# Arc second

Physical unit
Unit name Arc second, arc second
Unit symbol ${\ displaystyle ^ {\ prime \ prime}}$, ${\ displaystyle \ mathrm {arcsec}}$
Physical quantity (s) Flat angle
Formula symbol Preferred angle designations are Greek lowercase letters: ${\ displaystyle \ alpha, \ beta, \ gamma, \ dots}$
dimension ${\ displaystyle {\ mathsf {{\ frac {L} {L}} = 1}}}$
system Approved for use with the SI
In SI units ${\ displaystyle \ mathrm {1 ^ {\ prime \ prime} = {\ frac {\ pi} {648 \, 000}} rad \ approx 0 {,} 48 \ cdot 10 ^ {- 5} rad}}$
Named after Latin pars minuta secunda , 'second diminished part'
Derived from Arc minute

An arc second or arc second or second (from latin pars minuta Secunda , second reduced part ') is a unit of measurement of the angle and the means 3600. part of a degree . It almost corresponds to the angle at which a five millimeter wide object appears from a distance of one kilometer. The second symbol or arcsec are used as symbols. The arcsec symbol is also used for the arc secan .

One arc second thus corresponds ${\ displaystyle {\ tfrac {\; 1 ^ {\ circ}} {3600}} = 0 {,} 0002 {\ overline {7}} {} ^ {\ circ}}$

60 arc seconds correspond to one arc minute , 60 arc minutes correspond to one degree. In astronomy and earth measurements , the arcsecond is used with further subdivisions that follow the decimal system: A milli- arcsecond ( English milliarcsecond , mas ) is one thousandth of an arcsecond (0.001 ″), a micro-arcsecond ( µas ) is one millionth of an arcsecond.

A further division of the second into 60 tertien used to be common; This classification is still used today for some procedures in navigation .

Although the arc second does not belong to the International System of Units (SI), it is approved for use with the SI. This makes it a legal unit of measurement .

## conversion

{\ displaystyle {\ begin {aligned} {\ text {angle (in degrees)}} & = {\ text {degrees}} + {\ frac {\ text {angular minutes}} {60}} + {\ frac {\ text {angular seconds}} {3600}} \\ & = {\ text {degrees}} + {\ frac {{\ text {angular minutes}} + {\ frac {\ text {angular seconds}} {60}}} {60 }} \ end {aligned}}}

The conversion into radians takes place accordingly, see conversion between radians and degrees .

## symbol

The symbol for arc seconds is arcsec or the seconds sign . The latter consists of two straight, inclined lines: 1 = 1 arc second and thus corresponds to the customs symbol . The typographically correct character in Unicode has code U + 2033. Two vertical bars ( " ) are used as a substitute.

## Examples

• 60 arc seconds (one arc minute) corresponds roughly to the angle at which a 1 m wide object appears from a distance of 3438 m.
• 20 arc seconds corresponds roughly to the angle at which a 1 cm wide object appears from a distance of 100 m.
• An arc second roughly corresponds to the angle at which a one euro coin appears from a distance of 4800 m.
• One arc second of a longitude , i.e. the distance between two circles of latitude whose geographical latitude differs by one arc second, corresponds to about 30.9 m; 60 times that (corresponding to one arc minute) used to define a nautical mile . At the equator, this also applies to an arc second of a parallel, i.e. the distance between two longitudes whose geographical longitude differs by one arc second; In other places it is less because the circles of latitude become smaller with increasing distance from the equator or the circles of longitude come closer to each other as the pole approaches. On the northern latitude of Germany, a parallel arc second only corresponds to a length of about 21.1 m (Oberstdorf, about 47 ° n. Br.) To about 17.7 m (for List on Sylt, about 55 ° n. Br.) ). In the geographic center of Germany it corresponds to about 19.5 m.
• In astronomy and geodesy most of the reduction quantities of measuring instruments are given in angular seconds , e.g. B. the tilt axis inclination (with large hanging vials approx. 0.1 ″ can be measured). Micrometers and small angle differences (e.g. parallaxes of stars) are also given in this dimension.
• A milli-arcsecond (one thousandth of an arc second) is roughly the angle at which a distance of 1.9 m appears to us on the lunar surface. Viewed from the center of the earth, it corresponds to only 3 cm on the earth's surface.
• At an angle of about 0.03 ″, the stars Betelgeuse , Mira and Antares appear to be the only three stars (apart from the sun) that the best telescopes do not just represent as points of light.
• A micro-arcsecond (one millionth of an arc second) roughly corresponds to the angle at which a medicine ball lying on the surface of Mars would appear at an average opposition distance from Earth.
• A right triangle with an angle of 1 ″ and an opposing cathet of length 1  AU has an adjacent cathet of length 1  parsec .

## Relation to the human eye

The human eye has a resolution of around 1 angular minute (corresponds to 60 ″). So it can theoretically still separate two bars with this angular distance from each other. In fact, the shape of the objects or poor contrast reduce this value. The closest double star (ε in the constellation Lyra ), which only very sharp eyes can still see separately, has an angular distance of 208 " . On the other hand, our eyes have the ability to recognize much finer details if they are linear and stimulate several visual cells . For example, a ship's mast can still be made out on the horizon when its visible width extends over 20 ″.

## 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 édition, 2006)". In: PTB-Mitteilungen . tape 117 , no. 2 , 2007 ( Online [PDF; 1.4 MB ]).
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.