Minute and second of arc
A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol ′, is a unit of angular measurement equal to 1/60 of one degree.[1] 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, so the actual Earth circumference is very near 21600 nmi. A minute of arc is π/10800 of a radian.
For the SI units of angle, see radian and milliradian.Arcminute
Non-SI units mentioned in the SI
′, arcmin
Dimensionless with an arc length of approx. ≈ 0.2909/1000 of the radius, i.e. 0.2909 mm/m
1/60° = 0.016°
60″
π/10800 ≈ 0.000290888 rad
π·1000/10800 ≈ 0.2909 mrad
9/600g = 0.015g
1/21600
A second of arc, arcsecond (arcsec), or arc second, denoted by the symbol ″,[2] is 1/60 of an arcminute, 1/3600 of a degree,[1] 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 three-dimensional area such as on a sphere, square arcminutes or seconds may be used.
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).[6] An arcsecond 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:
History[edit]
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.[9] Each degree was subdivided into 60 minutes and each minute into 60 seconds.[10][11] 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.