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
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
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.
A-type main-sequence star
An A-type main-sequence star or A dwarf star is a main-sequence star of spectral type A and luminosity class V. These stars have spectra, they have masses from 1.4 to 2.1 times the mass of the Sun and surface temperatures between 7600 and 10,000 K. Bright and nearby examples are Altair, Sirius A, Vega. A-type stars don't have a convective zone and thus aren't expected to harbor a magnetic dynamo; as a consequence, because they don't have strong stellar winds they lack a means to generate X-ray emission. The revised Yerkes Atlas system listed a dense grid of A-type dwarf spectral standard stars, but not all of these have survived to this day as standards; the "anchor points" and "dagger standards" of the MK spectral classification system among the A-type main-sequence dwarf stars, i.e. those standard stars that have remain unchanged over years and can be considered to define the system, are Vega, Gamma Ursae Majoris, Fomalhaut. The seminal review of MK classification by Morgan & Keenan didn't provide any dagger standards between types A3 V and F2 V. HD 23886 was suggested as an A5 V standard in 1978.
Richard Gray & Robert Garrison provided the most recent contributions to the A dwarf spectral sequence in a pair of papers in 1987 and 1989. They list an assortment of fast- and slow-rotating A-type dwarf spectral standards, including HD 45320, HD 88955, 2 Hydri, 21 Leonis Minoris, 44 Ceti. Besides the MK standards provided in Morgan's papers and the Gray & Garrison papers, one occasionally sees Delta Leonis listed as a standard. There are no published A6 A8 V standard stars. A-type stars are young and many emit infrared radiation beyond what would be expected from the star alone; this IR excess is attributable to dust emission from a debris disk. Surveys indicate massive planets form around A-type stars although these planets are difficult to detect using the Doppler spectroscopy method; this is because A-type stars rotate quickly, which makes it difficult to measure the small Doppler shifts induced by orbiting planets since the spectral lines are broad. However, this type of massive star evolves into a cooler red giant which rotates more and thus can be measured using the radial velocity method.
As of early 2011 about 30 Jupiter class planets have been found around evolved K-giant stars including Pollux, Gamma Cephei and Iota Draconis. Doppler surveys around a wide variety of stars indicate about 1 in 6 stars having twice the mass of the Sun are orbited by one or more Jupiter-sized planets, compared to about 1 in 16 for Sun-like stars. A-type star systems known to feature planets include Fomalhaut, HD 15082, Beta Pictoris and HD 95086 b. Star count, survey of stars B-type main-sequence star
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
Stellar parallax is the apparent shift of position of any nearby star against the background of distant objects. Created by the different orbital positions of Earth, the small observed shift is largest at time intervals of about six months, when Earth arrives at opposite sides of the Sun in its orbit, giving a baseline distance of about two astronomical units between observations; the parallax itself is considered to be half of this maximum, about equivalent to the observational shift that would occur due to the different positions of Earth and the Sun, a baseline of one astronomical unit. Stellar parallax is so difficult to detect that its existence was the subject of much debate in astronomy for hundreds of years, it was first observed in 1806 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, for the star 61 Cygni, using a Fraunhofer heliometer at Königsberg Observatory.
Once a star's parallax is known, its distance from Earth can be computed trigonometrically. But the more distant an object is, the smaller its parallax. 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; this limits the applicability of parallax as a measurement of distance to objects that are close on a galactic scale. Other techniques, such as spectral red-shift, are required to measure the distance of more remote objects. Stellar parallax measures are given in the tiny units of arcseconds, or in thousandths 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, where the other leg is 1 AU long. Because stellar parallaxes and distances all involve such skinny right triangles, a convenient trigonometric approximation can be used to convert parallaxes to distance.
The approximate distance is the reciprocal of the parallax: d ≃ 1 / p. For example, Proxima Centauri, whose parallax is 0.7687, is 1 / 0.7687 parsecs = 1.3009 parsecs distant. Stellar parallax is so small that its apparent absence was used as a scientific argument against heliocentrism during the early modern age, it is clear from Euclid's geometry that the effect would be undetectable if the stars were far enough away, but for various reasons such gigantic distances involved seemed implausible: it was one of Tycho Brahe's principal objections to Copernican heliocentrism that in order for it to be compatible with the lack of observable stellar parallax, there would have to be an enormous and unlikely void between the orbit of Saturn and the eighth sphere. 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 Earth's axis, catalogued 3222 stars. Stellar parallax is most measured using annual parallax, defined as the difference in position of a star as seen from Earth and Sun, i.e. the angle subtended at a star by the mean radius of Earth's orbit around the Sun.
The parsec is defined as the distance. Annual parallax is 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 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. Stellar parallax remains the standard for calibrating other measurement methods. Accurate calculations of distance based on stellar parallax require a measurement of the distance from Earth to the Sun, now known to exquisite accuracy based on radar reflection off the surfaces of planets.
The angles involved in these calculations are 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 that subtended by an object 2 centimeters in diameter located 5.3 kilometers away. In 1989 the satellite Hipparcos was launched for obtaining parallaxes and proper motions of nearby stars, increasing the number of stellar parallaxes measured to milliarcsecond accuracy a thousandfold. So, Hipparcos is only able to measure parallax angles for stars up to about 1,600 light-years away, a little more than one percent of the diameter of the Milky Way Galaxy; the Hubble telescope WFC3 now has a precision of 20 to 40 microarcseconds, enabling reliable distance measurements u
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