Geographic coordinate system

For broader coverage of this topic, seeSpatial reference system.

Longitude lines are perpendicular to and latitude lines are parallel to the Equator

Ageographic coordinate system(GCS) is asphericalorgeodetic coordinatesystem for measuring and communicatingpositionsdirectly onEarthaslatitudeandlongitude.It is the simplest, oldest and most widely used of the variousspatial reference systemsthat are in use, and forms the basis for most others. Although latitude and longitude form a coordinatetuplelike acartesian coordinate system,the geographic coordinate system is not cartesian because the measurements are angles and are not on a planar surface.

A full GCS specification, such as those listed in theEPSGand ISO 19111 standards, also includes a choice ofgeodetic datum(including anEarth ellipsoid), as different datums will yield different latitude and longitude values for the same location.

History

See also:History of geodesy

Theinventionof a geographic coordinate system is generally credited toEratosthenesofCyrene,who composed his now-lostGeographyat theLibrary of Alexandriain the 3rd century BC.A century later,HipparchusofNicaeaimproved on this system by determining latitude from stellar measurements rather than solar altitude and determining longitude by timings oflunar eclipses,rather thandead reckoning.In the 1st or 2nd century,Marinus of Tyrecompiled an extensive gazetteer andmathematically plotted world mapusing coordinates measured east from aprime meridianat the westernmost known land, designated theFortunate Isles,off the coast of western Africa around theCanaryorCape Verde Islands,and measured north or south of the island ofRhodesoffAsia Minor.Ptolemycredited him with the full adoption of longitude and latitude, rather than measuring latitude in terms of the length of themidsummerday.

Ptolemy's 2nd-centuryGeographyused the same prime meridian but measured latitude from theEquatorinstead. After their work was translated intoArabicin the 9th century,Al-Khwārizmī'sBook of the Description of the Earthcorrected Marinus' and Ptolemy's errors regarding the length of theMediterranean Sea,causingmedieval Arabic cartographyto use a prime meridian around 10° east of Ptolemy's line. Mathematical cartography resumed in Europe followingMaximus Planudes' recovery of Ptolemy's text a little before 1300; the text was translated intoLatinatFlorencebyJacopo d'Angeloaround 1407.

In 1884, theUnited Stateshosted theInternational Meridian Conference,attended by representatives from twenty-five nations. Twenty-two of them agreed to adopt the longitude of theRoyal ObservatoryinGreenwich,England as the zero-reference line. TheDominican Republicvoted against the motion, while France andBrazilabstained.France adoptedGreenwich Mean Timein place of local determinations by theParis Observatoryin 1911.

Latitude and longitude

Diagram of the latitudeϕand longitudeλangle measurements for a spherical model of the Earth.

Main articles:LatitudeandLongitude

Thelatitudeϕof 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.Lines joining points of the same latitude trace circles on the surface of Earth calledparallels,as they are parallel to the Equator and to each other. TheNorth Poleis 90° N; theSouth Poleis 90° S. The 0° parallel of latitude is designated theEquator,thefundamental planeof all geographic coordinate systems. The Equator divides the globe intoNorthernandSouthern Hemispheres.

Thelongitudeλof a point on Earth's surface is the angle east or west of a referencemeridianto another meridian that passes through that point. All meridians are halves of greatellipses(often calledgreat circles), which converge at the North and South Poles. The meridian of the BritishRoyal ObservatoryinGreenwich,in southeast London, England, is the internationalprime meridian,although some organizations—such as the FrenchInstitut national de l'information géographique et forestière—continue to use other meridians for internal purposes. The prime meridian determines the properEasternandWestern Hemispheres,although maps often divide these hemispheres further west in order to keep theOld Worldon a single side. Theantipodalmeridian of Greenwich is both 180°W and 180°E. This is not to be conflated with theInternational Date Line,which diverges from it in several places for political and convenience reasons, including between far eastern Russia and the far westernAleutian Islands.

The combination of these two components specifies the position of any location on the surface of Earth, without consideration ofaltitudeor depth. The visual grid on a map formed by lines of latitude and longitude is known as agraticule.The origin/zero point of this system is located in theGulf of Guineaabout 625 km (390 mi) south ofTema,Ghana,a location often facetiously calledNull Island.

Geodetic datum

Main article:Geodetic datum

Further information:Figure of the Earth,Reference ellipsoid,Geographic coordinate conversion,andSpatial reference system

In order to use the theoretical definitions of latitude, longitude, and height to precisely measure actual locations on the physical earth, ageodetic datummust be used. Ahorizonal datumis used to precisely measure latitude and longitude, while avertical datumis used to measure elevation or altitude. Both types of datum bind a mathematical model of the shape of the earth (usually areference ellipsoidfor a horizontal datum, and a more precisegeoidfor a vertical datum) to the earth. Traditionally, this binding was created by a network ofcontrol 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 thecenter of massof 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 anyspatial reference systemormap projectionis ultimately calculated from latitude and longitude, it is crucial that they clearly state the datum on which they are based. For example, aUTMcoordinate based onWGS84will be different than a UTM coordinate based onNAD27for the same location. Converting coordinates from one datum to another requires adatum transformationsuch as aHelmert transformation,although in certain situations a simpletranslationmay be sufficient.

