View source for Galactic coordinate system

{{short description|Celestial coordinate system in spherical coordinates, with the Sun as its center}}
<!-- linked from redirects North galactic pole and South galactic pole -->
[[File:Artist's impression of the Milky Way (updated - annotated).jpg|thumb|upright=1.3|Artist's depiction of the Milky Way Galaxy, showing the galactic longitude. A vector matching the plane of the galaxy, at 0° longitude, notably has the [[Galactic Center|Galactic Center]] and intersects arms directly beyond.  Far less of the galaxy lies at all points with opposing 180° longitude]]

The '''galactic coordinate system''' is a [[Astronomy:Celestial coordinate system|celestial coordinate system]] in spherical coordinates, with the [[Astronomy:Sun|Sun]] as its center, the primary direction aligned with the approximate center of the [[Astronomy:Milky Way|Milky Way]] [[Astronomy:Galaxy|Galaxy]], and the [[Fundamental plane (spherical coordinates)|fundamental plane]] parallel to an approximation of the [[Astronomy:Galactic plane|galactic plane]] but offset to its north. It uses the [[Physics:Right-hand rule|right-handed convention]], meaning that coordinates are positive toward the north and toward the east in the [[Fundamental plane (spherical coordinates)|fundamental plane]].<ref name="Blaauwetal" />

==Spherical coordinates==
=== Galactic longitude ===
[[File:Galactic coordinates.JPG|thumb| The galactic coordinates use the Sun as the origin. Galactic longitude ({{math|''l''}}) is measured with primary direction from the Sun to the center of the galaxy in the galactic plane, while the galactic latitude ({{math|''b''}}) measures the [[Angle|angle]] of the object above the galactic plane.]]

Longitude (symbol {{math|''l''}}) measures the [[Angle|angular distance]] of an object eastward along the galactic equator from the Galactic Center. Analogous to terrestrial [[Earth:Longitude|longitude]], galactic longitude is usually measured in degrees (°).

=== Galactic latitude ===
Latitude (symbol {{math|''b''}}) measures the [[Angle|angle]] of an object northward of the galactic equator (or midplane) as viewed from Earth. Analogous to terrestrial [[Earth:Latitude|latitude]], galactic latitude is usually measured in degrees (°).

== Definition ==

The first galactic coordinate system was used by William Herschel in 1785. A number of different coordinate systems, each differing by a few degrees, were used until 1932, when Lund Observatory assembled a set of conversion tables that defined a standard galactic coordinate system based on a galactic north pole at [[Right ascension|RA]] {{nowrap|12<sup>h</sup>&thinsp;40<sup>m</sup>}}, [[Declination|dec]] +28° (in the B1900.0 epoch convention) and a 0° longitude at the point where the [[Astronomy:Galactic plane|galactic plane]] and equatorial plane intersected.<ref name="Blaauwetal" />

In 1958, the [[Organization:International Astronomical Union|International Astronomical Union]] (IAU) defined the galactic coordinate system in reference to radio observations of galactic neutral [[Chemistry:Hydrogen|hydrogen]] through the [[Physics:Hydrogen line|hydrogen line]], changing the definition of the Galactic longitude by 32° and the latitude by 1.5°.<ref name="Blaauwetal" /> In the [[Astronomy:Equatorial coordinate system|equatorial coordinate system]], for [[Astronomy:Epoch|equinox and equator of 1950.0]], the north galactic pole is defined at [[Right ascension|right ascension]] {{nowrap|12<sup>h</sup>&thinsp;49<sup>m</sup>}}, [[Declination|declination]] +27.4°, in the constellation [[Astronomy:Coma Berenices|Coma Berenices]], with a probable error of ±0.1°.<ref name="Reidetal" /> Longitude 0° is the great semicircle that originates from this point along the line in [[Astronomy:Position angle|position angle]] 123° with respect to the [[Astronomy:Celestial pole|equatorial pole]]. The galactic longitude increases in the same direction as right ascension. Galactic latitude is positive towards the north galactic pole, with a plane passing through the Sun and parallel to the galactic equator being 0°, whilst the poles are ±90°.<ref name="Binney" /> Based on this definition, the galactic poles and equator can be found from [[Spherical trigonometry|spherical trigonometry]] and can be [[Astronomy:Axial precession|precessed]] to other [[Astronomy:Epoch|epochs]]; see the table.

