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61-432: This star has two Bayer designations : β Tauri (Latinised to Beta Tauri) and γ Aurigae (Latinised to Gamma Aurigae). Ptolemy considered the star to be shared by Auriga , and Johann Bayer assigned it a designation in both constellations. When the modern constellation boundaries were fixed in 1930, the designation γ Aurigae largely dropped from use. The traditional name Elnath , variously El Nath or Alnath , comes from

122-529: A 1 MOA rifle should be capable, under ideal conditions, of repeatably shooting 1-inch groups at 100 yards. Most higher-end rifles are warrantied by their manufacturer to shoot under a given MOA threshold (typically 1 MOA or better) with specific ammunition and no error on the shooter's part. For example, Remington's M24 Sniper Weapon System is required to shoot 0.8 MOA or better, or be rejected from sale by quality control . Rifle manufacturers and gun magazines often refer to this capability as sub-MOA , meaning

183-416: A to avoid confusion with α ). However, a number of stars in southern constellations have uppercase letter designations, like B Centauri and G Scorpii . These letters were assigned by later astronomers, notably Lacaille in his Coelum Australe Stelliferum and Gould in his Uranometria Argentina . Lacaille followed Bayer's use of Greek letters, but this was insufficient for many constellations. He used first

244-495: A visual angle of one minute of arc, from a distance of twenty feet . A 20/20 letter subtends 5 minutes of arc total. The deviation from parallelism between two surfaces, for instance in optical engineering , is usually measured in arcminutes or arcseconds. In addition, arcseconds are sometimes used in rocking curve (ω-scan) x ray diffraction measurements of high-quality epitaxial thin films. Some measurement devices make use of arcminutes and arcseconds to measure angles when

305-546: A "SrCrEu star" or even an Ap star . Its limb-darkened angular diameter has been measured at 1.090 ± 0.076  mas . At a distance of 41.1 pc , this corresponds to a linear radius of 4.82 ± 0.34  R ☉ . At the southern edge of the narrow plane of the Milky Way Galaxy a few degrees west of the galactic anticenter , β Tauri figures (appears) as a foreground object south of many nebulae and star clusters such as M36 , M37 , and M38 . It

366-513: A Latin letter (A, b, c, etc.) to each star he catalogued, combined with the Latin name of the star's parent constellation in genitive (possessive) form. The constellation name is frequently abbreviated to a standard three-letter form. For example, Aldebaran in the constellation Taurus (the Bull) is designated α Tauri (abbreviated α Tau , pronounced Alpha Tauri ), which means "Alpha of

427-687: A circle with a diameter of 1.047 inches (which is often rounded to just 1 inch) at 100 yards (2.66 cm at 91 m or 2.908 cm at 100 m), a traditional distance on American target ranges . The subtension is linear with the distance, for example, at 500 yards, 1 MOA subtends 5.235 inches, and at 1000 yards 1 MOA subtends 10.47 inches. Since many modern telescopic sights are adjustable in half ( ⁠ 1 / 2 ⁠ ), quarter ( ⁠ 1 / 4 ⁠ ) or eighth ( ⁠ 1 / 8 ⁠ ) MOA increments, also known as clicks , zeroing and adjustments are made by counting 2, 4 and 8 clicks per MOA respectively. For example, if

488-459: A degree) and specify locations within about 120 metres (390 feet). For navigational purposes positions are given in degrees and decimal minutes, for instance The Needles lighthouse is at 50º 39.734’N 001º 35.500’W. Related to cartography, property boundary surveying using the metes and bounds system and cadastral surveying relies on fractions of a degree to describe property lines' angles in reference to cardinal directions . A boundary "mete"

549-560: A degree/day in the Earth's annual rotation around the Sun, which is off by roughly 1%. The same ratios hold for seconds, due to the consistent factor of 60 on both sides. The arcsecond is also often used to describe small astronomical angles such as the angular diameters of planets (e.g. the angular diameter of Venus which varies between 10″ and 60″); the proper motion of stars; the separation of components of binary star systems ; and parallax ,

