View source for Geographic coordinate system

{{Short description|System to specify locations on Earth}}
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{{Pp-pc|small=yes}}
{{Broader|Spatial reference system}}
{{Use dmy dates|date=May 2019}}
{{Use American English|date=June 2024}}
[[File:FedStats Lat long.svg|thumb|upright=1.2|Longitude lines are perpendicular to and latitude lines are parallel to the Equator]]
{{Geodesy}}

A '''geographic coordinate system''' ('''GCS''') is a [[spherical coordinate system|spherical]] or [[geodetic coordinates|geodetic coordinate]] system for measuring and communicating [[position (geometry)|positions]] directly on [[Earth]] as [[latitude]] and [[longitude]].<ref name="chang2016">{{cite book |last1=Chang |first1=Kang-tsung |title=Introduction to Geographic Information Systems |date=2016 |publisher=McGraw-Hill |isbn=978-1-259-92964-9 |page=24 |edition=9th}}</ref> It is the simplest, oldest and most widely used of the various [[spatial reference systems]] that are in use, and forms the basis for most others. Although latitude and longitude form a coordinate [[tuple]] like a [[cartesian coordinate system]], the geographic coordinate system is not cartesian because the measurements are angles and are not on a planar surface.<ref name="DiBiase">{{cite web |last=DiBiase |first=David |title=The Nature of Geographic Information |url=https://www.e-education.psu.edu/natureofgeoinfo/c2_p10.html |access-date=18 February 2024 |archive-date=19 February 2024 |archive-url=https://web.archive.org/web/20240219075125/https://www.e-education.psu.edu/natureofgeoinfo/c2_p10.html |url-status=live }}</ref>

A full GCS specification, such as those listed in the [[EPSG Geodetic Parameter Dataset|EPSG]] and ISO 19111 standards, also includes a choice of [[geodetic datum]] (including an [[Earth ellipsoid]]), as different datums will yield different latitude and longitude values for the same location.<ref name="epsg">{{cite web |title=Using the EPSG geodetic parameter dataset, Guidance Note 7-1 |url=https://epsg.org/guidance-notes.html |website=EPSG Geodetic Parameter Dataset |publisher=Geomatic Solutions |access-date=15 December 2021 |archive-date=15 December 2021 |archive-url=https://web.archive.org/web/20211215215824/https://epsg.org/guidance-notes.html |url-status=live }}</ref>

== History ==
{{also|History of geodesy}}

The [[invention]] of a geographic coordinate system is generally credited to [[Eratosthenes]] of [[Cyrene, Libya|Cyrene]], who composed his now-lost ''[[Geography (Eratosthenes)|Geography]]'' at the [[Library of Alexandria]] in the 3rd century&nbsp;BC.<ref>{{Citation |last=McPhail |first=Cameron |title=Reconstructing Eratosthenes'<!--sic--> Map of the World |pages=20–24 |url=https://ourarchive.otago.ac.nz/bitstream/handle/10523/1713/McPhailCameron2011MA.pdf |year=2011 |publisher=University of Otago |location=[[Dunedin]] |access-date=14 March 2015 |archive-date=2 April 2015 |archive-url=https://web.archive.org/web/20150402095830/https://ourarchive.otago.ac.nz/bitstream/handle/10523/1713/McPhailCameron2011MA.pdf |url-status=live }}.</ref> A century later, [[Hipparchus#Geography|Hipparchus]] of [[Nicaea]] improved on this system by determining latitude from stellar measurements rather than solar altitude and determining longitude by timings of [[lunar eclipse]]s, rather than [[dead reckoning]]. In the 1st or 2nd century, [[Marinus of Tyre]] compiled an extensive gazetteer and [[equirectangular projection|mathematically plotted world map]] using coordinates measured east from a [[prime meridian]] at the westernmost known land, designated the [[Fortunate Isles]], off the coast of western Africa around the [[Canary Islands|Canary]] or [[Cape Verde|Cape Verde Islands]], and measured north or south of the island of [[Rhodes]] off [[Asia Minor]]. [[Ptolemy]] credited him with the full adoption of longitude and latitude, rather than measuring latitude in terms of the length of the [[midsummer]] day.<ref>{{Citation |last=Evans |first=James |title=The History and Practice of Ancient Astronomy |url=https://books.google.com/books?id=LVp_gkwyvC8C&pg=PA102 |pages=102–103 |publisher=Oxford University Press |year=1998 |location=Oxford, England |isbn=9780199874453 |access-date=5 May 2020 |archive-date=17 March 2023 |archive-url=https://web.archive.org/web/20230317171201/https://books.google.com/books?id=LVp_gkwyvC8C&pg=PA102 |url-status=live }}.</ref>

