A minute of arc, arcminute, or MOA is a unit of angular measurement, equal to one sixtieth (1/60) of one degree. Since one degree is defined as one three hundred sixtieth (1/360) of a circle, 1 MOA is 1/21600 of the amount of arc in a closed circle. It is used in those fields which require a unit for the expression of small angles, such as astronomy or marksmanship.
The subdivision of the minute of arc is the second of arc, or arcsecond. There are 60 arcseconds in an arcminute. Therefore, the arcsecond is 1/1296000 of a circle, or (π/648000) radians, which is approximately 1/206265 radian. The symbol for the arcsecond is the double prime (″) (
U+2033). To express even smaller angles, standard SI prefixes can be employed; in particular, the milliarcsecond, abbreviated mas, is sometimes used in astronomy.
|degree (angle)||1/360 circle||°||deg||17.4532925 mrad|
|arcminute||1/60 degree||′ (prime)||arcmin, amin, , MOA||290.8882087 µrad|
|arcsecond||1/60 arcminute||″ (double prime)||arcsec||4.8481368 µrad|
|milliarcsecond||1/1000 arcsecond||mas||4.8481368 nrad|
Calculating the physical equivalent group size equal to one minute of arc can be done using the equation: equivalent group size = tan(MOA ∕ 60)*distance. In the example previously given and substituting 3600 inches for 100 yards, tan(1 MOA ∕ 60)∙ 3600 inches = 1.0471975511966 inches.
In metric units 1 MOA at 100 meters = 2.90888208665722 centimeters.
Sometimes, a firearm's accuracy will be measured in MOA. This simply means that under ideal conditions, the gun is capable of repeatedly producing a group of shots whose center points (center-to-center) fit into a circle, the diameter of which can be subtended by that amount of arc. (E.g.: a "1 MOA rifle" should be capable, under ideal conditions, of shooting a 1-inch group at 100 yards, a "2 MOA rifle" a 2-inch group at 100 yards, etc.) Some manufacturers such as Weatherby and Cooper offer actual guarantees of real-world MOA performance.
Rifle manufacturers and gun magazines often refer to this capability as "Sub-MOA", meaning it shoots under 1 MOA. This is typically a single group of 3 to 5 shots at 100 yards, or the average of several groups. If larger samples are taken, i.e. more shots per group, then group size typically increases.
Traditionally positions are given using degrees, minutes, and seconds of angles in two measurements: one for latitude, the angle north or south of the equator; and one for longitude, the angle east or west of the Prime Meridian. Using this method, any position on or above the Earth's reference ellipsoid can be precisely given. However, because of the somewhat clumsy base-60 nature of MOA and SOA, many people now prefer to give positions using degrees only, expressed in decimal form to an equal amount of precision. Degrees, given to three decimal places (1/1000 of a degree), have about 1/4 the precision as degrees-minutes-seconds (1/3600 of a degree), and so identify locations within about 120 meters or 400 feet.
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 arcseconds. Due to 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.
Space telescopes are not affected by the Earth's atmosphere, but are diffraction limited; for example the Hubble space telescope can reach an angular size of stars down to about 0.1". Techniques exist for improving seeing on the ground, for example adaptive optics, which can give images around 0.05 arcsecond on a 10 m class telescope.
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