Minute and second of arc
A minute of arc, arc minute, or minute arc is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn, one minute of arc is 1/21600 of a turn – it is for this reason that the Earth's circumference is exactly 21,600 nautical miles. A minute of arc is π/10800 of a radian. A second of arc, arcsecond, or arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn, π/648000 of a radian; these units originated in Babylonian astronomy as sexagesimal subdivisions of the degree. To express smaller angles, standard SI prefixes can be employed; the number of square arcminutes in a complete sphere is 4 π 2 = 466 560 000 π ≈ 148510660 square arcminutes. The names "minute" and "second" have nothing to do with the identically named units of time "minute" or "second"; the identical names reflect the ancient Babylonian number system, based on the number 60. The standard symbol for marking the arcminute is the prime, though a single quote is used where only ASCII characters are permitted.
One arcminute is thus written 1′. It is abbreviated as arcmin or amin or, less the prime with a circumflex over it; the standard symbol for the arcsecond is the double prime, though a double quote is used where only ASCII characters are permitted. One arcsecond is thus written 1″, it is abbreviated as arcsec or asec. In celestial navigation, seconds of arc are used in calculations, the preference being for degrees and decimals of a minute, for example, written as 42° 25.32′ or 42° 25.322′. This notation has been carried over into marine GPS receivers, which display latitude and longitude in the latter format by default; the full moon's average apparent size is about 31 arcminutes. An arcminute is the resolution of the human eye. An arcsecond is the angle subtended by a U. S. dime coin at a distance of 4 kilometres. An arcsecond is the angle subtended by an object of diameter 725.27 km at a distance of one astronomical unit, an object of diameter 45866916 km at one light-year, an object of diameter one astronomical unit at a distance of one parsec, by definition.
A milliarcsecond is about the size of a dime atop the Eiffel Tower. A microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth. A nanoarcsecond is about the size of a penny on Neptune's moon Triton as observed from Earth. Notable examples of size in arcseconds are: Hubble Space Telescope has calculational resolution of 0.05 arcseconds and actual resolution of 0.1 arcseconds, close to the diffraction limit. Crescent Venus measures between 66 seconds of arc. Since antiquity the arcminute and arcsecond have been used in astronomy. In the ecliptic coordinate system and longitude; the principal exception is right ascension in equatorial coordinates, measured in time units of hours and seconds. The arcsecond is often used to describe small astronomical angles such as the angular diameters of planets, the proper motion of stars, the separation of components of binary star systems, parallax, the small change of position of a star in the course of a year or of a solar system body as the Earth rotates.
These small angles may be written in milliarcseconds, or thousandths of an arcsecond. The unit of distance, the parsec, named from the parallax of one arc second, was developed for such parallax measurements, it is the distance at which the mean radius of the Earth's orbit would subtend an angle of one arcsecond. The ESA astrometric space probe Gaia, launched in 2013, can approximate star positions to 7 microarcseconds. Apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red giant with a diameter of 0.05 arcsecond. Because of the effects of atmospheric seeing, ground-based telescopes will smear the image of a star to an angular diameter of about 0.5 arcsecond. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1 arcsecond. Space telescopes are diffraction limited. For example, the Hubble Space Telescope can reach an angular size of stars down to about 0.1″. Techniques exist for improving seeing on the ground. Adaptive optics, for example, can produce images around 0.05 arcsecond on a 10 m class telescope.
Minutes and seconds of arc are used in cartography and navigation. At sea level one minute of arc
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 Milky Way; 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 and Aristillus to discover Earth's precession. In doing so, he developed the brightness scale still in use today. Hipparchus compiled a catalogue with their positions. Hipparchus's successor, included a catalogue of 1,022 stars in his work the Almagest, giving their location and brightness. In the 10th century, Abd al-Rahman al-Sufi carried out observations on the stars and described their positions and star color. Ibn Yunus observed more than 10,000 entries for the Sun's position for many years using a large astrolabe with a diameter of nearly 1.4 metres.