Ptolemy's 2nd-century ''[[Geography (Ptolemy)|Geography]]'' used the same prime meridian but measured latitude from the [[Equator]] instead. After their work was translated into [[Arabic]] in the 9th century, [[Al-Khwarizmi|Al-Khwārizmī]]'s ''[[Book of the Description of the Earth]]'' corrected Marinus' and Ptolemy's errors regarding the length of the [[Mediterranean Sea]],{{NoteTag|The pair had accurate absolute distances within the Mediterranean but underestimated the [[circumference of the Earth]], causing their degree measurements to overstate its length west from Rhodes or Alexandria, respectively.}} causing [[Geography and cartography in the medieval Islamic world|medieval Arabic cartography]] to use a prime meridian around 10° east of Ptolemy's line. Mathematical cartography resumed in Europe following [[Maximus Planudes]]' recovery of Ptolemy's text a little before 1300; the text was translated into [[Latin]] at [[Republic of Florence|Florence]] by [[Jacopo d'Angelo]] around 1407.<!--more sources at linked pages-->

In 1884, the [[United States]] hosted the [[International Meridian Conference]], attended by representatives from twenty-five nations. Twenty-two of them agreed to adopt the longitude of the [[Royal Observatory, Greenwich|Royal Observatory]] in [[Greenwich]], England as the zero-reference line. The [[Dominican Republic]] voted against the motion, while France and [[Brazil]] abstained.<ref>{{cite web |publisher=Greenwich 2000 Limited |url = http://wwp.millennium-dome.com/info/conference.htm |title=The International Meridian Conference |website=Millennium Dome: The O2 in Greenwich |date=9 June 2011 |access-date=31 October 2012 |url-status=dead |archive-url = https://web.archive.org/web/20120806065207/http://wwp.millennium-dome.com/info/conference.htm |archive-date=6 August 2012 }}</ref> France adopted [[Greenwich Mean Time]] in place of local determinations by the [[Paris Observatory]] in 1911.

==Latitude and longitude==
[[File:Latitude_and_longitude_graticule_on_a_sphere.svg|thumb|upright=1.2|Diagram of the latitude {{mvar|ϕ}} and longitude {{mvar|λ}} angle measurements for a spherical model of the Earth.]]
{{Main|Latitude|Longitude}}

The ''latitude'' [[Phi|{{mvar|ϕ}}]] of a point on Earth's surface is the angle between the equatorial plane and the straight line that passes through that point and through (or close to) the center of the Earth.{{NoteTag|Alternative versions of latitude and longitude include geocentric coordinates, which measure with respect to Earth's center; geodetic coordinates, which model Earth as an [[ellipsoid]]; and geographic coordinates, which measure with respect to a plumb line at the location for which coordinates are given.}} Lines joining points of the same latitude trace circles on the surface of Earth called [[circle of latitude|parallels]], as they are parallel to the Equator and to each other. The [[North Pole]] is 90°&nbsp;N; the [[South Pole]] is 90°&nbsp;S. The 0° parallel of latitude is designated the [[Equator]], the [[fundamental plane (spherical coordinates)|fundamental plane]] of all geographic coordinate systems. The Equator divides the globe into [[Northern Hemisphere|Northern]] and [[Southern Hemisphere]]s.

The ''longitude'' [[lambda|{{mvar|λ}}]] of a point on Earth's surface is the angle east or west of a reference [[meridian (geography)|meridian]] to another meridian that passes through that point. All meridians are halves of great [[ellipse]]s (often called [[great circle]]s), which converge at the North and South Poles. The meridian of the British [[Royal Observatory, Greenwich|Royal Observatory]] in [[Greenwich]], in southeast London, England, is the international [[prime meridian]], although some organizations—such as the French {{Lang|fr|[[Institut national de l'information géographique et forestière]]|italic=no}}—continue to use other meridians for internal purposes. The prime meridian determines the proper [[Eastern Hemisphere|Eastern]] and [[Western Hemisphere]]s, although maps often divide these hemispheres further west in order to keep the [[Old World]] on a single side. The [[Antipodes|antipodal]] meridian of Greenwich is both 180°W and 180°E. This is not to be conflated with the [[International Date Line]], which diverges from it in several places for political and convenience reasons, including between far eastern Russia and the far western [[Aleutian Islands]].