610-491: A different constellation. Bayer's Gamma and Omicron Scorpii, for example, were later reassigned from Scorpius to Libra and given the new names Sigma and Upsilon Librae . (To add to the confusion, the star now known as Omicron Scorpii was not named by Bayer but was assigned the designation o Scorpii (Latin lowercase 'o') by Lacaille—which later astronomers misinterpreted as omicron once Bayer's omicron had been reassigned to Libra.) A few stars no longer lie (according to

671-581: A distance of 0.1 ″ , but not confirmed by other observers. Radial velocity measurements indicate that Beta Tauri is a single-lined spectroscopic binary , but there is no published information about the companion or orbit. Bayer designation A Bayer designation is a stellar designation in which a specific star is identified by a Greek or Latin letter followed by the genitive form of its parent constellation's Latin name. The original list of Bayer designations contained 1,564 stars. The brighter stars were assigned their first systematic names by

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732-510: A double quote " (U+0022) is commonly used where only ASCII characters are permitted. One arcsecond is thus written as 1″. It is also abbreviated as arcsec or asec . In celestial navigation , seconds of arc are rarely used in calculations, the preference usually being for degrees, minutes, 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 and aviation GPS receivers, which normally display latitude and longitude in

793-422: A fraction of a mrad) are collectively called a mrad reticle. If the markings are round they are called mil-dots . In the table below conversions from mrad to metric values are exact (e.g. 0.1 mrad equals exactly 10 mm at 100 metres), while conversions of minutes of arc to both metric and imperial values are approximate. In humans, 20/20 vision is the ability to resolve a spatial pattern separated by

854-484: A group measuring 0.7 inches followed by a group that is 1.3 inches, this is not statistically abnormal. The metric system counterpart of the MOA is the milliradian (mrad or 'mil'), being equal to 1 ⁄ 1000 of the target range, laid out on a circle that has the observer as centre and the target range as radius. The number of milliradians on a full such circle therefore always is equal to 2 × π × 1000, regardless

915-400: A gun consistently shooting groups under 1 MOA. This means that a single group of 3 to 5 shots at 100 yards, or the average of several groups, will measure less than 1 MOA between the two furthest shots in the group, i.e. all shots fall within 1 MOA. If larger samples are taken (i.e., more shots per group) then group size typically increases, however this will ultimately average out. If a rifle

976-455: A line running from the starting point 85.69 feet in a direction 65° 39′ 18″ (or 65.655°) away from north toward the west. The arcminute is commonly found in the firearms industry and literature, particularly concerning the precision of rifles , though the industry refers to it as minute of angle (MOA). It is especially popular as a unit of measurement with shooters familiar with the imperial measurement system because 1 MOA subtends

1037-431: A modern second. Since antiquity, the arcminute and arcsecond have been used in astronomy : in the ecliptic coordinate system as latitude (β) and longitude (λ); in the horizon system as altitude (Alt) and azimuth (Az); and in the equatorial coordinate system as declination (δ). All are measured in degrees, arcminutes, and arcseconds. The principal exception is right ascension (RA) in equatorial coordinates, which

1098-468: A precision-oriented firearm's performance will be measured in MOA. This simply means that under ideal conditions (i.e. no wind, high-grade ammo, clean barrel, and a stable mounting platform such as a vise or a benchrest used to eliminate shooter error), the gun is capable of producing a group of shots whose center points (center-to-center) fit into a circle, the average diameter of circles in several groups can be subtended by that amount of arc. For example,

1159-521: A radian. These units originated in Babylonian astronomy as sexagesimal (base 60) subdivisions of the degree; they are used in fields that involve very small angles, such as astronomy , optometry , ophthalmology , optics , navigation , land surveying , and marksmanship . To express even smaller angles, standard SI prefixes can be employed; the milliarcsecond (mas) and microarcsecond (μas), for instance, are commonly used in astronomy. For

1220-592: A table of the first two batches of names approved by the WGSN; which included Elnath for this star. In Chinese , 五車 ( Wǔ Chē ), meaning Five Chariots , refers to an asterism consisting of β Tauri, ι Aurigae , Capella , β Aurigae and θ Aurigae . Consequently, the Chinese name for β Tauri itself is 五車五 ( Wǔ Chē Wǔ ; English: Fifth of the Five Chariots .) The absolute magnitude of Beta Tauri