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 includeWorld Geodetic System(WGS84, also known as EPSG:4326), the default datum used for theGlobal Positioning System,and theInternational Terrestrial Reference System and Frame(ITRF), used for estimatingcontinental driftandcrustal deformation.The distance to Earth's center can be used both for very deep positions and for positions in space.

Local datums chosen by a national cartographical organization include theNorth American Datum,the EuropeanED50,and the BritishOSGB36.Given a location, the datum provides the latitude$\phi$and longitude$\lambda$.In the United Kingdom there are three common latitude, longitude, and height systems in use. WGS84 differs at Greenwich from the one used on published maps OSGB36 by approximately 112m. The military systemED50,used byNATO,differs from about 120m to 180m.

Points on the Earth's surface move relative to each other due to continental plate motion, subsidence, and diurnalEarth tidalmovement caused by theMoonand the Sun. This daily movement can be as much as a meter. Continental movement can be up to10 cma year, or10 min a century. Aweather systemhigh-pressure area can cause a sinking of5 mm.Scandinaviais rising by1 cma year as a result of the melting of the ice sheets of thelast ice age,but neighboringScotlandis rising by only0.2 cm.These changes are insignificant if a local datum is used, but are statistically significant if a global datum is used.

Length of a degree

Main articles:Length of a degree of latitudeandLength of a degree of longitude

See also:Arc length § Great circles on Earth

On the GRS80 orWGS84spheroid atsea levelat the Equator, one latitudinal second measures 30.715m,one latitudinal minute is 1843 m and one latitudinal degree is 110.6 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 theEquatorat sea level, one longitudinal second measures 30.92 m, a longitudinal minute is 1855 m and a longitudinal degree is 111.3 km. At 30° a longitudinal second is 26.76 m, at Greenwich (51°28′38″N) 19.22 m, and at 60° it is 15.42 m.

On the WGS84 spheroid, the length in meters of a degree of latitude at latitudeϕ(that is, the number of meters you would have to travel along a north–south line to move 1 degree in latitude, when at latitudeϕ), is about

$111132.92-559.82\,\cos 2\phi +1.175\,\cos 4\phi -0.0023\,\cos 6\phi$

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

$111412.84\,\cos \phi -93.5\,\cos 3\phi +0.118\,\cos 5\phi$

(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$\phi$is to assume a spherical Earth (to get the width per minute and second, divide by 60 and 3600, respectively):

${\frac {\pi }{180}}M_{r}\cos \phi \!$

whereEarth's average meridional radius$\textstyle {M_{r}}\,\!$is6,367,449 m.Since the Earth is anoblate spheroid,not spherical, that result can be off by several tenths of a percent; a better approximation of a longitudinal degree at latitude$\phi$is

${\frac {\pi }{180}}a\cos \beta \,\!$

where Earth's equatorial radius$a$equals 6,378,137 m and$\textstyle {\tan \beta ={\frac {b}{a}}\tan \phi }\,\!$;for the GRS80 and WGS84 spheroids,${\textstyle {\tfrac {b}{a}}=0.99664719}$.($\textstyle {\beta }\,\!$is known as thereduced (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.

Longitudinal length equivalents at selected latitudes

Latitude	City	Degree	Minute	Second	±0.0001°
60°	Saint Petersburg	55.80 km	0.930 km	15.50 m	5.58 m
51° 28′ 38″ N	Greenwich	69.47 km	1.158 km	19.30 m	6.95 m
45°	Bordeaux	78.85 km	1.31 km	21.90 m	7.89 m
30°	New Orleans	96.49 km	1.61 km	26.80 m	9.65 m
0°	Quito	111.3 km	1.855 km	30.92 m	11.13 m

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 Alpha numeric strings or words:

• theMaidenhead Locator System,popular with radio operators.
• theWorld Geographic Reference System(GEOREF), developed for global military operations, replaced by the currentGlobal Area Reference System(GARS).
• Open Location Codeor "Plus Codes", developed by Google and released into the public domain.
• Geohash,a public domain system based on the MortonZ-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

• Decimal degrees– Angular measurements, typically for latitude and longitude
• Geographical distance– Distance measured along the surface of the Earth
• Geographic information system– System to capture, manage, and present geographic data
• Geo URI scheme– System of geographic location identifiers
• ISO 6709,standard representation of geographic point location by coordinates
• Linear referencing– method of spatial referencingPages displaying wikidata descriptions as a fallback
• Primary direction– Celestial coordinate system used to specify the positions of celestial objectsPages displaying short descriptions of redirect targets
• Planetary coordinate system
  • Selenographic coordinate system
• Spatial reference system– System to specify locations on Earth
• Jan Smits (2015).Mathematical data for bibliographic descriptions of cartographic materials and spatial data.Geographical co-ordinates.ICACommission on Map Projections.

References

Sources

• Portions of this article are from Jason Harris' "Astroinfo" which is distributed withKStars,a desktop planetarium forLinux/KDE.SeeThe KDE Education Project – KStarsArchived17 May 2008 at theWayback Machine

External links

• Media related toGeographic coordinate systemat Wikimedia Commons