The combination of these two components specifies the position of any location on the surface of Earth, without consideration of [[altitude]] or depth. The visual grid on a map formed by lines of latitude and longitude is known as a ''[[Graticule (cartography)|graticule]]''.<ref>{{cite book |url = https://books.google.com/books?id=jPVxSDzVRP0C&q=graticule&pg=PA224 |title=Glossary of the Mapping Sciences |last=American Society of Civil Engineers |date=1 January 1994 |publisher=ASCE Publications|isbn=9780784475706|language=en|page= 224 }}</ref> The origin/zero point of this system is located in the [[Gulf of Guinea]] about {{convert|625|km|sp=us|abbr=on|sigfig=2}} south of [[Tema]], [[Ghana]], a location often facetiously called [[Null Island]].

== Geodetic datum ==
{{Main|Geodetic datum}}
{{further|Figure of the Earth|Reference ellipsoid|Geographic coordinate conversion|Spatial reference system}}

In order to use the theoretical definitions of latitude, longitude, and height to precisely measure actual locations on the physical earth, a ''[[geodetic datum]]'' must be used. A ''horizonal datum'' is used to precisely measure latitude and longitude, while a ''vertical datum'' is used to measure elevation or altitude. Both types of datum bind a mathematical model of the shape of the earth (usually a [[reference ellipsoid]] for a horizontal datum, and a more precise [[geoid]] for a vertical datum) to the earth. Traditionally, this binding was created by a network of [[geodetic control network |control points]], surveyed locations at which monuments are installed, and were only accurate for a region of the surface of the Earth. Some newer datums are bound to the [[center of mass]] of the Earth. 

This combination of mathematical model and physical binding mean that anyone using the same datum will obtain the same location measurement for the same physical location. However, two different datums will usually yield different location measurements for the same physical location, which may appear to differ by as much as several hundred meters; this not because the location has moved, but because the reference system used to measure it has shifted. Because any [[spatial reference system]] or [[map projection]] is ultimately calculated from latitude and longitude, it is crucial that they clearly state the datum on which they are based. For example, a [[Universal transverse mercator |UTM]] coordinate based on [[WGS84]] will be different than a UTM coordinate based on [[NAD27]] for the same location. Converting coordinates from one datum to another requires a [[Geographic coordinate conversion#Datum transformations|datum transformation]] such as a [[Helmert transformation]], although in certain situations a simple [[Translation (geometry)|translation]] may be sufficient.<ref name=Irish>{{cite web |url = http://www.osi.ie/GetAttachment.aspx?id=25113681-c086-485a-b113-bab7c75de6fa |title=Making maps compatible with GPS |publisher=Government of Ireland 1999 |access-date=15 April 2008 |archive-url = https://web.archive.org/web/20110721130505/http://www.osi.ie/GetAttachment.aspx?id=25113681-c086-485a-b113-bab7c75de6fa |archive-date=21 July 2011 |url-status=dead }}</ref>

Datums may be global, meaning that they represent the whole Earth, or they may be local, meaning that they represent an ellipsoid best-fit to only a portion of the Earth. Examples of global datums include [[World Geodetic System]] (WGS{{nbsp}}84, also known as EPSG:4326<ref>{{Cite web|url=https://spatialreference.org/ref/epsg/4326/|title=WGS 84: EPSG Projection -- Spatial Reference|website=spatialreference.org|access-date=5 May 2020|archive-date=13 May 2020|archive-url=https://web.archive.org/web/20200513113544/https://spatialreference.org/ref/epsg/4326/|url-status=live}}</ref>), the default datum used for the [[Global Positioning System]],{{NoteTag|WGS 84 is the default datum used in most GPS equipment, but other datums can be selected.}} and the [[International Terrestrial Reference System and Frame]] (ITRF), used for estimating [[continental drift]] and [[crustal deformation]].<ref name=Bolstad>{{cite book |last=Bolstad |first=Paul |title=GIS Fundamentals |year=2012 |edition=5th |publisher=Atlas books |isbn=978-0-9717647-3-6 |page=102 |url=http://www.paulbolstad.net/5thedition/samplechaps/Chapter3_5th_small.pdf |access-date=27 January 2018 |archive-date=15 October 2020 |archive-url=https://web.archive.org/web/20201015162738/http://www.paulbolstad.net/5thedition/samplechaps/Chapter3_5th_small.pdf |url-status=dead }}</ref> The distance to Earth's center can be used both for very deep positions and for positions in space.<ref name="OSGB"/>

Local datums chosen by a national cartographical organization include the [[North American Datum]], the European [[ED50]], and the British [[OSGB36]]. Given a location, the datum provides the latitude <math>\phi</math> and longitude <math>\lambda</math>. In the United Kingdom there are three common latitude, longitude, and height systems in use. WGS{{nbsp}}84 differs at Greenwich from the one used on published maps OSGB36 by approximately 112{{nbsp}}m. The military system [[ED50]], used by [[NATO]], differs from about 120{{nbsp}}m to 180{{nbsp}}m.<ref name=OSGB/>

