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[[File:WorldMapLongLat-eq-circles-tropics-non.png|thumb|440px|Map of [[Earth]] showing lines of [[latitude]] (horizontally) and [[longitude]] (vertically), Eckert VI projection; [https://www.cia.gov/library/publications/the-world-factbook/graphics/ref_maps/pdf/political_world.pdf large version] (pdf, 3.12MB)]]

A '''geographic coordinate system''' is a [[coordinate system]] that enables every location on the Earth to be specified by a set of numbers. The coordinates are often chosen such that one of the numbers represent [[altitude|vertical position]], and two [[n-vector|or three]] of the numbers represent [[horizontal position representation|horizontal position]]. A common choice of coordinates is [[latitude]], [[longitude]] and [[height#In geodesy|ellipsoid height]].<ref name=OSGB>[http://www.ordnancesurvey.co.uk/oswebsite/gps/docs/A_Guide_to_Coordinate_Systems_in_Great_Britain.pdf A Guide to coordinate systems in Great Britain] v1.7 Oct 2007 D00659 accessed 14.4.2008</ref>

== Geographic Latitude and longitude ==
{{Main|Latitude|Longitude}}
[[File:Geographic coordinates sphere.svg|thumb|Latitude phi (φ) and Longitude lambda (λ)]]

[[Latitude]] (abbreviation: Lat., [[φ]], or phi) is the angle between the equatorial plane and a line that is normal to the reference ellipsoid, which approximates the shape of Earth to account for flattening of the poles and bulging of the equator. Lines joining points of the same latitude are called [[circle of latitude|parallels]], which trace concentric circles on the surface of the Earth, parallel to the equator. The [[north pole]] is 90° N; the [[south pole]] is 90° 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 and Southern Hemispheres.

[[Longitude]] (abbreviation: Long., [[λ]], or lambda) is the angle east or west of a reference meridian between the two geographical poles to another [[meridian (geography)|meridian]] that passes through an arbitrary point. All meridians are halves of great circles, and are not parallel. They converge at the north and south poles.

A line passing to the rear of the [[Royal Observatory, Greenwich]] (near London in the [[United Kingdom|UK]]) has been chosen as the international zero-longitude reference line, the [[Prime Meridian]]. Places to the east are in the eastern hemisphere, and places to the west are in the western hemisphere. The [[Antipodes|antipodal]] meridian of Greenwich is both 180°W and 180°E.

In 1884, the United States hosted the [[International Meridian Conference]] and twenty-five nations attended. Twenty-two of them agreed to adopt the location of Greenwich as the zero-reference line. [[Dominican Republic|San Domingo]] voted against the adoption of that motion, while [[France]] and [[Brazil]] abstained.<ref>http://wwp.millennium-dome.com/info/conference.htm</ref> To date, there exist organizations around the world which continue using historical prime meridians before the acceptance of Greenwich and the ill-attended conference became common-place.<ref name=ign>The French Institut Géographique National (IGN) still displays a latitude and longitude on its maps centred on a meridian that passes through Paris</ref>

The combination of these two components specifies the position of any location on the planet, but does not consider [[altitude]] nor [[:wikt:depth|depth]].

This latitude/longitude "webbing" is known as the '''''conjugate graticule'''''.

In defining an [[ellipse]], the short (vertical) diameter is known as the '''''conjugate diameter''''', and the long (horizontal) diameter—perpendicular, or "transverse", to the conjugate—is the '''''transverse diameter'''''.<ref>{{cite book | last = Haswell | first = Charles Haynes | url = http://books.google.com/books?id=Uk4wAAAAMAAJ&pg=RA1-PA381&zoom=3&hl=en&sig=3QTM7ZfZARnGnPoqQSDMbx8JeHg | title = Mechanics' and Engineers' Pocket-book of Tables, Rules, and Formulas | publisher = Harper & Brothers | year = 1920 | accessdate = 2007-04-09 }}</ref> With a sphere or ellipsoid, the conjugate diameter is known as the '''''[[Semi-minor axis|polar axis]]''''' and the transverse as the '''''[[Semi-major axis|equatorial axis]]'''''. The graticule [[Perspective (graphical)|perspective]] is based on this designation: As the longitudinal rings — geographically defined, all great circles — converge at the poles, it is the poles that the conjugate graticule is defined. If the polar vertex is "pulled down" 90°, so that the vertex is on the equator, or transverse diameter, then it becomes the '''transverse graticule''', upon which all [[spherical trigonometry]] is ultimately based (if the longitudinal vertex is between the poles and equator, then it is considered an '''''oblique graticule''''').


==UTM and UPS systems==
{{main|Universal Transverse Mercator|Universal Polar Stereographic}}
The [[Universal Transverse Mercator]] (UTM) and [[Universal Polar Stereographic]] (UPS) coordinate systems both use a metric-based cartesian grid laid out on a conformally projected surface to locate positions on the surface of the Earth. The UTM system is not a single map projection but a series of map projections, one for each of sixty zones. The UPS system is used for the polar regions, which are not covered by the UTM system.