His observations on eclipses were still used centuries in Simon Newcomb's investigations on the motion of the Moon, while his other observations of the motions of the planets Jupiter and Saturn inspired Laplace's Obliquity of the Ecliptic and Inequalities of Jupiter and Saturn. In the 15th century, the Timurid astronomer Ulugh Beg compiled the Zij-i-Sultani, in which he catalogued 1,019 stars. Like the earlier catalogs of Hipparchus and Ptolemy, Ulugh Beg's catalogue is estimated to have been precise to within 20 minutes of arc. In the 16th century, Tycho Brahe used improved instruments, including large mural instruments, to measure star positions more than with a precision of 15–35 arcsec. Taqi al-Din measured the right ascension of the stars at the Constantinople Observatory of Taqi ad-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 Earth's axis.
His cataloguing of 3222 stars was refined in 1807 by Friedrich Bessel, the father of modern astrometry. He made the first measurement of stellar parallax: 0.3 arcsec for the binary star 61 Cygni. Being difficult to measure, only about 60 stellar parallaxes had been obtained by the end of the 19th century by use of the filar micrometer. Astrographs using astronomical photographic plates sped the process in the early 20th century. Automated plate-measuring machines and more sophisticated computer 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; this technology made astrometry less expensive. In 1989, the European Space Agency's Hipparcos satellite took astrometry into orbit, where it could be less affected by mechanical forces of the Earth and optical distortions from its atmosphere. 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 an unprecedented 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 used is USNO-B1.0, an all-sky catalogue that tracks proper motions, positions and other characteristics for over one billion stellar objects. 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. Apart from the fundamental function of providing astronomers with a reference frame to report their observations in, astrometry is fundamental for fields like celestial mechanics, stellar dynamics and galactic astronomy. In observational astronomy, astrometric techniques help identify stellar objects by their unique motions, it is instrumental for keeping time, in that UTC is the atomic time synchronized to Earth's rotation by means of exact astronomical observations.
Astrometry is an important step in the cosmic distance ladder because it establishes parallax distance estimates for stars in the Milky Way. Astrometry has been used to support claims of extrasolar planet detection by measuring the displacement the proposed planets cause in their parent star's apparent position on the sky, due to their mutual orbit around the center of mass of the system. Astrometry is more accurate in space missions that are not affected by the distorting effects of the Earth's atmosphere. NASA's planned Space Interferometry Mission was to utilize astrometric techniques to detect terrestrial planets orbiting 200 or so of the nearest solar-type stars; the European Space Agency's Gaia Mission, launched in 2013, applies astrometric techniques in its stellar census. In addition to the detection of exoplanets, it can be used to determine their mass. Astrometric measurements are used by astrophysicists to constrain certain models in celestial mechanics. By measuring the velocities of pulsars, it is possible to put a limit on the asymmetry of supernova explosions.
Proper motion is the astronomical measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the center of mass of the Solar System, compared to the abstract background of the more distant stars. The components for proper motion in the equatorial coordinate system are given in the direction of right ascension and of declination, their combined value is computed as the total proper motion. It has dimensions of angle per time arcseconds per year or milliarcseconds per year. Knowledge of the proper motion and radial velocity allows calculations of true stellar motion or velocity in space in respect to the Sun, by coordinate transformation, the motion in respect to the Milky Way. Proper motion is not "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. However, precise long-term observations show that the constellations change shape, albeit slowly, that each star has an independent motion; this motion is caused by the movement of the stars relative to the Solar System. The Sun travels in a nearly circular orbit about the center of the Milky Way at a speed of about 220 km/s at a radius of 8 kPc from the center, which can be taken as the rate of rotation of the Milky Way itself at this radius; the proper motion is a two-dimensional vector and is thus defined by two quantities: its position angle and its magnitude. The first quantity indicates the direction of the proper motion on the celestial sphere, the second quantity is the motion's magnitude expressed in arcseconds per year or milliarcsecond per year. Proper motion may alternatively be defined by the angular changes per year in the star's right ascension and declination, using a constant epoch in defining these; the components of proper motion by convention are arrived at.