Points on the Earth's surface move relative to each other due to continental plate motion, subsidence, and diurnal [[Earth tide|Earth tidal]] movement caused by the [[Moon]] and the Sun. This daily movement can be as much as a meter. Continental movement can be up to {{nowrap|10 cm}} a year, or {{nowrap|10 m}} in a century. A [[weather system]] high-pressure area can cause a sinking of {{nowrap|5 mm}}. [[Scandinavia]] is rising by {{nowrap|1 cm}} a year as a result of the melting of the ice sheets of the [[quaternary glaciation|last ice age]], but neighboring [[Scotland]] is rising by only {{nowrap|0.2 cm}}. These changes are insignificant if a local datum is used, but are statistically significant if a global datum is used.<ref name="OSGB">{{Citation |title=A guide to coordinate systems in Great Britain |date=2020 |series=D00659 v3.6 |access-date=17 December 2021|publisher=Ordnance Survey |url=https://www.ordnancesurvey.co.uk/documents/resources/guide-coordinate-systems-great-britain.pdf |archive-url=https://web.archive.org/web/20200402024515/http://www.ordnancesurvey.co.uk/documents/resources/guide-coordinate-systems-great-britain.pdf |archive-date=2020-04-02 |url-status=live }}</ref>

==Length of a degree==
{{Main|Length of a degree of latitude|Length of a degree of longitude}}
{{See also|Arc length#Great circles on Earth}}

On the GRS{{nbsp}}80 or [[World Geodetic System#WGS84|WGS{{nbsp}}84]] spheroid at [[sea level]] at the Equator, one latitudinal second measures 30.715 [[metre|m]], one latitudinal minute is 1843 m and one latitudinal degree is 110.6&nbsp;km. The circles of longitude, meridians, meet at the geographical poles, with the west–east width of a second naturally decreasing as latitude increases. On the [[Equator]] at sea level, one longitudinal second measures 30.92&nbsp;m, a longitudinal minute is 1855&nbsp;m and a longitudinal degree is 111.3&nbsp;km. At 30° a longitudinal second is 26.76&nbsp;m, at Greenwich (51°28′38″N) 19.22&nbsp;m, and at 60° it is 15.42 m.

On the WGS{{nbsp}}84 spheroid, the length in meters of a degree of latitude at latitude {{mvar|ϕ}} (that is, the number of meters you would have to travel along a north–south line to move 1 degree in latitude, when at latitude {{mvar|ϕ}}), is about

{{block indent|1=
<math>111132.92 - 559.82\, \cos 2\phi + 1.175\, \cos 4\phi - 0.0023\, \cos 6\phi</math><ref name=GISS>[http://gis.stackexchange.com/questions/75528/length-of-a-degree-where-do-the-terms-in-this-formula-come-from] {{Webarchive|url=https://web.archive.org/web/20160629203521/http://gis.stackexchange.com/questions/75528/length-of-a-degree-where-do-the-terms-in-this-formula-come-from |date=29 June 2016 }} Geographic Information Systems – Stackexchange</ref>
}}

The returned measure of meters per degree latitude varies continuously with latitude.

Similarly, the length in meters of a degree of longitude can be calculated as

{{block indent|1=
<math>111412.84\, \cos \phi - 93.5\, \cos 3\phi + 0.118\, \cos 5\phi</math><ref name=GISS/>
}}

(Those coefficients can be improved, but as they stand the distance they give is correct within a centimeter.)

The formulae both return units of meters per degree.

An alternative method to estimate the length of a longitudinal degree at latitude <math>\phi</math> is to assume a spherical Earth (to get the width per minute and second, divide by 60 and 3600, respectively):

{{block indent|1=
<math> \frac{\pi}{180}M_r\cos \phi \!</math>
}}

where [[Earth radius#Meridional Earth radius|Earth's average meridional radius]] <math>\textstyle{M_r}\,\!</math> is {{nowrap|6,367,449 m}}. Since the Earth is an [[Spheroid#Oblate spheroids|oblate spheroid]], not spherical, that result can be off by several tenths of a percent; a better approximation of a longitudinal degree at latitude <math>\phi</math> is

{{block indent|1=
<math>\frac{\pi}{180}a \cos \beta \,\!</math>
}}

where Earth's equatorial radius <math>a</math> equals 6,378,137 m and <math>\textstyle{\tan \beta = \frac{b}{a}\tan\phi}\,\!</math>; for the GRS{{nbsp}}80 and WGS{{nbsp}}84 spheroids, <math display="inline">\tfrac{b}{a}=0.99664719</math>. (<math>\textstyle{\beta}\,\!</math> is known as the [[Latitude#Parametric (or reduced) latitude|reduced (or parametric) latitude]]). Aside from rounding, this is the exact distance along a parallel of latitude; getting the distance along the shortest route will be more work, but those two distances are always within 0.6 m of each other if the two points are one degree of longitude apart.