1281-413: A three-dimensional area such as on a sphere, square arcminutes or seconds may be used. The prime symbol ′ ( U+ 2032 ) designates the arcminute, though a single quote ' (U+0027) is commonly used where only ASCII characters are permitted. One arcminute is thus written as 1′. It is also abbreviated as arcmin or amin . Similarly, double prime ″ (U+2033) designates the arcsecond, though

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1342-704: Is 5.39 degrees north of the ecliptic , still few enough to be occultable by the Moon . Such occultations occur when the Moon's ascending node is near the March equinox , as in 2007. Most are visible only in the Southern Hemisphere , because the star is at the northern edge of the lunar occultation zone – but rarely as far north as southern California . A faint star is, angularly from our viewpoint, close enough for astronomers to consider, and guides to mention,

1403-725: Is also the angle subtended by One milliarcsecond is about the size of a half dollar, seen from a distance equal to that between the Washington Monument and the Eiffel Tower . One 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. One nanoarcsecond is about the size of a penny on Neptune 's moon Triton as observed from Earth. Also notable examples of size in arcseconds are: The concepts of degrees, minutes, and seconds—as they relate to

1464-486: Is described with a beginning reference point, the cardinal direction North or South followed by an angle less than 90 degrees and a second cardinal direction, and a linear distance. The boundary runs the specified linear distance from the beginning point, the direction of the distance being determined by rotating the first cardinal direction the specified angle toward the second cardinal direction. For example, North 65° 39′ 18″ West 85.69 feet would describe

1525-423: Is measured in time units of hours, minutes, and seconds. Contrary to what one might assume, minutes and seconds of arc do not directly relate to minutes and seconds of time, in either the rotational frame of the Earth around its own axis (day), or the Earth's rotational frame around the Sun (year). The Earth's rotational rate around its own axis is 15 minutes of arc per minute of time (360 degrees / 24 hours in day);

1586-503: Is roughly 30 metres (98 feet). The exact distance varies along meridian arcs or any other great circle arcs because the figure of the Earth is slightly oblate (bulges a third of a percent at the equator). Positions are traditionally given using degrees, minutes, and seconds of arcs for latitude , the arc north or south of the equator, and for longitude , the arc east or west of the Prime Meridian . Any position on or above

1647-626: Is that some MOA scopes, including some higher-end models, are calibrated such that an adjustment of 1 MOA on the scope knobs corresponds to exactly 1 inch of impact adjustment on a target at 100 yards, rather than the mathematically correct 1.047 inches. This is commonly known as the Shooter's MOA (SMOA) or Inches Per Hundred Yards (IPHY). While the difference between one true MOA and one SMOA is less than half of an inch even at 1000 yards, this error compounds significantly on longer range shots that may require adjustment upwards of 20–30 MOA to compensate for

1708-432: Is very near 21 600  nmi . A minute of arc is ⁠ π / 10 800 ⁠ of a radian . A second of arc , arcsecond (arcsec), or arc second , denoted by the symbol ″ , is ⁠ 1 / 60 ⁠ of an arcminute, ⁠ 1 / 3600 ⁠ of a degree, ⁠ 1 / 1 296 000 ⁠ of a turn, and ⁠ π / 648 000 ⁠ (about ⁠ 1 / 206 264 .8 ⁠ ) of

1769-535: Is −1.34, similar to another star in Taurus, Maia in the Pleiades star cluster . Like Maia, β Tauri is a B-class giant with a luminosity 700 times solar ( L ☉ ). It has evolved to become a giant star, larger and cooler than when it was on the main sequence . However, being approximately 130 light-years distant compared to Maia's estimated 360 light-years, β Tauri ranks as the second-brightest star in

1830-605: The Arabic word النطح an-naţħ , meaning "the butting" ( i.e. the bull's horns). As in many other Arabic star names, the article ال is transliterated literally as el , yet overwhelmingly in Arabic pronunciation it is assimilated to the n , meaning it is omitted. In 2016, the International Astronomical Union organized a Working Group on Star Names (WGSN) to catalog and standardize proper names for stars. The WGSN's first bulletin of July 2016 included

