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Encyclopedia > Geographic coordinate system
Map of Earth showing lines of latitude (horizontally) and longitude (vertically), Eckert VI projection; large version (pdf, 1.8MB)

A geographic coordinate system enables every location on the earth to be specified, using mainly a spherical coordinate system. There are three coordinates: latititude, longitude and geodesic height. Based on a screenshot of a CIA World Factbook PDF. I cropped it, added text labels, and changed file format. ... Based on a screenshot of a CIA World Factbook PDF. I cropped it, added text labels, and changed file format. ... This article is about Earth as a planet. ... This article is about the geographical term. ... Longitude is the east-west geographic coordinate measurement most commonly utilized in cartography and global navigation. ... This article describes some of the common coordinate systems that appear in elementary mathematics. ...

The earth is not a sphere, but an irregular changing shape approximating to an ellipsoid; the challenge is to define a coordinate system that can accurately state each topographical feature as an unambiguous set of numbers. [1] For other uses, see Sphere (disambiguation). ... 3D rendering of an ellipsoid In mathematics, an ellipsoid is a type of quadric that is a higher dimensional analogue of an ellipse. ...

Latitude phi (φ) and Longitude lambda (λ)

Latitude (abbreviation: Lat. or (φ) pronounced phi ) is the angle from a point on the earth's surface and the equatorial plane, measured from the centre of the sphere. Lines joining points of the same latitude are called parallels, and they trace concentric circles on the surface of the earth, parallel to the equator. The north pole 90° N; the south pole 90° S. The 0° parallel of latitude is designated the equator. The equator is the fundamental plane of all geographic coordinate systems. The equator divides the globe into the Northern and Southern Hemispheres. This article is about the geographical term. ... Image File history File links Geographic_coordinates_sphere. ... Image File history File links Geographic_coordinates_sphere. ... This article is about the geographical term. ... World map showing the equator in red In tourist areas, the equator is often marked on the sides of roads The equator marked as it crosses IlhÃ©u das Rolas, in SÃ£o TomÃ© and PrÃ­ncipe. ... On the Earth, a circle of latitude is an imaginary east-west circle that connects all locations with a given latitude. ... For other uses, see North Pole (disambiguation). ... For other uses, see South Pole (disambiguation). ... The fundamental plane in a spherical coordinate system is a plane which divides the sphere into two hemispheres. ...

Longitude (abbreviation: Long. or (λ)pronounced lambda) is the angle east or west of north–south line between the two geographical poles, that passes through an arbitrary point. Lines joining points of the same longitude are called meridians. All meridians are halves of great circles, and are not parallel. They converge at the north and south poles. Longitude is the east-west geographic coordinate measurement most commonly utilized in cartography and global navigation. ... On the earth, a meridian is a north-south line between the North Pole and the South Pole. ...

The line passing through the (former) Royal Observatory, Greenwich (near London in the UK) has been chosen as the international zero-longitude reference line, the Prime Meridian. Places to east are in the eastern hemisphere, and places to the west in the western hemisphere. The antipodal meridian of Greenwich is both 180°W and 180°E. The choice of Greenwich is arbitrary, and in other cultures and times in history other locations have been used as the prime meridian.[2] Royal Observatory, Greenwich. ... Location of the Prime Meridian Image:Prime Meridian. ... This map shows the antipodes of each point on the Earths surface â€“ the points where the blue and pink overlap are land antipodes. ...

### Degrees: a measurement of angle

For a further discussion of angular measure on Wikipedia pages see: Angle

[3] Before Arabic numbers replaced roman numerals, i.e. before place value was used, decimal fractions were not possible and the number sixty was very important, so we have 60 minutes in an hour to this day. Similarly a degree was divided in sixty parts,minutes and the minute into 60 seconds. This provided sufficient accuracy for navigation systems, but not for today's needs. A minute is designated by ′ or "m" and the second is designated by ″ or "s". Today, if greater accuracy is required, the second can be represented as a decimal number. Alternatively, angle can be expressed as a decimal number. The letters N,S, E,W can be used to indicate the hemisphere, or we can use "+" and "-" to show this. North and East are "+", and South and West are "-". Latitude and Longitude can be separated by a space or a comma. This article is about angles in geometry. ... A minute of arc, arcminute, or MOA is a unit of angular measurement, equal to one sixtieth (1/60) of one degree. ... A second of arc or arcsecond is a unit of angular measurement which comprises one-sixtieth of an arcminute, or 1/3600 of a degree of arc or 1/1296000 â‰ˆ 7. ...

Thus there are several formats for writing degrees, all of them appearing in the same Lat,Long order.

• DMS Degree:Minute:Second (49°30'02"N, 123°30'30") or (49d30m02.5s,-123d30m30.17s)
• DM Degree:Minute (49°30.0'-123°30.0'), (49d30.0m,-123°30.0')
• DD Decimal Degree (49.5000°,-123.5000°), generally with 4 decimal numbers.

DMS is the most common format, and is standard on all charts and maps, as well as global positioning systems and geographic information systems.

## Geodesic 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 sphere, or from the surface of the sphere. Because of the ambiguity of "surface" and "vertical", it is more commonly expressed relative to a more precisely defined vertical datum such as mean sea level at a named point. Each country has defined its own datum. In the United Kingdom the reference point is Newlyn. The distance to the earth's centre can be used both for very deep positions and for positions in space. [1] It has been suggested that this article or section be merged with Geodetic system. ... For considerations of sea level change, in particular rise associated with possible global warming, see sea level rise. ... Newlyn Map sources for Newlyn at grid reference SW461284 Newlyn (Cornish: Lulynn) is a town in southwest Cornwall, UK. The town forms a small conurbation with neighbouring Penzance, and part of the civil parish of Penzance. ...

