Minute and second of arc

masarcsecondarc secondarcminutearcsecondsminutesMOAarcminutesmilliarcsecond
A minute of arc, arcminute (arcmin), arc minute, or minute arc is a unit of angular measurement equal to 1⁄60 of one degree.wikipedia
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Earth's circumference

circumference of the Earthcircumference of EarthEquatorial circumferences
Since one degree is 1⁄360 of a turn (or complete rotation), one minute of arc is 1⁄21,600 of a turn – it is for this reason that the Earth's circumference is almost exactly 21,600 nautical miles.
Earth's polar circumference is almost exactly 40,000 km because the metre was originally calibrated on this measurement (1/10-millionth of the distance between the poles and the equator), which is almost exactly 21,600 nautical miles (being defined as one minute of a degree – i.e. 360 multiplied by 60).

Angular unit

angular measurementsangular
A minute of arc, arcminute (arcmin), arc minute, or minute arc is a unit of angular measurement equal to 1⁄60 of one degree.
Subdivisions of the degree are minute (symbol ', 1' = 1/60°) and second {symbol ", 1" = 1/3600°}.

Degree (angle)

°degreesdegree
A minute of arc, arcminute (arcmin), arc minute, or minute arc is a unit of angular measurement equal to 1⁄60 of one degree.
Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes.

Prime (symbol)

prime symbolprimeprime mark
The standard symbol for marking the arcminute is the prime (U+2032), though a single quote (U+0027) is commonly used where only ASCII characters are permitted.
The prime symbol is commonly used to represent feet (ft) and arcminutes (arcmin).

Parsec

Mpcpckpc
an object of diameter one astronomical unit (149,597,871 km) at a distance of one parsec, by definition.
A parsec is defined as the distance at which one astronomical unit subtends an angle of one arcsecond, which corresponds to 1⁄648000 astronomical units.

Angular diameter

apparent diameterangular sizeapparent size
The full moon's average apparent size is about 31 arcminutes (or 0.52°). Apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red supergiant with a diameter of 0.05 arcsecond.
Since these angular diameters are typically small, it is common to present them in arcseconds .

Degree symbol

°degreedegree sign
In the case of degrees of angular arc, the degree symbol follows the number without any intervening space (e.g., 30°). The addition of minute and second of arc units follow the degree units, with intervening spaces between the units but no spaces between the numbers and arc symbols (e.g., 30° 12′ 5″).

Celestial navigation

astronavigationnavigationcelestial
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′.
Navigators measure distance on the globe in degrees, arcminutes and arcseconds.

Hubble Space Telescope

HubbleHSTNASA/ESA HST
Hubble Space Telescope has calculational resolution of 0.05 arcseconds and actual resolution of almost 0.1 arcseconds, which is close to the diffraction limit.
At that time ground-based telescopes were limited to resolutions of 0.5–1.0 arcseconds, compared to a theoretical diffraction-limited resolution of about 0.05 arcsec for a telescope with a mirror 2.5 m in diameter.

Light-year

light yearlight yearsly
an object of diameter 45,866,916 km at one light-year,
The unit most commonly used in professional astrometry is the parsec (symbol: pc, about 3.26 light-years; the distance at which one astronomical unit subtends an angle of one second of arc).

Eiffel Tower

the Eiffel TowerTour Eiffela tower
A milliarcsecond is about the size of a dime atop the Eiffel Tower as seen from New York City.
The task of drawing the components was complicated by the complex angles involved in the design and the degree of precision required: the position of rivet holes was specified to within 0.1 mm and angles worked out to one second of arc.

Declination

DecDec.declinations
In the ecliptic coordinate system, latitude and longitude ; in the horizon system, altitude (Alt) and azimuth (Az); and in the equatorial coordinate system, declination, are all measured in degrees, arcminutes and arcseconds.
Any units of angular measure can be used for declination, but it is customarily measured in the degrees, minutes, and seconds of sexagesimal measure, with 90° equivalent to a quarter circle.

Proper motion

proper motionsproper-motionhigh proper motion star
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, the small change of position of a star in the course of a year or of a solar system body as the Earth rotates.
It has dimensions of angle per time, typically arcseconds per year or milliarcseconds per year.

Sexagesimal

sexagesimal systembase 60base-60
These units originated in Babylonian astronomy as sexagesimal 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.
There are 60 minutes of arc in a degree, and 60 arcseconds in a minute.

Astronomical unit

AUastronomical unitsAUs
an object of diameter 725.27 km at a distance of one astronomical unit,
The parsec (parallax arcsecond) is defined in terms of the astronomical unit, being the distance of an object with a parallax of 1 arcsecond.

Parallax

trigonometric parallaxsolar parallaxmotion parallax
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, the small change of position of a star in the course of a year or of a solar system body as the Earth rotates.
The parsec (3.26 light-years) is defined as the distance for which the annual parallax is 1 arcsecond.

Geographical mile

mile (geographical)miles
At sea level one minute of arc along the equator or a meridian (indeed, any great circle) equals exactly one geographical mile along the Earth's equator or approximately one nautical mile (1852 meters, or ≈1.15078 statute miles).
The geographical mile is a unit of length determined by 1 minute of arc along the Earth's equator.

Babylonian astronomy

Babylonian astronomersBabylonianastronomer
These units originated in Babylonian astronomy as sexagesimal 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.
first Greek known to divide the circle in 360 degrees of 60 arc minutes.

Astrometry

astrometricastrometricalastrometrist
The ESA astrometric space probe Gaia, launched in 2013, can approximate star positions to 7 microarcseconds (µas).
Like the earlier catalogs of Hipparchus and Ptolemy, Ulugh Beg's catalogue is estimated to have been precise to within approximately 20 minutes of arc.

Astronomical seeing

seeingatmospheric seeingatmospheric turbulence
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; in poor seeing conditions this increases to 1.5 arcseconds or even more.
The best conditions give a seeing disk diameter of ~0.4 arcseconds and are found at high-altitude observatories on small islands such as Mauna Kea or La Palma.

Radian

radiansradmicroradian
A minute of arc is undefined⁄10,800 of a radian.
More common is arc second, which is undefined⁄648,000 rad (around 4.8481 microradians).

Gaia (spacecraft)

GaiaGaia spacecraftGaia'' spacecraft
The ESA astrometric space probe Gaia, launched in 2013, can approximate star positions to 7 microarcseconds (µas).
Determine the position, parallax, and annual proper motion of 1 billion stars with an accuracy of about 20 microarcseconds (µas) at 15 mag, and 200 µas at 20 mag.

R Doradus

R Dor
Apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red supergiant with a diameter of 0.05 arcsecond.
Having a uniform disk diameter of 0.057 ± 0.005 arcsec, it is currently believed to be the extrasolar star with the largest apparent size as viewed from Earth.

Latitude

Southlatitudeslatitudinal
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.
It is measured in degrees, minutes and seconds or decimal degrees, north or south of the equator.

Adaptive optics

adaptive optics (AO)AOadaptive optic
Adaptive optics, for example, can produce images around 0.05 arcsecond on a 10 m class telescope.
For example, an 8–10 m telescope (like the VLT or Keck) can produce AO-corrected images with an angular resolution of 30–60 milliarcsecond (mas) resolution at infrared wavelengths, while the resolution without correction is of the order of 1 arcsecond.