Uses Minute and second of arc

1 uses

1.1 astronomy
1.2 cartography
1.3 property cadastral surveying
1.4 firearms
1.5 human vision
1.6 materials

uses
astronomy

comparison of angular diameter of sun, moon, planets , international space station. true representation of sizes achieved when image viewed @ distance of 103 times width of moon: max. circle. example, if moon: max. circle 10 cm wide on monitor, viewing 10.3 m away show true representation of sizes.

since antiquity arcminute , arcsecond have been used in astronomy. in ecliptic coordinate system, latitude (β) , longitude (λ); in horizon system, altitude (alt) , azimuth (az); , in equatorial coordinate system, declination (δ), measured in degrees, arcminutes , arcseconds. principal exception right ascension (ra) in equatorial coordinates, measured in time units of hours, minutes, , seconds.

the arcsecond used describe small astronomical angles such angular diameters of planets (e.g. angular diameter of venus varies between 10″ , 60″), proper motion of stars, separation of components of binary star systems, , parallax, small change of position of star in course of year or of solar system body earth rotates. these small angles may written in milliarcseconds (mas), or thousandths of arcsecond. unit of distance, parsec, named parallax of 1 arcsecond, developed such parallax measurements. distance @ mean radius of earth s orbit subtend angle of 1 arcsecond.

the esa astrometric space probe gaia hoped measure star positions 20 microarcseconds (µas) when begins producing catalog positions sometime after 2016. there 1.3 trillion µas in turn. best catalog positions of stars measured in terms of milliarcseconds, u.s. naval observatory.

apart sun, star largest angular diameter earth r doradus, red supergiant diameter of 0.05 arcsecond. because of effects of atmospheric seeing, ground-based telescopes smear image of star angular diameter of 0.5 arcsecond; in poor seeing conditions increases 1.5 arcseconds or more. dwarf planet pluto has proven difficult resolve because angular diameter 0.1 arcsecond.

space telescopes not affected earth s atmosphere diffraction limited. example, hubble space telescope can reach angular size of stars down 0.1″. techniques exist improving seeing on ground. adaptive optics, example, can produce images around 0.05 arcsecond on 10 m class telescope.

cartography

minutes (′) , seconds (″) of arc used in cartography , navigation. @ sea level 1 minute of arc along equator or meridian (indeed, great circle) equals 1 geographical mile along earth s equator or approximately 1 nautical mile (1852 meters, or ≈1.15078 statute miles). second of arc, 1 sixtieth of amount, 30 meters or 100 feet. exact distance varies along meridian arcs because figure of earth oblate (bulges third of percent @ equator).

positions traditionally given using degrees, minutes, , seconds of arcs latitude, arc north or south of equator, , longitude, arc east or west of prime meridian. position on or above earth s reference ellipsoid can precisely given method. however, when inconvenient use base-60 minutes , seconds, positions expressed decimal fractional degrees equal amount of precision. degrees given 3 decimal places (1/7003100000000000000♠1000 of degree) have 1/4 precision of degrees-minutes-seconds (1/7003360000000000000♠3600 of degree) , specify locations within 120 meters or 400 feet.

property cadastral surveying

related cartography, property boundary surveying using metes , bounds system relies on fractions of degree describe property lines angles in reference cardinal directions. boundary mete described beginning reference point, cardinal direction north or south followed angle less 90 degrees , second cardinal direction, , linear distance. boundary runs specified linear distance beginning point, direction of distance being determined rotating first cardinal direction specified angle toward second cardinal direction. example, north 65° 39′ 18″ west 85.69 feet describe line running starting point 85.69 feet in direction 65° 39′ 18″ (or 65.655°) away north toward west.

firearms

example ballistic table given 7.62×51mm nato load. bullet drop , wind drift shown both in mil , minute of angle.

the arcminute commonly found in firearms industry , literature, particularly concerning accuracy of rifles, though industry refers minute of angle (moa). popular shooters familiar imperial measurement system because 1 moa subtended sphere diameter of 1.047 inches @ 100 yards (2.908 cm @ 100 m), traditional distance on u.s. target ranges. subtension linear distance, example, @ 500 yards, 1 moa subtended sphere diameter of 5.235 inches, , @ 1000 yards 1 moa subtended sphere diameter of 10.47 inches. since many modern telescopic sights adjustable in half (1/2), quarter (1/4), or eighth (1/8) moa increments, known clicks, zeroing , adjustments made counting 2, 4 , 8 clicks per moa respectively.