1891-619: The Bull". Bayer used Greek letters for the brighter stars, but the Greek alphabet has only twenty-four letters, while a single constellation may contain fifty or more stars visible to the naked eye. When the Greek letters ran out, Bayer continued with Latin letters: uppercase A , followed by lowercase b through z (omitting j and v , but o was included), for a total of another 24 letters. Bayer did not label "permanent" stars with uppercase letters (except for A , which he used instead of

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1952-451: The Earth's reference ellipsoid can be precisely given with this method. However, when it is inconvenient to use base -60 for minutes and seconds, positions are frequently expressed as decimal fractional degrees to an equal amount of precision. Degrees given to three decimal places ( ⁠ 1 / 1000 ⁠ of a degree) have about ⁠ 1 / 4 ⁠ the precision of degrees-minutes-seconds ( ⁠ 1 / 3600 ⁠ of

2013-606: The Earth's atmosphere but are diffraction limited . For example, the Hubble Space Telescope can reach an angular size of stars down to about 0.1″. Minutes (′) and seconds (″) of arc are also used in cartography and navigation . At sea level one minute of arc along the equator equals exactly one geographical mile (not to be confused with international mile or statute mile) along the Earth's equator or approximately one nautical mile (1,852 metres ; 1.151 miles ). A second of arc, one sixtieth of this amount,

2074-475: The Earth's rotational rate around the Sun (not entirely constant) is roughly 24 minutes of time per minute of arc (from 24 hours in day), which tracks the annual progression of the Zodiac. Both of these factor in what astronomical objects you can see from surface telescopes (time of year) and when you can best see them (time of day), but neither are in unit correspondence. For simplicity, the explanations given assume

2135-519: The German astronomer Johann Bayer in 1603, in his star atlas Uranometria . Bayer catalogued only a few stars too far south to be seen from Germany, but later astronomers (including Nicolas-Louis de Lacaille and Benjamin Apthorp Gould ) supplemented Bayer's catalog with entries for southern constellations. Bayer assigned a lowercase Greek letter (alpha (α), beta (β), gamma (γ), etc.) or

2196-628: The Greek letters, Bayer sometimes used the leftover Greek letters for miscellaneous labels as well. Ptolemy designated four stars as "border stars", each shared by two constellations: Alpheratz (in Andromeda and Pegasus ), Elnath (in Taurus and Auriga ), Nu Boötis ( Nu and Nu )(in Boötes and Hercules ) and Fomalhaut (in Piscis Austrinus and Aquarius ). Bayer assigned

2257-566: The Tropic of Cancer. In Cygnus , for example, Bayer's fixed stars run through g , and on this chart Bayer employs H through P as miscellaneous labels, mostly for neighboring constellations. Bayer did not intend such labels as catalog designations, but some have survived to refer to astronomical objects: P Cygni for example is still used as a designation for Nova Cyg 1600. Tycho's Star ( SN 1572 ), another "temporary star", appears as B Cassiopeiae. In charts for constellations that did not exhaust

2318-451: The angle, measured in arcseconds, of the object's apparent movement caused by parallax. The European Space Agency 's astrometric satellite Gaia , launched in 2013, can approximate star positions to 7 microarcseconds (μas). 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″. Because of the effects of atmospheric blurring , ground-based telescopes will smear

2379-564: The assignment of those letters to variable stars or have actually turned out to be variable. In most constellations, Bayer assigned Greek and Latin letters to stars within a constellation in rough order of apparent brightness , from brightest to dimmest. The order is not necessarily a precise labeling from brightest to dimmest: in Bayer's day stellar brightness could not be measured precisely. Instead, stars were traditionally assigned to one of six magnitude classes (the brightest to first magnitude,

2440-628: The bullet drop. If a shot requires an adjustment of 20 MOA or more, the difference between true MOA and SMOA will add up to 1 inch or more. In competitive target shooting, this might mean the difference between a hit and a miss. The physical group size equivalent to m minutes of arc can be calculated as follows: group size = tan( ⁠ m / 60 ⁠ ) × distance. In the example previously given, for 1 minute of arc, and substituting 3,600 inches for 100 yards, 3,600 tan( ⁠ 1 / 60 ⁠ ) ≈ 1.047 inches. In metric units 1 MOA at 100 metres ≈ 2.908 centimetres. Sometimes,

