detected. Instead, astrophysicists come to understand how stars evolve by observing numerous stars at various points in their lifetime, in June 2015, astronomers reported evidence for Population III stars in the Cosmos Redshift 7 galaxy at z =6.60. Stellar evolution starts with the collapse of a giant molecular cloud. Typical giant molecular clouds are roughly 100 light-years across and contain up to 6,000,000 solar masses, as it collapses, a giant molecular cloud breaks into smaller and 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, further development is determined by its mass. Protostars are encompassed in dust, and are more readily visible at infrared wavelengths.
Observations from the Wide-field Infrared Survey Explorer have been important for unveiling numerous Galactic protostars. Protostars with masses less than roughly 0.08 M☉ never reach 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 slowly, cooling gradually over hundreds of millions of years