{| class="wikitable" style="float: right;"
|+'''[[Astronomy:Epoch|J2000.0]] [[Astronomy:Equatorial coordinate system|equatorial coordinates]] approximating the galactic reference points'''<ref name="Blaauwetal"/>
| style="background:#e9d66b;"| &nbsp;
|  style="text-align:center; background:#e9d66b;"| '''[[Right ascension]]'''
|  style="text-align:center; background:#e9d66b;"| '''[[Declination]]''' 
|  style="text-align:center; background:#e9d66b;"| '''[[Astronomy:Constellation|Constellation]]''' 
|- style="text-align:center;"
| style="background:#e9d66b;"| '''North Pole'''<br/>+90° latitude
|12<sup>h</sup>&thinsp;51.4<sup>m</sup>
| +27.13°
| [[Astronomy:Coma Berenices|Coma Berenices]]<br/><small>(near [[Astronomy:31 Comae Berenices|31 Com]])</small>
|- style="text-align:center;"
| style="background:#e9d66b;"| '''South Pole'''<br/>−90° latitude
|0<sup>h</sup>&thinsp;51.4<sup>m</sup>
| −27.13°
| [[Astronomy:Sculptor (constellation)|Sculptor]]<br/><small>(near [[Astronomy:NGC 288|NGC 288]])</small>
|- style="text-align:center;"
| style="background:#e9d66b;"| '''[[Galactic Center|Center]]'''<br/>0° longitude
| 17<sup>h</sup>&thinsp;45.6<sup>m</sup>
| −28.94°
| [[Astronomy:Sagittarius (constellation)|Sagittarius]]<br/><small>(in [[Astronomy:Sagittarius A|Sagittarius A]])</small>
|- style="text-align:center;"
| style="background:#e9d66b;"| '''[[Astronomy:Galactic anticenter|Anticenter]]'''<br/>180° longitude
| 5<sup>h</sup>&thinsp;45.6<sup>m</sup>
| +28.94°
| [[Astronomy:Auriga (constellation)|Auriga]]<br/><small>(near [[Astronomy:Hipparcos|HIP]] 27180)</small>
|-
|colspan=4|
{|
![[File:Galactic_north_pole.png|160px]]<br/>Galactic north
![[File:Galactic_south_pole.png|160px]]<br/>Galactic south
![[File:Galactic_zero_longitude.png|160px]]<br/>Galactic center
|}
|}

The IAU recommended that during the transition period from the old, pre-1958 system to the new, the old longitude and latitude should be designated {{math|''l''{{isup|I}}}} and {{math|''b''{{isup|I}}}} while the new should be designated {{math|''l''{{isup|II}}}} and {{math|''b''{{isup|II}}}}.<ref name=Binney/> This convention is occasionally seen.<ref>For example in {{Cite journal |last=Kogut |first=A. |date=1993 |title=Dipole Anisotropy in the COBE Differential Microwave Radiometers First-Year Sky Maps |journal=Astrophysical Journal |volume=419 |page=1 |arxiv=astro-ph/9312056 |doi=10.1086/173453|bibcode = 1993ApJ...419....1K |display-authors=0}}</ref>

[[Astronomy:Radio astronomy|Radio source]] [[Astronomy:Sagittarius A*|Sagittarius A*]], which is the best physical marker of the true [[Galactic Center]], is located at {{nowrap|17<sup>h</sup>&thinsp;45<sup>m</sup>&thinsp;40.0409<sup>s</sup>}}, {{nowrap|−29°&thinsp;00′&thinsp;28.118″}} (J2000).<ref name="Reidetal"/> Rounded to the same number of digits as the table, {{nowrap|17<sup>h</sup>&thinsp;45.7<sup>m</sup>}}, −29.01° (J2000), there is an offset of about 0.07° from the defined coordinate center, well within the 1958 error estimate of ±0.1°. Due to the Sun's position, which currently lies {{val|56.75|6.20|ul=ly}} north of the midplane, and the heliocentric definition adopted by the IAU, the galactic coordinates of Sgr&nbsp;A* are latitude {{nowrap|+0°&thinsp;07′&thinsp;12″}} south, longitude {{nowrap|0°&thinsp;04′&thinsp;06″}}. Since as defined the galactic coordinate system does not rotate with time, Sgr&nbsp;A* is actually decreasing in longitude at the rate of galactic rotation at the sun, {{mvar|Ω}}, approximately 5.7 milliarcseconds per year (see [[Physics:Oort constants|Oort constants]]).

