Minute of arc

Aminute of arc (MOA), arcminute, orminute arc, isa unit of angular measurement equal to 1⁄60 of one degree.Because one degree is 1⁄360 of a circle, one minute of arcis 1⁄₂₁,₆₀₀ of a circle, or π⁄₁₀,₈₀₀ radians.It is used in fields that involve very small angles, such asastronomy, optometry, ophthalmology, optics, navigationand marksmanship.The number of square arc minutes in a completesphere is 4π

(10,800

π

)2= 466,560,000

π = approximately148,510,660 square arc minutes.A second of arc (arcsecond, arcsec) is 1⁄60 of an arcminute, 1⁄₃,₆₀₀ of a degree, 1⁄₁,₂₉₆,₀₀₀ of a circle, andπ⁄₆₄₈,₀₀₀ (about 1⁄₂₀₆,₂₆₅) of a radian. This is approximatelythe angle subtended by a U.S. dime coin at a distance of4 kilometres (about 2.5 mi).[1]

To express even smaller angles, standard SI prefixes canbe employed. In particular, the milliarcsecond, abbre-viated mas, is commonly used in astronomy.

1 Symbols and abbreviations

The standard symbol for marking the arcminute is theprime (′) (U+2032), though a single quote (') (U+0027)is commonly used where only ASCII characters are per-mitted. One arcminute is thus written 1′. It is also abbre-viated as arcmin or amin or, less commonly, the primewith a circumflex over it ( ′̂ ).The standard symbol for the arcsecond is the doubleprime (″) (U+2033), though a double quote ( extquot-edbl) (U+0022) is commonly used where only ASCIIcharacters are permitted. One arcsecond is thus written1″. It is also abbreviated as arcsec or asec.In celestial navigation, seconds of arc are rarely used incalculations, the preference usually being for degrees,minutes and decimals of a minute, written for exam-ple as 42° 25.32′ or 42° 25.322′.[2][3] This notation hasbeen carried over into marine GPS receivers, which nor-mally display latitude and longitude in the latter formatby default.[4]

2 Uses

2.1 Firearms

The arcminute is commonly found in the firearms indus-try and literature, particularly concerning the accuracy ofrifles, though the industry refers to it asminute of angle.It is especially popular with shooters familiar with theImperial measurement system because 1 MOA subtendsapproximately one inch at 100 yards, a traditional dis-tance on target ranges. Since most modern rifle scopesare adjustable in half (1⁄2), quarter (1⁄4), or eighth (1⁄8)MOA increments, also known as clicks, this makes ze-roing and adjustments much easier. For example, if thepoint of impact is 3” high and 1.5” left of the point ofaim at 100 yards, the scope needs to be adjusted 3 MOAdown, and 1.5 MOA right. Such adjustments are trivialwhen the scope’s adjustment dials have an MOA scaleprinted on them, and even figuring the right number ofclicks is relatively easy on scopes that click in fractions ofMOA.One thing to be aware of is that some scopes, includingsome higher-end models, are calibrated such that an ad-justment of 1 MOA corresponds to exactly 1 inch, ratherthan 1.047”. This is commonly known as the Shooter’sMOA (SMOA) or Inches Per Hundred Yards (IPHY).While the difference between one true MOA and oneSMOA is less than half of an inch even at 1000 yards,[5]this error compounds significantly on longer range shotsthat may require adjustment upwards of 20-30 MOA tocompensate for the bullet drop. If a shot requires an ad-justment of 20 MOA or more, the difference betweentrue MOA and SMOA will add up to 1 inch or more. Incompetitive target shooting, this might mean the differ-ence between a hit and a miss.The physical group size equivalent tomminutes of arc canbe calculated as follows: group size = tan(m⁄60) × distance.In the example previously given, for 1 minute of arc, andsubstituting 3,600 inches for 100 yards, 3,600 tan(1⁄60)= 1.047 inches. In metric units 1 MOA at 100 meters =2.908 centimeters.Sometimes, a precision firearm’s accuracy will be mea-sured in MOA. This simply means that under ideal condi-tions i.e. no wind, match-grade ammo, clean barrel, anda vise or a benchrest used to eliminate shooter error, thegun is capable of producing a group of shots whose cen-ter points (center-to-center) fit into a circle, the averagediameter of circles in several groups can be subtended bythat amount of arc. For example, a 1 MOA rifle shouldbe capable, under ideal conditions, of shooting an aver-age 1-inch groups at 100 yards. Most higher-end rifles are

