A minute of arc, arcminute (abbreviated as arcmin), arc minute, or minute arc, denoted by the symbol ′, is a unit of angular measurement equal to 1/60 of a degree. Since one degree is 1/360 of a turn, or complete rotation, one arcminute is 1/21600 of a turn. The nautical mile (nmi) was originally defined as the arc length of a minute of latitude on a spherical Earth; therefore, the actual Earth's circumference is approximately 21600 nmi. A minute of arc is π/10800 of a radian. A second of arc, arcsecond (abbreviated as arcsec), or arc second, denoted by the symbol ″, is a unit of angular measurement equal to 1/60 of a minute of arc, 1/3600 of a degree, 1/1296000 of a turn, and π/648000 (about 1/206264.8) of 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 a two-dimensional area, such as on (the surface of) a sphere, square arcminutes or seconds may be used.
Symbols and abbreviations 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 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 the latter format by default. However, degrees, minutes, seconds (DMS notation) is not uncommon.
Common examples In general, by simple trigonometry, it can be derived that the angle θ {\displaystyle \theta } subtended by an object of diameter or length d {\displaystyle d} at a distance D {\displaystyle D} is given by the following expression:
θ = 2 arctan ( d 2 D ) {\displaystyle \theta =2\arctan \left({\frac {d}{2D}}\right)}
One arcminute (1′) is the approximate distance two contours can be separated, and can still be distinguished, by a person with 20/20 vision. The average apparent diameter of the full Moon is about 31′, or 0.52°. One arcsecond (1″) is the angle subtended by:
a U.S. dime coin (0.705 in; 17.9 mm) at a distance of 3.7 kilometres (2.3 mi) object 0.485 millimetres from 100 metres, alternatively 1 millimetre from 206.265 metres. in Imperial system, object 1/16 inch viewed from 67 feet 1 3⁄4 inches 66.48 ms of stars' movement across sky (15.041″/s) an object of diameter 725.27 km at a distance of one astronomical unit (149597870.7 km) an object of diameter 45866916 km at one light-year (9460730472580.8 km) an object of diameter one astronomical unit at a distance of one parsec, per the definition of the latter. Also notable examples of size in arcseconds are:
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 crescent phase, Venus measures between 60.2 and 66 seconds of arc. One milliarcsecond (1 mas) is about the size of a half dollar (1.205 in; 30.6 mm), seen from a distance equal to that between the Washington Monument and the Eiffel Tower (around 6,300 km or 3,900 mi). 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 nickel (0.835 in; 21.2 mm) on the surface of Neptune as observed from Earth.
History The concepts of degrees, minutes, and seconds—as they relate to 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 a modern second.
Uses
Astronomy
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