{| class="wikitable"
|+ Longitudinal length equivalents at selected latitudes
|-
! style="width:100px;" | Latitude
! style="width:150px;" | City
! style="width:100px;" | Degree
! style="width:100px;" | Minute
! style="width:100px;" | Second
! style="width:100px;" | ±0.0001°
|-
| 60°
| [[Saint Petersburg]]
| style="text-align:center;" | 55.80&nbsp;km
| style="text-align:center;" | 0.930&nbsp;km
| style="text-align:center;" | 15.50&nbsp;m
| style="text-align:center;" | 5.58&nbsp;m
|-
| 51° 28′ 38″ N
| [[Greenwich]]
| style="text-align:center;" | 69.47&nbsp;km
| style="text-align:center;" | 1.158&nbsp;km
| style="text-align:center;" | 19.30&nbsp;m
| style="text-align:center;" | 6.95&nbsp;m
|-
| 45°
| [[Bordeaux]]
| style="text-align:center;" | 78.85&nbsp;km
| style="text-align:center;" | 1.31&nbsp;km
| style="text-align:center;" | 21.90&nbsp;m
| style="text-align:center;" | 7.89&nbsp;m
|-
| 30°
| [[New Orleans]]
| style="text-align:center;" | 96.49&nbsp;km
| style="text-align:center;" | 1.61&nbsp;km
| style="text-align:center;" | 26.80&nbsp;m
| style="text-align:center;" | 9.65&nbsp;m
|-
| 0°
| [[Quito]]
| style="text-align:center;" | 111.3&nbsp;km
| style="text-align:center;" | 1.855&nbsp;km
| style="text-align:center;" | 30.92&nbsp;m
| style="text-align:center;" | 11.13&nbsp;m
|}
<!--The Equator is the [[fundamental plane (spherical coordinates)|fundamental plane]] of all geographic coordinate systems. All spherical coordinate systems define such a fundamental plane.-->

==Alternate encodings==
Like any series of multiple-digit numbers, latitude-longitude pairs can be challenging to communicate and remember. Therefore, alternative schemes have been developed for encoding GCS coordinates into alphanumeric strings or words:
* the [[Maidenhead Locator System]], popular with radio operators.
* the [[World Geographic Reference System]] (GEOREF), developed for global military operations, replaced by the current [[Global Area Reference System]] (GARS).
* [[Open Location Code]] or "Plus Codes", developed by Google and released into the public domain.
* [[Geohash]], a public domain system based on the Morton [[Z-order curve]].
* [[Mapcode]], an open-source system originally developed at TomTom.
* [[What3words]], a proprietary system that encodes GCS coordinates as pseudorandom sets of words by dividing the coordinates into three numbers and looking up words in an indexed dictionary.

These are not distinct coordinate systems, only alternative methods for expressing latitude and longitude measurements.

== See also ==
* {{annotated link|Decimal degrees}}
* {{annotated link|Geographical distance}}
* {{annotated link|Geographic information system}}
* {{annotated link|Geo URI scheme}}
* [[ISO 6709]], standard representation of geographic point location by coordinates
* {{annotated link|Linear referencing}}
* {{annotated link|Primary direction}}
* [[Planetary coordinate system]]
** [[Selenographic coordinate system]]
* {{annotated link|Spatial reference system}}
* Jan Smits (2015). [http://ica-proj.kartografija.hr/for-librarians.en.html#co Mathematical data for bibliographic descriptions of cartographic materials and spatial data]. ''Geographical co-ordinates''. [[International Cartographic Association|ICA]] Commission on Map Projections.

== Notes ==
{{NoteFoot}}

== References ==
{{Reflist}}

=== Sources ===
{{refbegin}}
* ''Portions of this article are from Jason Harris' "Astroinfo" which is distributed with [[KStars]], a desktop planetarium for [[Linux]]/[[KDE]]. See [http://edu.kde.org/kstars/index.phtml The KDE Education Project – KStars] {{Webarchive|url=https://web.archive.org/web/20080517043629/http://edu.kde.org/kstars/index.phtml |date=17 May 2008 }}''
{{refend}}

== External links ==
* {{Commons category-inline}}

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