1

2 2 USES

warrantied by their manufacturer to shoot under a givenMOA threshold (typically 1 MOA or better) with specificammunition and no error on the shooter’s part. For exam-ple, Remington’s M24 SniperWeapon System is requiredto shoot 0.8 MOA or better, or be rejected.Rifle manufacturers and gun magazines often refer to thiscapability as sub-MOA, meaning it shoots 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 1MOA 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 in-creases, however this will ultimately average out. If a ri-fle was truly a 1 MOA rifle, it would be just as likely thattwo consecutive shots land exactly on top of each other asthat they land 1 MOA apart. For 5 shot groups, based on95% confidence a rifle that normally shoots 1 MOA canbe expected to shoot groups between 0.58MOA and 1.47MOA, although the majority of these groups will be un-der 1 MOA. What this means in practice is if a rifle thatshoots 1” groups on average at 100 yards shoots a groupmeasuring .7” followed by a group that is 1.3” this is notstatistically abnormal.[6][7]

The Metric System counterpart of the MOA is theMil-Rad, being equal to one 1000th of the target range, laidout on a circle that has the observer as centre and the tar-get range as radius. The number ofMilRads on a full suchcircle therefore always is equal to 2 x π x 1000, regard-less the target range. Therefore 1 MOA = 0.2908 Mil-Rad. This means that an object which spans 1 MilRadon the reticle is at a range that is in meters equal to theobject’s size in millimeters (e.g. an object of 100 mm @1 Milrad is 100 meters away). So there is no conversionfactor required, contrary to the MOA system. The mark-ings on a reticle that mark MilRads are called MilDots.Such reticle is called a MilDot Reticle.

2.2 Cartography

Minutes of arc (and its subunit, seconds of arc or SOA—equal to a sixtieth of aMOA) are also used in cartographyand navigation. At sea level one minute of arc along theequator or a meridian equals approximately one Nauticalmile (1.852 km or 1.151 mi). A second of arc, one sixti-eth of this amount, is about 30meters or roughly 100 feet.The exact distance varies along meridian arcs because thefigure of the Earth is slightly oblate.Positions are traditionally given using degrees, minutes,and seconds of arcs for latitude, the arc north or southof the equator, and for longitude, the arc east or westof the Prime Meridian. Any position on or above theEarth’s reference ellipsoid can be precisely given withthis method. However, because of the somewhat clumsybase−60 nature of minutes and seconds, positions arefrequently expressed in fractional degrees only, expressedin decimal form to an equal amount of precision. De-

grees given to three decimal places (1⁄₁,₀₀₀ of a degree)have about 1⁄4 the precision of degrees-minutes-seconds(1⁄₃,₆₀₀ of a degree) and specify locations within about 120meters or 400 feet.

2.3 Property cadastral surveying

Related to cartography, property boundary surveying us-ing the metes and bounds system relies on fractions of adegree to describe property lines’ angles in reference tocardinal directions. A boundary “mete” is described witha beginning reference point, the cardinal direction Northor South followed by an angle less than 90 degrees anda second cardinal direction, and a linear distance. Theboundary runs the specified linear distance from the be-ginning point, the direction of the distance being deter-mined by rotating the first cardinal direction the specifiedangle toward the second cardinal direction. For exam-ple, North 65° 39′ 18″ West 85.69 feet would describe aline running from the starting point 85.69 feet in a direc-tion 65° 39′ 18″ (or 65.655°) away from north toward thewest.

2.4 Astronomy

Sun: max. 32.7'Sun: min. 31.6'

Moon: max. 33.5'Moon: min.29.43'

Venus: 9.7"- 66.0"Jupiter: 29.8"- 50.1"Mars: 3.5"- 25.1"Saturn: 14.5"- 20.1"Mercury: 4.5"- 13.0"Uranus: 3.3"- 4.1"Neptune:2.2"- 2.4"

Human 20/20 visual acuity:about 1' or 60"

International Space Station:max. about 1' or 60"(depends on orientation)

Letter E f rom 20/20 (eighth) row ofSnellen chart, at 20 feet: 5' tall and wide

Comparison of angular diameter of the Sun, Moon, planets andthe International Space Station. To get a true representation ofthe sizes, view the image at a distance of 103 times the width ofthe “Moon: max.” circle. For example, if this circle is 10 cm wideon your monitor, view it from 10.3 m away.