==Stereographic coordinate system==
During medieval times, the stereographic coordinate system was used for navigation purposes.{{Citation needed|date=December 2007}} The stereographic coordinate system was superseded by the latitude-longitude system.

Although no longer used in navigations, the stereographic coordinate system is still used in modern times to describe crystallographic orientations in the field of materials science.{{Citation needed|date=December 2007}}

==Geodetic height==
To completely specify a location of a topographical feature on, in, or above the Earth, one has to also specify the vertical distance from the centre of the Earth, or from the surface of the Earth. Because of the ambiguity of "surface" and "vertical", it is more commonly expressed relative to a precisely defined [[datum (geodesy)|vertical datum]] which holds fixed a some known point. Each country has defined its own datum. For example, in the [[United Kingdom]] the reference point is [[Newlyn]], while in Canada, Mexico and the United States, the point is near [[Rimouski]], [[Quebec]], [[Canada]]. The distance to Earth's centre can be used both for very deep positions and for positions in space.<ref name=OSGB/>

==Cartesian coordinates==
Every point that is expressed in ellipsoidal coordinates can be expressed as an {{nowrap|x y z}} ([[Cartesian coordinate|Cartesian]]) coordinate. Cartesian coordinates simplify many mathematical calculations. The origin is usually the center of mass of the earth, a point close to the Earth's [[center of figure]].

==Shape of the Earth==
{{Main|Figure of the Earth|Reference ellipsoid}}
The Earth is not a sphere, but an irregular shape approximating a [[Earth ellipsoid|biaxial ellipsoid]]. It is nearly spherical, but has an equatorial bulge making the radius at the equator about 0.3% larger than the radius measured through the poles. The shorter axis approximately coincides with axis of rotation. Map-makers choose the true ellipsoid that best fits their need for the area they are mapping. They then choose the most appropriate mapping of the spherical coordinate system onto that ellipsoid. In the United Kingdom there are three common latitude, longitude, height systems in use. The system used by GPS, [[World Geodetic System|WGS84]], differs at Greenwich from the one used on published maps [[OSGB36]] by approximately 112m. The military system [[ED50]], used by [[NATO]], differs by about 120m to 180m.<ref name=OSGB/>

Though early navigators thought of the sea as a flat surface that could be used as a vertical datum, this is far from reality. The Earth can be thought to have a series of layers of equal [[potential energy]] within its [[gravitational field]]. Height is a measurement at right angles to this surface, and although gravity pulls mainly toward the centre of Earth, the geocentre, there are local variations. The shape of these layers is irregular but essentially ellipsoidal. The choice of which layer to use for defining height is arbitrary. The reference height we have chosen is the one closest to the average height of the world's oceans. This is called the [[geoid]].<ref name=OSGB/><ref name=USDOD>[http://www.ngs.noaa.gov/PUBS_LIB/Geodesy4Layman/geo4lay.pdf DMA Technical Report] Geodesy for the Layman, The Defense Mapping Agency, 1983</ref>

The Earth is not static as points move relative to each other due to continental plate motion, subsidence, and diurnal movement caused by the [[Moon]] and the [[tide]]s. The daily movement can be as much as a metre. 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 last [[ice age]], but neighbouring [[Scotland]] is only rising by {{nowrap|0.2 cm}}. These changes are insignificant if a local datum is used, but are significant if the global GPS datum is used.<ref name=OSGB/>{{Why|date=July 2009}}

== Expressing latitude and longitude as linear units==
On the GRS80 or WGS84 spheroid at [[sea level]] at the equator, one latitudinal second measures ''30.715 [[metre]]s'', one latitudinal minute is ''1843 metres'' and one latitudinal degree is ''110.6 kilometres''. 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 metres'', a longitudinal minute is ''1855 metres'' and a longitudinal degree is ''111.3 kilometres''. At 30° a longitudinal second is ''26.76 metres'', at Greenwich (51° 28' 38" N) ''19.22 metres'', and at 60° it is ''15.42 metres''.

The width of one longitudinal degree at latitude <math>\scriptstyle{\phi}\,\!</math> can be calculated by this formula (to get the width per minute and second, divide by 60 and 3600, respectively):

:::::<math> \frac{\pi}{180}\cos \phi (M_r) \!</math>
where [[Earth radius#Meridional Earth radius|Earth's average meridional radius]] <math>\scriptstyle{M_r}\,\!</math> approximately equals {{nowrap|6,367,449 m}}. Due to the average radius value used, this formula is of course not precise. A better approximation of a longitudinal degree at latitude <math>\scriptstyle{\phi}\,\!</math> is

:::::<math>\frac{\pi}{180}a \cos \beta \,\!</math>
where Earth's equatorial radius <math>a</math> equals ''6,378,137 m'' and <math>\scriptstyle{\tan \beta = \frac{b}{a}\tan\phi}\,\!</math>; for the GRS80 and WGS84 spheroids, b/a calculates to be 0.99664719. (<math>\scriptstyle{\beta}\,\!</math> is known as the parametric or [[Latitude#Reduced_latitude|reduced 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 meter of each other if the two points are one degree of longitude apart.

