
A minute of arc (MOA), arcminute (arcmin) or minute arc is a unit of angular measurement equal to onesixtieth () of one degree. As one degree is of a circle, one minute of arc is of a circle (or, in radians, ). It is used in fields that involve very small angles, such as astronomy, optometry, ophthalmology, optics, navigation, land surveying and marksmanship. The number of square arcminutes in a complete sphere is $4\; \backslash pi\; \backslash left(\backslash frac\backslash right)^2\; =\; \backslash frac\; =$ approximately 148,510,660 square arcminutes. A second of arc (arcsecond, arcsec) is of an arcminute, of a degree, of a circle, and (about ) of a radian. This is approximately the angle subtended by a U.S. dime coin (18mm) at a distance of .〔Filippenko, Alex, ''Understanding the Universe'' (of ''The Great Courses'', on DVD), Lecture 43, time 12:05, The Teaching Company, Chantilly, VA, USA, 2007〕 To express even smaller angles, standard SI prefixes can be employed; the milliarcsecond (mas), for instance, is commonly used in astronomy. ==Symbols and abbreviations== The standard symbol for marking the arcminute is the prime (′) (U+2032), though a single quote (') (U+0027) is commonly used where only ASCII characters are permitted. One arcminute is thus written 1′. It is also abbreviated as arcmin or amin or, less commonly, the prime with a circumflex over it ($\backslash hat$). The standard symbol for the arcsecond is the double prime (″) (U+2033), though a double quote (") (U+0022) is commonly used where only ASCII characters are permitted. One arcsecond is thus written 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, written for example as 42° 25.32′ or 42° 25.322′.〔(【引用サイトリンク】url=http://www.kumquatdata.com/Astro%20Navigation%20Syllabus.htm )〕 This notation has been carried over into marine GPS receivers, which normally display latitude and longitude in the latter format by default.〔(【引用サイトリンク】url=http://norinco.co.in/NCMS/index.php?option=com_content&task=view&id=53&Itemid=81 )〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Minute and second of arc」の詳細全文を読む スポンサード リンク