Suppose an object moves from coordinates to coordinates in a time Δt. The proper motions are given by: μ α = α 2 − α 1 Δ t, μ δ = δ 2 − δ 1 Δ t; the magnitude of the proper motion μ is given by the Pythagorean theorem: μ 2 = μ δ 2 + μ α 2 ⋅ cos 2 δ, μ 2 = μ δ 2 + μ α ∗ 2, where δ is the declination. The factor in cos2δ accounts for the fact that the radius from the axis of the sphere to its surface varies as cosδ, for example, zero at the pole. Thus, the component of velocity parallel to the equator corresponding to a given angular change in α is smaller the further north the object's location; the change μα, which must be multiplied by cosδ to become a component of the proper motion, is sometimes called the "proper motion in right ascension", μδ the "proper motion in declination". If the proper motion in right ascension has been converted by cosδ, the result is designated μα*. For example, the proper motion results in right ascension in the Hipparcos Catalogue have been converted. Hence, the individual proper motions in right ascension and declination are made equivalent for straightforward calculations of various other stellar motions.
The position angle θ is related to these components by: μ sin θ = μ α cos δ = μ α ∗, μ cos θ = μ δ. 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 small and unremarkable; such stars are either faint or are distant, have changes of below 10 milliarcseconds per year, do not appear to move appreciably over many millennia. A few do have significant motions, are called high-proper motion stars. Motions can be in seemingly random directions. Two or more stars, double stars or open star clusters, which are moving in similar directions, exhibit so-called shared or common proper motion, suggesting they may be gravitationally attached or share similar motion in space. Barnard's Star has the largest proper motion of all stars, moving at 10.3 seconds of arc per year. L
In astronomy, the main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Hertzsprung and Henry Norris Russell. Stars on this band are known as main-sequence stars or dwarf stars; these are the most numerous true stars in the universe, include the Earth's Sun. After condensation and ignition of a star, it generates thermal energy in its dense core region through nuclear fusion of hydrogen into helium. During this stage of the star's lifetime, it is located on the main sequence at a position determined by its mass, but based upon its chemical composition and age; the cores of main-sequence stars are in hydrostatic equilibrium, where outward thermal pressure from the hot core is balanced by the inward pressure of gravitational collapse from the overlying layers. The strong dependence of the rate of energy generation on temperature and pressure helps to sustain this balance.
Energy generated at the core is radiated away at the photosphere. The energy is carried by either radiation or convection, with the latter occurring in regions with steeper temperature gradients, higher opacity or both; the main sequence is sometimes divided into upper and lower parts, based on the dominant process that a star uses to generate energy. Stars below about 1.5 times the mass of the Sun fuse hydrogen atoms together in a series of stages to form helium, a sequence called the proton–proton chain. Above this mass, in the upper main sequence, the nuclear fusion process uses atoms of carbon and oxygen as intermediaries in the CNO cycle that produces helium from hydrogen atoms. Main-sequence stars with more than two solar masses undergo convection in their core regions, which acts to stir up the newly created helium and maintain the proportion of fuel needed for fusion to occur. Below this mass, stars have cores that are radiative with convective zones near the surface. With decreasing stellar mass, the proportion of the star forming a convective envelope increases.
Main-sequence stars below 0.4 M☉ undergo convection throughout their mass. When core convection does not occur, a helium-rich core develops surrounded by an outer layer of hydrogen. In general, the more massive a star is, the shorter its lifespan on the main sequence. After the hydrogen fuel at the core has been consumed, the star evolves away from the main sequence on the HR diagram, into a supergiant, red giant, or directly to a white dwarf. In the early part of the 20th century, information about the types and distances of stars became more available; the spectra of stars were shown to have distinctive features. Annie Jump Cannon and Edward C. Pickering at Harvard College Observatory developed a method of categorization that became known as the Harvard Classification Scheme, published in the Harvard Annals in 1901. In Potsdam in 1906, the Danish astronomer Ejnar Hertzsprung noticed that the reddest stars—classified as K and M in the Harvard scheme—could be divided into two distinct groups; these stars are either much brighter than the Sun, or much fainter.
To distinguish these groups, he called them. The following year he began studying star clusters, he published the first plots of color versus luminosity for these stars. These plots showed a continuous sequence of stars, which he named the Main Sequence. At Princeton University, Henry Norris Russell was following a similar course of research, he was studying the relationship between the spectral classification of stars and their actual brightness as corrected for distance—their absolute magnitude. For this purpose he used a set of stars that had reliable parallaxes and many of, categorized at Harvard; when he plotted the spectral types of these stars against their absolute magnitude, he found that dwarf stars followed a distinct relationship. This allowed the real brightness of a dwarf star to be predicted with reasonable accuracy. Of the red stars observed by Hertzsprung, the dwarf stars followed the spectra-luminosity relationship discovered by Russell. However, the giant stars are much brighter than so do not follow the same relationship.