for example, if point of impact 3 inches high , 1.5 inches left of point of aim @ 100 yards (which instance measured using spotting scope calibrated reticle), scope needs adjusted 3 moa down, , 1.5 moa right. such adjustments trivial when scope s adjustment dials have moa scale printed on them, , figuring right number of clicks relatively easy on scopes click in fractions of moa. makes zeroing , adjustments easier:

to adjust  ⁄2 moa scope 3 moa down , 1.5 moa right, scope needs adjusted 3 × 2 = 6 clicks down , 1.5 x 2 = 3 clicks right
to adjust  ⁄4 moa scope 3 moa down , 1.5 moa right, scope needs adjusted 3 x 4 = 12 clicks down , 1.5 × 4 = 6 clicks right
to adjust  ⁄8 moa scope 3 moa down , 1.5 moa right, scope needs adjusted 3 x 8 = 24 clicks down , 1.5 × 8 = 12 clicks right

another common system of measurement in firearm scopes milliradian. zeroing mil based scope easy users familiar base ten systems. common adjustment value in mil based scopes 1/10 mil (which approximates  ⁄3 moa).

to adjust 1/10 mil scope 0.9 mil down , 0.4 mil right, scope needs adjusted 9 clicks down , 4 clicks right (which equals approximately 3 , 1.5 moa respectively).

one thing aware of moa scopes, including higher-end models, calibrated such adjustment of 1 moa on scope knobs corresponds 1 inch of impact adjustment on target @ 100 yards, rather mathematically correct 1.047 . commonly known shooter s moa (smoa) or inches per hundred yards (iphy). while difference between 1 true moa , 1 smoa less half of inch @ 1000 yards, error compounds on longer range shots may require adjustment upwards of 20-30 moa compensate bullet drop. if shot requires adjustment of 20 moa or more, difference between true moa , smoa add 1 inch or more. in competitive target shooting, might mean difference between hit , miss.

the physical group size equivalent m minutes of arc can calculated follows: group size = tan(m/60) × distance. in example given, 1 minute of arc, , substituting 3,600 inches 100 yards, 3,600 tan(1/60) ≈ 1.047 inches. in metric units 1 moa @ 100 meters ≈ 2.908 centimeters.

sometimes, precision firearm s accuracy measured in moa. means under ideal conditions i.e. no wind, match-grade ammo, clean barrel, , vise or benchrest used eliminate shooter error, gun capable of producing group of shots center points (center-to-center) fit circle, average diameter of circles in several groups can subtended amount of arc. example, 1 moa rifle should capable, under ideal conditions, of shooting average 1-inch groups @ 100 yards. higher-end rifles warrantied manufacturer shoot under given moa threshold (typically 1 moa or better) specific ammunition , no error on shooter s part. example, remington s m24 sniper weapon system required shoot 0.8 moa or better, or rejected.

rifle manufacturers , gun magazines refer capability sub-moa, meaning shoots under 1 moa. means single group of 3 5 shots @ 100 yards, or average of several groups, measure less 1 moa between 2 furthest shots in group, i.e. shots fall within 1 moa. if larger samples taken (i.e., more shots per group) group size typically increases, average out. if rifle 1 moa rifle, 2 consecutive shots land on top of each other land 1 moa apart. 5 shot groups, based on 95% confidence rifle shoots 1 moa can expected shoot groups between 0.58 moa , 1.47 moa, although majority of these groups under 1 moa. means in practice if rifle shoots 1-inch groups on average @ 100 yards shoots group measuring 0.7 inches followed group 1.3 inches not statistically abnormal.

the metric system counterpart of moa milliradian or mil, being equal 1 1000th of target range, laid out on circle has observer centre , target range radius. number of mils on full such circle therefore equal 2 × π × 1000, regardless target range. therefore, 1 moa ≈ 0.2908 mil. means object spans 1 mil on reticle @ range in meters equal object s size in millimeters (e.g. object of 100 mm @ 1 mrad 100 meters away). there no conversion factor required, contrary moa system. reticle markings (hashes or dots) spaced 1 mil apart (or fraction of mil) collectively called mil reticle. if markings round called mil-dots.

in table below conversions mil metric values exact (e.g. 0.1 mil equals 1 cm @ 100 meters), while conversions of minutes of arc both metric , imperial values approximate.

comparison of milliradian (mil) , minute of arc (moa).

(values in bold face exact. mil fractions given in tenths, more convenient practical use.)

1′ @ 100 yards equals 22619/ 21600 = 1.04717593 in ≈ 1.047 inches
1′ ≈ 0.291 mil (or 2.91 cm @ 100 m, approximately 3 cm @ 100 m)
1 mil ≈ 3.44′, 1/10 mil ≈ 1/3′
0.1 mil equals 1 cm @ 100 m, or approximately 0.36 inches @ 100 yards

human vision

in humans, 20/20 vision ability resolve spatial pattern separated visual angle of 1 minute of arc. 20/20 letter subtends 5 minutes of arc total.

materials

the deviation parallelism between 2 surfaces, instance in optical engineering, measured in arcminutes or arcseconds. in addition, arcseconds used in rocking curve (ω-scan) x ray diffraction measurements of high-quality epitaxial thin films.

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