2501-491: The chain of stars π , π , π , π , π and π Orionis . The most stars given the same Bayer designation but with an extra number attached to it is Psi Aurigae . ( ψ , ψ , ψ , ψ , ψ , ψ , ψ , ψ , ψ , ψ , although according to the modern IAU constellation boundaries, ψ lies in Lynx ). Minute and second of arc A minute of arc , arcminute ( arcmin ), arc minute , or minute arc , denoted by

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2562-520: The constellation. It is a mercury-manganese star , a type of non-magnetic chemically peculiar star with unusually large signatures of some heavy elements in its spectrum . Relative to the Sun , β Tauri is notable for a high abundance of manganese , but little calcium and magnesium . However, the lack of strong mercury signatures, together with notably high levels of silicon and chromium , have led some authors to give other classifications, including as

2623-402: The designation "Alpha". A good example is the constellation Gemini , where Pollux is Beta Geminorum and the slightly dimmer Castor is Alpha Geminorum. In addition, Bayer did not always follow the magnitude class rule; he sometimes assigned letters to stars according to their location within a constellation, or the order of their rising, or to historical or mythological details. Occasionally

2684-434: The dimmest to sixth), and Bayer typically ordered stars within a constellation by class: all the first-magnitude stars (in some order), followed by all the second-magnitude stars, and so on. Within each magnitude class, Bayer made no attempt to arrange stars by relative brightness. As a result, the brightest star in each class did not always get listed first in Bayer's order—and the brightest star overall did not necessarily get

2745-452: The first three of these stars a Greek letter from both constellations: Alpha Andromedae = Delta Pegasi , Beta Tauri = Gamma Aurigae , and Nu Boötis = Psi Herculis . (He catalogued Fomalhaut only once, as Alpha Piscis Austrini .) When the International Astronomical Union (IAU) assigned definite boundaries to the constellations in 1930, it declared that stars and other celestial objects can belong to only one constellation. Consequently,

2806-405: The image of a star to an angular diameter of about 0.5″; in poor conditions this increases to 1.5″ or even more. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1″. Techniques exist for improving seeing on the ground. Adaptive optics , for example, can produce images around 0.05″ on a 10 m class telescope. Space telescopes are not affected by

2867-409: The latter format by default. The average apparent diameter of the full Moon is about 31 arcminutes, or 0.52°. One arcminute is the approximate distance two contours can be separated by, and still be distinguished by, a person with 20/20 vision . One arcsecond is the approximate angle subtended by a U.S. dime coin (18 mm) at a distance of 4 kilometres (about 2.5 mi). An arcsecond

2928-600: The latter is usually the brighter. (Betelgeuse is a variable star and can at its maximum occasionally outshine Rigel.) Bayer then repeated the procedure for the stars of the 2nd magnitude, labeling them from gamma through zeta in "top-down" (north-to-south) order. Letters as far as Latin p were used for stars of the sixth magnitude. Although Bayer did not use uppercase Latin letters (except A ) for "fixed stars", he did use them to label other items shown on his charts, such as neighboring constellations, "temporary stars", miscellaneous astronomical objects, or reference lines like

2989-591: The lowercase letters, starting with a , and if needed the uppercase letters, starting with A , thus deviating somewhat from Bayer's practice. Lacaille used the Latin alphabet three times over in the large constellation Argo Navis , once for each of the three areas that are now the constellations of Carina , Puppis and Vela . That was still insufficient for the number of stars, so he also used uppercase Latin letters such as N Velorum and Q Puppis . Lacaille assigned uppercase letters between R and Z in several constellations, but these have either been dropped to allow

3050-590: The measure of both angles and time—derive from Babylonian astronomy and time-keeping. Influenced by the Sumerians , the ancient Babylonians divided the Sun's perceived motion across the sky over the course of one full day into 360 degrees. Each degree was subdivided into 60 minutes and each minute into 60 seconds. Thus, one Babylonian degree was equal to four minutes in modern terminology, one Babylonian minute to four modern seconds, and one Babylonian second to ⁠ 1 / 15 ⁠ (approximately 0.067) of