==Conversion between equatorial and galactic coordinates==
An object's location expressed in the [[Astronomy:Equatorial coordinate system|equatorial coordinate system]] can be transformed into the galactic coordinate system. In these equations, {{math|''α''}} is [[Right ascension|right ascension]], {{math|''δ''}} is [[Declination|declination]]. NGP refers to the coordinate values of the north galactic pole and NCP to those of the north celestial pole.<ref>{{cite book |last1=Carroll |first1=Bradley |last2=Ostlie |first2=Dale |title=An Introduction to Modern Astrophysics |year=2007 |publisher=Pearson Addison-Wesley |isbn=978-0805304022 |page=900-901 |edition=2nd}}</ref>

:<math>
\begin{align}
\sin(b) &= \sin(\delta_\text{NGP})\sin(\delta)+\cos(\delta_\text{NGP})\cos(\delta)\cos(\alpha-\alpha_\text{NGP}) \\
\cos(b) \sin(l_\text{NCP}-l) &= \cos(\delta)\sin(\alpha-\alpha_\text{NGP}) \\
\cos(b) \cos(l_\text{NCP}-l) &= \cos(\delta_\text{NGP}) \sin(\delta) - \sin(\delta_\text{NGP}) \cos(\delta) \cos(\alpha - \alpha_\text{NGP})
\end{align}
</math>

The reverse (galactic to equatorial) can also be accomplished with the following conversion formulas.
:<math>
\begin{align}
\sin (\delta) &= \sin (\delta_\text{NGP}) \sin(b) + \cos (\delta_\text{NGP}) \cos(b) \cos(l_\text{NCP} - l) \\
\cos (\delta) \sin(\alpha - \alpha_\text{NGP}) &= \cos(b) \sin(l_\text{NCP} - l) \\
\cos (\delta) \cos(\alpha - \alpha_\text{NGP}) &= \cos (\delta_\text{NGP}) \sin(b) - \sin(\delta_\text{NGP}) \cos(b) \cos(l_\text{NCP} - l)
\end{align}
</math>

Where:

:<math>\alpha_\text{NGP}=12^h 51.4^m \qquad \delta_\text{NGP}=27.13^{\circ} \qquad l_\text{NCP}=122.93314^{\circ}</math>

==Rectangular coordinates==
In some applications use is made of rectangular coordinates based on galactic longitude and latitude and distance. In some work regarding the distant past or future the galactic coordinate system is taken as rotating so that the {{math|''x''}}-axis always goes to the centre of the galaxy.<ref>For example {{cite journal |last=Bobylev |first=Vadim V. | date=March 2010 |title=Searching for Stars Closely Encountering with the Solar System |journal=Astronomy Letters |volume=36 |issue=3 |pages=220–226 |doi=10.1134/S1063773710030060 |arxiv=1003.2160 |bibcode=2010AstL...36..220B|s2cid=118374161 }}</ref>

There are two major [[Cartesian coordinate system|rectangular]] variations of galactic coordinates, commonly used for computing space velocities of galactic objects. In these systems the {{math|''xyz''}}-axes are designated {{math|''UVW''}}, but the definitions vary by author. In one system, the {{math|''U''}} axis is directed toward the Galactic Center ({{math|''l''}} = 0°), and it is a [[Physics:Right-hand rule|right-handed]] system (positive towards the east and towards the north galactic pole); in the other, the {{math|''U''}} axis is directed toward the galactic anticenter ({{math|''l''}} = 180°), and it is a left-handed system (positive towards the east and towards the north galactic pole).<ref name="Johnson" />

[[Image:Milky Way infrared.jpg|thumb|250px|The [[Anisotropy|anisotropy]] of the star density in the night sky makes the galactic coordinate system very useful for coordinating surveys, both those that require high densities of stars at low galactic latitudes, and those that require a low density of stars at high galactic latitudes. For this image the [[Mollweide projection|Mollweide projection]] has been applied, typical in maps using galactic coordinates.]]
==In the constellations==

