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## Minute of angle (MOA)

Snippet from Wikipedia: Minute and second of arc

A minute of arc, arcminute (arcmin), arc minute, or minute arc is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn (or complete rotation), one minute of arc is 1/21600 of a turn. The nautical mile was originally defined as a minute of latitude on a hypothetical spherical Earth so the actual Earth circumference is very near 21 600 nautical miles. A minute of arc is π/10800 of a radian.

A second of arc, arcsecond (arcsec), or arc second is 1/60 of an arcminute, 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 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.

The number of square arcminutes in a complete sphere is ${\displaystyle 4\pi \left({\frac {10\,800}{\pi }}\right)^{2}={\frac {466\,560\,000}{\pi }}\approx }$ 148510660 square arcminutes (the surface area of a unit sphere in square units divided by the solid angle area subtended by a square arcminute, also in square units – so that the final result is a dimensionless number).

The fact that the terms "minute" and "second" also denote units of time derives from Babylonian astronomy, where the corresponding time-related terms denoted the duration of the Sun's apparent motion of one minute or one second of arc, respectively, through the ecliptic. In present terms, the Babylonian degree of time was four minutes long so the "minute" of time was four seconds long and the "second" 1/15 of a second.