3111-627: The modern constellation Carina . Norma's Alpha and Beta were reassigned to Scorpius and re-designated N and H Scorpii respectively, leaving Norma with no Alpha. Francis Baily died before designating an Alpha in Leo Minor , so it also has no Alpha. (The star 46 Leonis Minoris would have been the obvious candidate.) In Orion , Bayer first designated Betelgeuse and Rigel , the two 1st-magnitude stars (those of magnitude 1.5 or less), as Alpha and Beta from north to south, with Betelgeuse (the shoulder) coming ahead of Rigel (the foot), even though

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3172-484: The modern constellation boundaries) within the constellation for which they are named. The proper motion of Rho Aquilae , for example, carried it across the boundary into Delphinus in 1992. A further complication is the use of numeric superscripts to distinguish neighboring stars that Bayer (or a later astronomer) labeled with a common letter. Usually these are double stars (mostly optical doubles rather than true binary stars ), but there are some exceptions such as

3233-418: The order looks quite arbitrary. Of the 88 modern constellations, there are at least 30 in which Alpha is not the brightest star, and four of those lack a star labeled "Alpha" altogether. The constellations with no Alpha-designated star include Vela and Puppis —both formerly part of Argo Navis , whose Greek-letter stars were split among three constellations. Canopus , the former α Argus, is now α Carinae in

3294-405: The pair as a double star . This visual companion, BD+28°795B, has a position angle of 239 degrees and is separated from the main star by 33.4 arcseconds (″). Six angularly closer, even fainter stars have been found in a search for brown dwarf and planetary companions – all considered background objects. A very close companion was reported from lunar occultation measurements at

3355-403: The point of impact is 3 inches high and 1.5 inches left of the point of aim at 100 yards (which for instance could be measured by using a spotting scope with a calibrated reticle, or a target delineated for such purposes), the scope needs to be adjusted 3 MOA down, and 1.5 MOA right. Such adjustments are trivial when the scope's adjustment dials have a MOA scale printed on them, and even figuring

3416-466: The redundant second designation in each pair above has dropped out of use. Bayer assigned two stars duplicate names by mistake: Xi Arietis (duplicated as Psi Ceti ) and Kappa Ceti ( Kappa and Kappa ) (duplicated as g Tauri ). He corrected these in a later atlas, and the duplicate names were no longer used. Other cases of multiple Bayer designations arose when stars named by Bayer in one constellation were transferred by later astronomers to

3477-470: The right number of clicks is relatively easy on scopes that click in fractions of MOA. This makes zeroing and adjustments much easier: Another common system of measurement in firearm scopes is the milliradian (mrad). Zeroing an mrad based scope is easy for users familiar with base ten systems. The most common adjustment value in mrad based scopes is ⁠ 1 / 10 ⁠  mrad (which approximates 1 ⁄ 3 MOA). One thing to be aware of

3538-411: The small change of position of a star or Solar System body as the Earth revolves about the Sun. These small angles may also be written in milliarcseconds (mas), or thousandths of an arcsecond. The unit of distance called the parsec , abbreviated from the par allax angle of one arc sec ond, was developed for such parallax measurements. The distance from the Sun to a celestial object is the reciprocal of

3599-409: The symbol ′ , is a unit of angular measurement equal to ⁠ 1 / 60 ⁠ of one degree . Since one degree is ⁠ 1 / 360 ⁠ of a turn, or complete rotation , one arcminute is ⁠ 1 / 21 600 ⁠ of a turn. The nautical mile (nmi) was originally defined as the arc length of a minute of latitude on a spherical Earth, so the actual Earth's circumference

3660-419: The target range. Therefore, 1 MOA ≈ 0.2909 mrad. This means that an object which spans 1 mrad on the reticle is at a range that is in metres equal to the object's linear size in millimetres (e.g. an object of 100 mm subtending 1 mrad is 100 metres away). So there is no conversion factor required, contrary to the MOA system. A reticle with markings (hashes or dots) spaced with a one mrad apart (or

3721-446: Was truly a 1 MOA rifle, it would be just as likely that two consecutive shots land exactly on top of each other as that they land 1 MOA apart. For 5-shot groups, based on 95% confidence , a rifle that normally shoots 1 MOA can be expected to shoot groups between 0.58 MOA and 1.47 MOA, although the majority of these groups will be under 1 MOA. What this means in practice is if a rifle that shoots 1-inch groups on average at 100 yards shoots

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