Russell proposed that the "giant stars must have low density or great surface-brightness, the reverse is true of dwarf stars". The same curve showed that there were few faint white stars. In 1933, Bengt Strömgren introduced the term Hertzsprung–Russell diagram to denote a luminosity-spectral class diagram; this name reflected the parallel development of this technique by both Hertzsprung and Russell earlier in the century. As evolutionary models of stars were developed during the 1930s, it was shown that, for stars of a uniform chemical composition, a relationship exists between a star's mass and its luminosity and radius; that is, for a given mass and composition, there is a unique solution for determining the star's radius and luminosity. This became known as the Vogt–Russell theorem. By this theorem, when a star's chemical composition and its position on the main sequence is known, so too is the star's mass and radius. A refined scheme for stellar classification was published in 1943 by William Wilson Morgan and Philip Childs Keenan.
The MK classification assigned each star a spectral type—based on the Harvard classification—and a luminosity class. The Harvard classification had been developed by assigning a different lett
The radial velocity of an object with respect to a given point is the rate of change of the distance between the object and the point. That is, the radial velocity is the component of the object's velocity that points in the direction of the radius connecting the object and the point. In astronomy, the point is taken to be the observer on Earth, so the radial velocity denotes the speed with which the object moves away from or approaches the Earth. In astronomy, radial velocity is measured to the first order of approximation by Doppler spectroscopy; the quantity obtained by this method may be called the barycentric radial-velocity measure or spectroscopic radial velocity. However, due to relativistic and cosmological effects over the great distances that light travels to reach the observer from an astronomical object, this measure cannot be transformed to a geometric radial velocity without additional assumptions about the object and the space between it and the observer. By contrast, astrometric radial velocity is determined by astrometric observations.
Light from an object with a substantial relative radial velocity at emission will be subject to the Doppler effect, so the frequency of the light decreases for objects that were receding and increases for objects that were approaching. The radial velocity of a star or other luminous distant objects can be measured by taking a high-resolution spectrum and comparing the measured wavelengths of known spectral lines to wavelengths from laboratory measurements. A positive radial velocity indicates the distance between the objects was increasing. In many binary stars, the orbital motion causes radial velocity variations of several kilometers per second; as the spectra of these stars vary due to the Doppler effect, they are called spectroscopic binaries. Radial velocity can be used to estimate the ratio of the masses of the stars, some orbital elements, such as eccentricity and semimajor axis; the same method has been used to detect planets around stars, in the way that the movement's measurement determines the planet's orbital period, while the resulting radial-velocity amplitude allows the calculation of the lower bound on a planet's mass using the binary mass function.
Radial velocity methods alone may only reveal a lower bound, since a large planet orbiting at a high angle to the line of sight will perturb its star radially as much as a much smaller planet with an orbital plane on the line of sight. It has been suggested that planets with high eccentricities calculated by this method may in fact be two-planet systems of circular or near-circular resonant orbit; the radial velocity method to detect exoplanets is based on the detection of variations in the velocity of the central star, due to the changing direction of the gravitational pull from an exoplanet as it orbits the star. When the star moves towards us, its spectrum is blueshifted, while it is redshifted when it moves away from us. By looking at the spectrum of a star—and so, measuring its velocity—it can be determined if it moves periodically due to the influence of an exoplanet companion. From the instrumental perspective, velocities are measured relative to the telescope's motion. So an important first step of the data reduction is to remove the contributions of the Earth's elliptic motion around the sun at ± 30 km/s, a monthly rotation of ± 13 m/s of the Earth around the center of gravity of the Earth-Moon system, the daily rotation of the telescope with the Earth crust around the Earth axis, up to ±460 m/s at the equator and proportional to the cosine of the telescope's geographic latitude, small contributions from the Earth polar motion at the level of mm/s, contributions of 230 km/s from the motion around the Galactic center and associated proper motions.
