Arcsecond

A  minute of arc,  arcminute, or  minute arc ( MOA), is a unit of  angular measurement equal to one sixtieth ( 1 ⁄60 ) of one  degree ( circle ⁄21,600  ), or ( <sup style="line-height:1em;">π ⁄<sub style="line-height:1em;">10,800  <span style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;">)  radians<span style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;">. In turn, a  second of arc<span style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;"> or  arcsecond<span style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;"> is one sixtieth ( <span class="frac nowrap" style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;white-space:nowrap;"><sup style="line-height:1em;">1 ⁄<sub style="line-height:1em;">60 <span style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;">) of one arcminute. Since one degree is defined as one three hundred and sixtieth ( <span class="frac nowrap" style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;white-space:nowrap;"><sup style="line-height:1em;">1 ⁄<sub style="line-height:1em;">360 <span style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;">) of a rotation, one minute of arc is  <span class="frac nowrap" style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;white-space:nowrap;"><sup style="line-height:1em;">1 ⁄<sub style="line-height:1em;">21,600  <span style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;"> of a rotation. It is used in those fields which require a unit for the expression of small angles, such as  astronomy<span style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;">,  optometry<span style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;">,  ophthalmology<span style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;">,  optics<span style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;">,  navigation<span style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;"> and  marksmanship<span style="color:rgb(0,0,0);font-family:sans-serif;line-height:19px;">.

<p style="margin-top:0.4em;margin-bottom:0.5em;line-height:19px;color:rgb(0,0,0);font-family:sans-serif;">The number of square arcminutes in a complete sphere is <p style="line-height:19px;color:rgb(0,0,0);font-family:sans-serif;">or approximately 148,510,660.498 square arcminutes.

<p style="margin-top:0.4em;margin-bottom:0.5em;line-height:19px;color:rgb(0,0,0);font-family:sans-serif;">The arcsecond is  <sup style="line-height:1em;">1 ⁄<sub style="line-height:1em;">3,600  of a degree, or  <sup style="line-height:1em;">1 ⁄<sub style="line-height:1em;">1,296,000   of a circle, or ( <sup style="line-height:1em;">π ⁄<sub style="line-height:1em;">648,000  ) radians, which is approximately  <sup style="line-height:1em;">1 ⁄<sub style="line-height:1em;">206,265   radian.

<p style="margin-top:0.4em;margin-bottom:0.5em;line-height:19px;color:rgb(0,0,0);font-family:sans-serif;">To express even smaller angles, standard SI prefixes can be employed; in particular, the milliarcsecond, abbreviated mas, is used in astronomy.