{| class="wikitable" border="1"
|+ '''Longitudinal length equivalents at selected latitudes'''
|-
!width="100"|Latitude
!width="150"|Town
!width="100"|Degree
!width="100"|Minute
!width="100"|Second
!width="100"|±0.0001°
|-
|60°||[[Saint Petersburg]]||align="center" | 55.65 km||align="center" | 0.927 km||align="center" | 15.42m ||align="center" | 5.56m
|-
|51° 28' 38" N||[[Greenwich]]||align="center" | 69.29 km||align="center" | 1.155 km||align="center" | 19.24m||align="center" | 6.93m
|-
|45°||[[Bordeaux]]||align="center" | 78.7 km||align="center" | 1.31 km||align="center" | 21.86m||align="center" | 7.87m
|-
|30°||[[New Orleans]]||align="center" | 96.39 km||align="center" | 1.61 km||align="center" | 26.77m||align="center" | 9.63m
|-
|0°||[[Quito]]||align="center" | 111.3 km ||align="center" | 1.855 km ||align="center" | 30.92m || align="center" | 11.13m
|}


== Datums often encountered ==
{{Main|geodetic system|datum (geodesy)}}
Latitude and longitude values can be based on several different [[geodetic system]]s or [[datum (geodesy)|datum]]s, the most common being [[World Geodetic System|WGS 84]] used by all GPS equipment.<ref>WGS 84 is the ''default'' datum used in most GPS equipment, but other datums can be selected.</ref> Other datums however are significant because they were chosen by a national cartographical organisation as the best method for representing their region, and these are the datums used on printed maps. Using the latitude and longitude found on a map may not give the same reference as on a GPS receiver. Coordinates from the [[Figure of the Earth#Historical Earth ellipsoids|mapping system]] can sometimes be changed into another datum using a simple [[translation]]. For example, to convert from ETRF89 (GPS) to the Irish Grid add 49 metres to the east, and subtract 23.4 metres from the north.<ref name=irish>[http://www.osi.ie/GetAttachment.aspx?id=25113681-c086-485a-b113-bab7c75de6fa Making maps compatible with GPS] Government of Ireland 1999. Accessed 15.4.2008</ref> More generally one datum is changed into any other datum using a process called [[Helmert transformation]]s. This involves converting the spherical coordinates into Cartesian coordinates and applying a seven parameter transformation (translation, three-dimensional [[rotation]]), and converting back.<ref name=OSGB/>

In popular GIS software, data projected in latitude/longitude is often represented as a 'Geographic Coordinate System'. For example, data in latitude/longitude if the datum is the [[NAD83|North American Datum of 1983]] is denoted by 'GCS North American 1983'.

==Geostationary coordinates==
[[Geostationary]] satellites (e.g., television satellites) are over the equator at a specific point on Earth, so their position related to Earth is expressed in longitude degrees only. Their latitude is always zero, that is, over the equator.

==See also==
{{Portal|Atlas}}
* [[Automotive navigation system]]
* [[Geographic coordinate conversion]]
* [[Geocoding]]
* [[Geodetic system]]
* [[Geographical distance]]
* [[Geotagging]]
* [[Great-circle distance]] the shortest distance between any two points on the surface of a sphere.
* [[Lambert conformal conic projection|Lambert coordinate system]]
* [[Map projection]]
* [[Tropic of Cancer]]
* [[Tropic of Capricorn]]

== References ==
{{Reflist}}
* ''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]''

== External links ==
* [http://math.rice.edu/~lanius/pres/map/mapcoo.html Mathematics Topics-Coordinate Systems]
* [https://www.cia.gov/library/publications/the-world-factbook/index.html Geographic coordinates of countries (CIA World Factbook)]
* [http://www.fcc.gov/mb/audio/bickel/DDDMMSS-decimal.html FCC coordinates conversion tool (DD to DMS/DMS to DD)]
* [http://www.sunearthtools.com/dp/tools/conversion.php Coordinate converter, formats: DD, DMS, DM]

{{DEFAULTSORT:Geographic Coordinate System}}
[[Category:Geographic coordinate systems|*]]
[[Category:Cartography]]
[[Category:Navigation]]
[[Category:Geocodes]]

Geographic coordinate system - Revision history

imported>Koko CRAB at 12:30, 19 June 2024