Arc minute

Physical unit
Unit name	Arc minute, arc minute, minute
Unit symbol	${\displaystyle ^{\prime }}$, ${\displaystyle \mathrm {arcmin} }$
Physical quantity (s)	Flat angle
Formula symbol	The preferred angle designations are lowercase Greek letters ${\displaystyle (\alpha ,\beta ,\gamma ,\dots )}$
dimension	${\displaystyle {\mathsf {{\frac {L}{L}}=1}}}$
system	Approved for use with the SI
In SI units	${\displaystyle \mathrm {1^{\prime }={\frac {\pi }{10\,800}}\;rad\approx 0{,}291\cdot 10^{-3}\;rad} }$
Named after	Latin pars minuta , "reduced part"
Derived from	Degree
See also: angular dimensions

The arc minute , also arc minute or minute (from Latin pars minuta , reduced part), is the sixtieth part of an angular degree. It represents a subdivision of the unit level to indicate the size of plane angle is.

The full angle is divided into 360 degrees. A degree is further divided into 60 arc minutes: 1 ° = 60 ′. One angular minute thus corresponds ${\displaystyle {\frac {\;1^{\circ }}{60}}=0{,}01{\overline {6}}{}^{\circ }}$

An arc minute in turn consists of 60  arc seconds : 1 ′ = 60 ″; thus: 1 ° = 3600 ″. A decimal minute is a specification of the minutes with decimal places instead of angular seconds.

It should be noted that (according to this definition) a size specification in arc minutes despite the same prefix “arc-” has nothing to do with specification in radians . In addition, the angular units minutes and seconds are not to be confused with the specification of the right ascension in hours, minutes and seconds in the time measure of astronomy .

The angular minute does not belong to the International System of Units (SI), but is approved for use with the SI. This makes it a legal unit of measurement .

Notation

Analogous to the usual specification of times, angles are also specified in a notation that uses degrees, minutes and seconds together. The angle to be specified is shown as the sum of three angles, with the numerical values ​​in front of the minutes and seconds being less than 60. This notation is used, for example, for geographic coordinates to specify longitude and latitude . 51 ° 14 ′ 4.2 ″ is the notation for 51 degrees + 14 arc minutes + 4.2 arc seconds.

The unit symbol for the angular minute consists of a straight, inclined, superscript line: 1 ′ = 1 minute. The typographically correct character in Unicode is Prime , Code U + 2032. A vertical line ( ' ) is also used as a substitute . The apostrophe is often used on a typewriter or PC . The unit symbol is written immediately after the last digit of the numerical value without a gap, as is the case with the unit symbols for the angle units degrees and seconds. See also degree symbols .

conversion

${\displaystyle {\begin{aligned}&{\text{Winkel (in Grad)}}=\\&={\text{Grad}}+{\frac {\text{Winkelminuten}}{60}}+{\frac {\text{Winkelsekunden}}{3600}}\\&={\text{Grad}}+{\frac {{\text{Winkelminute}}+{\frac {\text{Winkelsekunden}}{60}}}{60}}\end{aligned}}}$

The latter notation is used in the following example:
51 ° 14 ′ 4.2 ″ (read: 51 degrees, 14 minutes, 4.2 seconds) can be converted into decimal notation as follows :

	◾ first the seconds in minutes		4.2 ″ · 1 ′ / 60 ″ = 0.07 ′
	◾ results		51 ° 14.07 ′
	◾ the minutes in degrees		14.07 'x 1 ° / 60' = 0.2345 °
	◾ in total		51 ° + 0.2345 ° = 51.2345 °.

The conversion from decimal degrees to degrees-minutes-seconds is done by first multiplying the decimal part by 60.

0.2345 ° 60 ′ / 1 ° = 14.07 ′

The resulting integer are the angular minutes. The remaining decimal part is multiplied by 60 again.

0.07 ′ · 60 ″ / 1 ′ = 4.2 ″

The resulting number is the seconds.

Examples

• One angular minute corresponds roughly to the angle at which a distance of 1 m in length appears from a distance of 3440 m.
• The moon can also be used as a size comparison for an angular minute. For an observer on earth, the entire diameter of the moon extends on average over an angular range of about 32 angular minutes.
• On the earth's surface, one angular minute corresponds to a great circle of the earth about 1852 m. The nautical mile is derived from this.
• At a distance of 100 m, one angular minute corresponds to approx. 2.91 cm. The unit angular minute (MOA) is used in ballistics, among other things, for the precision of scatter circles or when setting telescopic sights , which are mostly used in the Anglo-American region.

Individual evidence

1. ↑ The International System of Units (SI) . German translation of the BIPM brochure "Le Système international d'unités / The International System of Units (8e edition, 2006)". In: PTB-Mitteilungen . tape 117 , no. 2 , 2007, p. 156 ( online version (PDF file, 1.4 MB) ). Online version (PDF file, 1.4 MB) ( Memento of the original from March 4, 2016 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.  
2. ↑ Le Système international d'unités . 9e édition, 2019 (the so-called "SI brochure", French and English).
3. ↑ on the basis of EU Directive 80/181 / EEC in the states of the EU or the Federal Law on Metrology in Switzerland