In the case of spectroscopic measurements corrections of the order of ±20 cm/s with respect to aberration. Proper motion Peculiar velocity Relative velocity Space velocity The Radial Velocity Equation in the Search for Exoplanets
Hipparcos was a scientific satellite of the European Space Agency, launched in 1989 and operated until 1993. It was the first space experiment devoted to precision astrometry, the accurate measurement of the positions of celestial objects on the sky; this permitted the accurate determination of proper motions and parallaxes of stars, allowing a determination of their distance and tangential velocity. When combined with radial velocity measurements from spectroscopy, this pinpointed all six quantities needed to determine the motion of stars; the resulting Hipparcos Catalogue, a high-precision catalogue of more than 118,200 stars, was published in 1997. The lower-precision Tycho Catalogue of more than a million stars was published at the same time, while the enhanced Tycho-2 Catalogue of 2.5 million stars was published in 2000. Hipparcos' follow-up mission, was launched in 2013; the word "Hipparcos" is an acronym for HIgh Precision PARallax COllecting Satellite and a reference to the ancient Greek astronomer Hipparchus of Nicaea, noted for applications of trigonometry to astronomy and his discovery of the precession of the equinoxes.
By the second half of the 20th century, the accurate measurement of star positions from the ground was running into insurmountable barriers to improvements in accuracy for large-angle measurements and systematic terms. Problems were dominated by the effects of the Earth's atmosphere, but were compounded by complex optical terms and gravitational instrument flexures, the absence of all-sky visibility. A formal proposal to make these exacting observations from space was first put forward in 1967. Although proposed to the French space agency CNES, it was considered too complex and expensive for a single national programme, its acceptance within the European Space Agency's scientific programme, in 1980, was the result of a lengthy process of study and lobbying. The underlying scientific motivation was to determine the physical properties of the stars through the measurement of their distances and space motions, thus to place theoretical studies of stellar structure and evolution, studies of galactic structure and kinematics, on a more secure empirical basis.
Observationally, the objective was to provide the positions and annual proper motions for some 100,000 stars with an unprecedented accuracy of 0.002 arcseconds, a target in practice surpassed by a factor of two. The name of the space telescope, "Hipparcos" was an acronym for High Precision Parallax Collecting Satellite, it reflected the name of the ancient Greek astronomer Hipparchus, considered the founder of trigonometry and the discoverer of the precession of the equinoxes; the spacecraft carried a single all-reflective, eccentric Schmidt telescope, with an aperture of 29 cm. A special beam-combining mirror superimposed two fields of view, 58 degrees apart, into the common focal plane; this complex mirror consisted of two mirrors tilted in opposite directions, each occupying half of the rectangular entrance pupil, providing an unvignetted field of view of about 1°×1°. The telescope used a system of grids, at the focal surface, composed of 2688 alternate opaque and transparent bands, with a period of 1.208 arc-sec.
Behind this grid system, an image dissector tube with a sensitive field of view of about 38-arc-sec diameter converted the modulated light into a sequence of photon counts from which the phase of the entire pulse train from a star could be derived. The apparent angle between two stars in the combined fields of view, modulo the grid period, was obtained from the phase difference of the two star pulse trains. Targeting the observation of some 100,000 stars, with an astrometric accuracy of about 0.002 arc-sec, the final Hipparcos Catalogue comprised nearly 120,000 stars with a median accuracy of better than 0.001 arc-sec. An additional photomultiplier system viewed a beam splitter in the optical path and was used as a star mapper, its purpose was to monitor and determine the satellite attitude, in the process, to gather photometric and astrometric data of all stars down to about 11th magnitude. These measurements were made in two broad bands corresponding to B and V in the UBV photometric system.
The positions of these latter stars were to be determined to a precision of 0.03 arc-sec, a factor of 25 less than the main mission stars. Targeting the observation of around 400,000 stars, the resulting Tycho Catalogue comprised just over 1 million stars, with a subsequent analysis extending this to the Tycho-2 Catalogue of about 2.5 million stars. The attitude of the spacecraft about its center of gravity was controlled to scan the celestial sphere in a regular precessional motion maintaining a constant inclination between the spin axis and the direction to the Sun; the spacecraft spun around its Z-axis at the rate of 11.25 revolutions/day at an angle of 43° to the Sun. The Z-axis rotated about the sun-satellite line at 6.4 revolutions/year. The spacecraft consisted of two platforms and six vertical panels, all made of aluminum honeycomb; the solar array consisted of three deployable sections. Two S-band antennas were located on the top and bottom of the spacecraft, providing an omni-directional downlink data rate of 24 kbit/s.