The arcminute and arcsecond are also used in astronomy.Degrees (and therefore arcminutes) are used to measuredeclination, or angular distance north or south of thecelestial equator. The arcsecond is also often used todescribe parallax, due to very small parallax angles forstellar parallax, and tiny angular diameters (e.g., Venusvaries between 10′′ and 60′′). The parallax, proper mo-

3

tion and angular diameter of a star may also be writtenin milliarcseconds (mas), or thousandths of an arcsec-ond. The parsec gets its name from “parallax second”,for those arcseconds.The ESA astrometric space probe Gaia is hoped to mea-sure star positions to 20 microarcseconds (µas) when itbegins producing catalog positions sometime after 2016.There are about 1.3 trillion µas in a circle. As seen fromEarth, one µas is about the size of a period at the end of asentence in the Apollo mission manuals left on the moon.Currently the best catalog positions of stars actually mea-sured are in terms of milliarcseconds, by the U.S. NavalObservatory. Amilliarcsecond is about the size of a dimeatop the Eiffel Tower as seen from New York City.Apart from the Sun, the star with the largest angular di-ameter from Earth is R Doradus, a red supergiant with adiameter of 0.05 arcsecond.[8] Because of the effects ofatmospheric seeing, ground-based telescopes will smearthe image of a star to an angular diameter of about 0.5arcsecond; in poor seeing conditions this increases to 1.5arcseconds or even more. The dwarf planet Pluto hasproven difficult to resolve because its angular diameteris about 0.1 arcsecond.[9] This is roughly equivalent to a(40 mm) ping-pong ball viewed at a distance of 50 miles(80 km).Space telescopes are not affected by the Earth’s atmo-sphere but are diffraction limited. For example, theHubble space telescope can reach an angular size of starsdown to about 0.1″. Techniques exist for improving see-ing on the ground. Adaptive optics, for example, can pro-duce images around 0.05 arcsecond on a 10 m class tele-scope.

2.5 Human vision

In humans, 20/20 vision is the ability to resolve a spatialpattern separated by a visual angle of one minute of arc.A 20/20 letter subtends 5 minutes of arc total.

2.6 Materials

The deviation from parallelism between two surfaces, forinstance in optical engineering, is usually measured in ar-cminutes or arcseconds.

3 Notes and references[1] Filippenko, Alex, Understanding the Universe (of The

Great Courses, on DVD), Lecture 43, time 12:05, TheTeaching Company, Chantilly, VA, USA, 2007

[2] “CELESTIAL NAVIGATION COURSE”. InternationalNavigation School. Retrieved 4 November 2010. “It is astraight forward method [to obtain a position at sea] andrequires no mathematical calculation beyond addition and

subtraction of degrees and minutes and decimals of min-utes”

[3] “Astro Navigation Syllabus”. Retrieved 4 November2010. extquotedbl[Sextant errors] are sometimes [given]in seconds of arc, which will need to be converted to dec-imal minutes when you include them in your calculation.”

[4] “Shipmate GN30”. Norinco. Retrieved 4 November2010.

[5] http://www.shootingillustrated.com/index.php/6227/mil-moa-or-inches/

[6] Wheeler, Robert E. “Statistical notes on rifle group pat-terns”. Retrieved 21 May 2009.

[7] Bramwell, Denton (January 2009). “Group TherapyThe Problem: How accurate is your rifle? extquotedbl.Varmint Hunter 69. Retrieved 21 May 2009.

[8] Some studies have shown a larger angular diameter forBetelgeuse. Various studies have produced figures of be-tween 0.042 and 0.069 arcseconds for the star’s diameter.The variability of Betelgeuse and difficulties in produc-ing a precise reading for its angular diameter make anydefinitive figure conjectural.