The galactic equator runs through the following [[Astronomy:Constellation|constellation]]s:<ref name="SEDS" />
{{div col|colwidth=10em}}
*[[Astronomy:Sagittarius (constellation)|Sagittarius]]
*[[Astronomy:Serpens|Serpens]]
*[[Astronomy:Scutum (constellation)|Scutum]]
*[[Astronomy:Aquila (constellation)|Aquila]]
*[[Astronomy:Sagitta|Sagitta]]
*[[Astronomy:Vulpecula|Vulpecula]]
*[[Astronomy:Cygnus (constellation)|Cygnus]]
*[[Astronomy:Cepheus (constellation)|Cepheus]]
*[[Astronomy:Cassiopeia (constellation)|Cassiopeia]]
*[[Astronomy:Camelopardalis|Camelopardalis]]
*[[Astronomy:Perseus (constellation)|Perseus]]
*[[Astronomy:Auriga (constellation)|Auriga]]
*[[Astronomy:Taurus (constellation)|Taurus]]
*[[Astronomy:Gemini (constellation)|Gemini]]
*[[Astronomy:Orion (constellation)|Orion]]
*[[Astronomy:Monoceros (constellation)|Monoceros]]
*[[Astronomy:Canis Major|Canis Major]]
*[[Astronomy:Puppis|Puppis]]
*[[Astronomy:Vela (constellation)|Vela]]
*[[Astronomy:Carina (constellation)|Carina]]
*[[Astronomy:Crux|Crux]]
*[[Astronomy:Centaurus|Centaurus]]
*Circinus
*[[Astronomy:Norma (constellation)|Norma]]
*[[Astronomy:Ara (constellation)|Ara]]
*[[Astronomy:Scorpius|Scorpius]]
*[[Astronomy:Ophiuchus|Ophiuchus]]
{{div col end}}

== See also ==
* {{annotated link|Galactic quadrant}}
* {{annotated link|Astronomy:Supergalactic coordinate system}}
* {{annotated link|Astronomy:Astronomical coordinate systems}}
* {{annotated link|Astronomy:Galaxy formation and evolution}}
* {{annotated link|Astronomy:Milky Way}}

==References==
{{reflist|20em|refs=
<ref name="Blaauwetal">{{cite journal |title=The new IAU system of galactic coordinates (1958 revision) |first1=A. |last1=Blaauw
|last2=Gum |first2=C.S. |last3=Pawsey |first3=J.L. |last4=Westerhout |first4=G. |date=1960 |journal=[[Organization:Monthly Notices of the Royal Astronomical Society|Monthly Notices of the Royal Astronomical Society]] |volume=121 |number=2 |page=123 |bibcode = 1960MNRAS.121..123B |doi=10.1093/mnras/121.2.123|doi-access=free }}</ref>
<ref name="Reidetal">{{cite journal | last1=Reid | first1=M.J. | last2=Brunthaler | first2=A. | title=The Proper Motion of Sagittarius A* | journal=The Astrophysical Journal | volume=616 | issue=2 | pages=874, 883 | date=2004 | bibcode=2004ApJ...616..872R|arxiv = astro-ph/0408107 |doi = 10.1086/424960 | s2cid=16568545 }}</ref> 
<ref name="Binney">{{cite book |title=Galactic Astronomy |author=James Binney, Michael Merrifield |url=https://books.google.com/books?id=arYYRoYjKacC&q=rotation+%22proper+motion%22+galaxy+OR+galactic&pg=PA675 |pages= 30–31 |isbn=0-691-02565-7 |date=1998 |publisher=Princeton University Press}}</ref>
<ref name="Johnson">{{cite journal |title=Calculating galactic space velocities and their uncertainties, with an application to the Ursa Major group |last1=Johnson |first1=Dean R.H. |last2=Soderblom |first2=David R. |date=1987 |journal=Astronomical Journal |volume=93 |page=864|bibcode = 1987AJ.....93..864J |doi = 10.1086/114370}}</ref>
<ref name="SEDS">{{cite web | url=http://messier.seds.org/more/mw_con.html | title=SEDS Milky Way Constellations}}</ref>
}}

==External links==
* [http://heasarc.gsfc.nasa.gov/cgi-bin/Tools/convcoord/convcoord.pl  Universal coordinate converter].
* [http://demonstrations.wolfram.com/GalacticCoordinateSystem/  Galactic Coordinate System - Wolfram Demonstration]
* [https://www.daviddarling.info/encyclopedia/C/coordinate.html#galactic_coordinates Galactic coordinates], The Internet Encyclopedia of Science
* Fiona Vincent, [http://star-www.st-and.ac.uk/~fv/webnotes/chapter8.htm Positional Astronomy: Galactic coordinates], [[Organization:University of St Andrews|University of St Andrews]]
* [https://web.archive.org/web/20150718054637/http://www.atlasoftheuniverse.com/ An Atlas of the Universe]

{{Milky Way}}
{{Galaxy}}
{{Celestial coordinate systems}}

[[Category:Milky Way]]
[[Category:Orientation (geometry)]]

{{Sourceattribution|Galactic coordinate system}}