An attitude and orbit-control subsystem ensured correct dynamic attitude control and determination during the operational lifetim
Right ascension is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the point above the earth in question. When paired with declination, these astronomical coordinates specify the direction of a point on the celestial sphere in the equatorial coordinate system. An old term, right ascension refers to the ascension, or the point on the celestial equator that rises with any celestial object as seen from Earth's equator, where the celestial equator intersects the horizon at a right angle, it contrasts with oblique ascension, the point on the celestial equator that rises with any celestial object as seen from most latitudes on Earth, where the celestial equator intersects the horizon at an oblique angle. Right ascension is the celestial equivalent of terrestrial longitude. Both right ascension and longitude measure an angle from a primary direction on an equator. Right ascension is measured from the Sun at the March equinox i.e. the First Point of Aries, the place on the celestial sphere where the Sun crosses the celestial equator from south to north at the March equinox and is located in the constellation Pisces.
Right ascension is measured continuously in a full circle from that alignment of Earth and Sun in space, that equinox, the measurement increasing towards the east. As seen from Earth, objects noted to have 12h RA are longest visible at the March equinox. On those dates at midnight, such objects will reach their highest point. How high depends on their declination. Any units of angular measure could have been chosen for right ascension, but it is customarily measured in hours and seconds, with 24h being equivalent to a full circle. Astronomers have chosen this unit to measure right ascension because they measure a star's location by timing its passage through the highest point in the sky as the Earth rotates; the line which passes through the highest point in the sky, called the meridian, is the projection of a longitude line onto the celestial sphere. Since a complete circle contains 24h of right ascension or 360°, 1/24 of a circle is measured as 1h of right ascension, or 15°. A full circle, measured in right-ascension units, contains 24 × 60 × 60 = 86400s, or 24 × 60 = 1440m, or 24h.
Because right ascensions are measured in hours, they can be used to time the positions of objects in the sky. For example, if a star with RA = 1h 30m 00s is at its meridian a star with RA = 20h 00m 00s will be on the/at its meridian 18.5 sidereal hours later. Sidereal hour angle, used in celestial navigation, is similar to right ascension, but increases westward rather than eastward. Measured in degrees, it is the complement of right ascension with respect to 24h, it is important not to confuse sidereal hour angle with the astronomical concept of hour angle, which measures angular distance of an object westward from the local meridian. The Earth's axis rotates westward about the poles of the ecliptic, completing one cycle in about 26,000 years; this movement, known as precession, causes the coordinates of stationary celestial objects to change continuously, if rather slowly. Therefore, equatorial coordinates are inherently relative to the year of their observation, astronomers specify them with reference to a particular year, known as an epoch.
Coordinates from different epochs must be mathematically rotated to match each other, or to match a standard epoch. Right ascension for "fixed stars" near the ecliptic and equator increases by about 3.05 seconds per year on average, or 5.1 minutes per century, but for fixed stars further from the ecliptic the rate of change can be anything from negative infinity to positive infinity. The right ascension of Polaris is increasing quickly; the North Ecliptic Pole in Draco and the South Ecliptic Pole in Dorado are always at right ascension 18h and 6h respectively. The used standard epoch is J2000.0, January 1, 2000 at 12:00 TT. The prefix "J" indicates. Prior to J2000.0, astronomers used the successive Besselian epochs B1875.0, B1900.0, B1950.0. The concept of right ascension has been known at least as far back as Hipparchus who measured stars in equatorial coordinates in the 2nd century BC, but Hipparchus and his successors made their star catalogs in ecliptic coordinates, the use of RA was limited to special cases.
With the invention of the telescope, it became possible for astronomers to observe celestial objects in greater detail, provided that the telescope could be kept pointed at the object for a period of time. The easiest way to do, to use an equatorial mount, which allows the telescope to be aligned with one of its two pivots parallel to the Earth's axis. A motorized clock drive is used with an equatorial mount to cancel out the Earth's rotation; as the equatorial mount became adopted for observation, the equatorial coordinate system, which includes right ascension, was adopted at the same time for simplicity. Equatorial mounts could be pointed at objects with known right ascension and declination by the use of setting circles; the first star catalog to use right ascen