[9] NASA.gov Pluto Fact Sheet

4 External links• MOA: Rifle Reticles by Robert Simeone

4 5 TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

5 Text and image sources, contributors, and licenses

5.1 Text• Minute of arc Source: http://en.wikipedia.org/wiki/Minute_of_arc?oldid=608296017 Contributors: Bryan Derksen, Zundark, Tarquin,-- April, Andre Engels, PierreAbbat, Heron, B4hand, Romaq, Spiff, Michael Hardy, Wwwwolf, J'raxis, Glenn, Andres, Dysprosia, Head,Nnh, Jusjih, Twang, Robbot, Zandperl, Nilmerg, Lupo, DocWatson42, Tom harrison, Monedula, TomViza, P.T. Aufrette, Nkocharh,Lakefall, Sonjaaa, Antandrus, Elektron, Icairns, Thorwald, AliveFreeHappy, Florian Blaschke, Ponder, Ascánder, Kbh3rd, RJHall, Nigelj,Famousdog, Grutness, M3tainfo, Gene Nygaard, Klparrot, Sin-man, Graham87, Keeves, Rjwilmsi, Missmarple, ErikHaugen, Gudeldar,Psemmusa, AED, RobyWayne, Chobot, YurikBot, Shimirel, Jimp, Junky, Chris Capoccia, ENeville, MonMan, Dhollm, Kassie, Caer-wine, Blueyoshi321, Wsiegmund, Sambc, Hayden120, GMan552, Thomas Blomberg, Cmglee, SmackBot, Ma8thew, MHD, CapitalSasha,KingRaptor, Michael Patrick, Yaf, SundarBot, Decltype, Ohconfucius, Psyro, Euchiasmus, LWF, JorisvS, Bjankuloski06en, Gregorydavid,Civil Engineer III, Chrumps, Robin Kerrison, A876, Zginder, Thijs!bot, CharlotteWebb, AntiVandalBot, Ran4, JAnDbot, CosineKitty,IanOsgood, Mwarren us, Xact, DeclinedShadow, Thernlund, As530, DerHexer, .V., Cœur, Akurn, Glrx, Tgeairn, BJ Axel, J.delanoy,Nwbeeson, Uberdude85, Chapiown, Michael Angelkovich, Waraqa, Firstorm, Technopat, Hqb, Nfe, Sanjivdinakar, Otaku JD, ^demon-Bot2, Minuteofarc, UnitedStatesian, BotKung, Francis Flinch, Falcon8765, Spinningspark, MarkWolf1, SieBot, Interchange88, Adam37,Spartan-James, Ikonikre, Martarius, ClueBot, Piledhigheranddeeper, Terrorist96, Awickert, Three-quarter-ten, Thehelpfulone, DumZi-BoT, Cudakid69, RyanCross, SJSA, MatthewVanitas, Bags88, Nully, ,ماني Legobot, Yobot, User1428, Coulatssa, Rubinbot, Profanatas,Mikeskillz, Лев Дубовой, RibotBOT, Fotaun, Tavernsenses, Realimportantmail, Citation bot 1, Rapsar, Trappist the monk, Lotje, Dex-Dor, Уральский Кот, EmausBot, John of Reading, Sadalsuud, Fly by Night, ZéroBot, Lagaffe, Wayne Slam, ClueBot NG, Helvitica Bold,Mmhrmhrm, MusikAnimal, TomeHale, Ponderosa 74, Walksupright, Lindsay Hackett, Evensteven, Exoplanetaryscience, Coreyemotela,Uhmoortuhl, Monkbot, Stevesturz, Verdana Bold and Anonymous: 113

5.2 Images• File:Comparison_angular_diameter_solar_system.svg Source: http://upload.wikimedia.org/wikipedia/commons/f/f8/Comparison_angular_diameter_solar_system.svg License: CC-BY-SA-3.0 Contributors: Own work Original artist: Cmglee

• File:Folder_Hexagonal_Icon.svg Source: http://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg License: ? Con-tributors: ? Original artist: ?

• File:SI_base_unit.svg Source: http://upload.wikimedia.org/wikipedia/commons/c/c8/SI_base_unit.svg License: CC-BY-SA-3.0 Contrib-utors: I (Dono (talk)) created this work entirely by myself. Base on http://www.newscientist.com/data/images/archive/2622/26221501.jpgOriginal artist: Dono (talk)

• File:Symbol_book_class2.svg Source: http://upload.wikimedia.org/wikipedia/commons/8/89/Symbol_book_class2.svg License: CC-BY-SA-2.5 Contributors: Mad by Lokal_Profil by combining: Original artist: Lokal_Profil

5.3 Content license• Creative Commons Attribution-Share Alike 3.0