## Cartesian Coordinates

Every point that is expressed as spherical coordinate can be expressed as a x,y z (Cartesian) coordinate. This is not a useful method for recording the position on maps but is used to calculate distances, and to perform other mathematic operations. The source is usually the centre of the sphere, a point close the centre of the earth. Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ...

## The Shape of the Earth

The earth is not a sphere, but an irregular changing shape approximating to an biaxial ellipsoid. It is nearly spherical, but has an equatorial bulge making the radius at the equator about 0.3% bigger than the radius measured through the poles. The shorter axis very 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,WGS84 differs in Greenwich from the one used on published maps OSGB36 by approximately 112m. The military system ED50, used by NATO is different again and gives inaccuracies of about 120m, and 180m.[1] WGS 84 is the 1984 revision of the World Geodetic System. ... ED 50 (European Datum 1950) is a geodetic datum which was defined after World War II for the international connection of geodetic networks. ...

Though early navigators thought of the sea as a flat surface that could be used a vertical datum, this is far from reality. The earth can be thought a series of layers of equal potential energy within the earth gravitational field. Height is a measurement at right angles to this surface, and though gravity pulls mainly toward the centre of the earth, the geocentre, there are local variations. The shape of these layers is irregular but essentially ellipsoidal. The choice of which of these layers to choose is arbitrary. The reference height we have chosen is the one closest to the average height of the worlds oceans. This is called the Geoid.[1][4] The GOCE project will measure high-accuracy gravity gradients and provide an accurate geoid model based on the Earths gravity field. ...

The earth is not static, points move relative to each other due to continental plate motion, subsidence and diurnal movement caused by the moon and the tides. The daily movement can be as much as a metre. Continental movement can be up to 10 cm a year, or 10m in a century. A weather system 'high' pressure area can cause a sinking of 5mm. Scandinavia is rising by 1 cm a year as a result of the recession of the last Ice age, but neighboring Scotland is only rising by 0.2 cm. These changes are insignificant is a local datum is used. Wikipedia uses the global GPS datum so these changes are significant.[1] A large low-pressure system swirls off the southwestern coast of Iceland, illustrating the maxim that nature abhors a vacuum. ... For other uses, see Scandinavia (disambiguation). ... This article is about the country. ...

## Expressing latitude and longitude as linear units

On a spherical surface at sea level, one latitudinal second measures 30.82 metres and one latitudinal minute 1849 metres, and one latitudinal degree is 110.9 kilometres. The circles of longitude, the meridians, meet at the geographical poles, with the west-east width of a second being dependent on the latitude. On the equator at sea level, one longitudinal second measures 30.92 metres ,a longitudinal minute 1855 metres and a longitudinal degree111.3 kilometres.[5] For considerations of sea level change, in particular rise associated with possible global warming, see sea level rise. ... This article is about the unit of length. ... On the earth, a meridian is a north-south line between the North Pole and the South Pole. ... A geographical pole is either of two fixed points on the surface of a spinning body or planet, at 90 degrees from the equator, based on the axis around which a body spins. ... World map showing the equator in red In tourist areas, the equator is often marked on the sides of roads The equator marked as it crosses IlhÃ©u das Rolas, in SÃ£o TomÃ© and PrÃ­ncipe. ...

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

$frac{pi}{180^{circ}}cos(phi)M_r,,!$

where Earth's average meridional radius $scriptstyle{M_r},!$ approximately equals 6,367,449 m. Due to the average radius value used, this formula is of course not precise. You can get a better approximation of a longitudinal degree on latitude $scriptstyle{phi},!$ by: Because the Earth, like all planets, is not a perfect sphere, the radius of Earth can vary at different places on the surface. ...

$frac{pi}{180^{circ}}cos(phi)sqrt{frac{a^4cos(phi)^2+b^4sin(phi)^2}{(acos(phi))^2+(bsin(phi))^2}},,!$

where Earth's equatorial and polar radii, $scriptstyle{a,b},!$ equal 6,378,137 m, 6,356,752.3 m, respectively.

Length Equivalent at Selected Latitudes in km
Latitude Town Degree Minute Second Decimal Degree at 4 dp
60 Saint Petersburg 55.65km 0.927km 15.42m 5.56m
51° 28' 38" N Greenwich 69.29km 1.155km 19.24m 6.93m
45 Bordeaux 78.7km 1.31km 21.86m 7.87m
30 New Orleans 96.39km 1.61km 26.77m 9.63m
0 Quito 111.3km 1.855km 30.92m 11.13m

Saint Petersburg (Russian: Санкт-Петербу́рг, English transliteration: Sankt-Peterburg), colloquially known as Питер (transliterated Piter), formerly known as Leningrad (Ленингра́д, 1924–1991) and Petrograd (Петрогра́д, 1914–1924), is a city located in Northwestern Russia on the delta of the river Neva at the east end of the Gulf of Finland... This article is about Greenwich in England. ... For other uses, see Bordeaux (disambiguation). ... New Orleans is the largest city in the state of Louisiana, United States of America. ... For other uses, see Quito (disambiguation). ...

## Datums often encountered

Latitude and longitude values can be based on several different geodetic systems or datums, the most common being the WGS 84 used by all GPS equipment, and by Wikipedia. Other datums however are significant because they were chosen by national cartographical organisation as the best method for representing their region, and these are the datum used on printed maps. Using the latitude and longitude found on a map, will not give the same reference as on a GPS receiver. Coordinates from the mapping system can be sometimes be changed into another datum using a simple translation. For example to convert from ETRF89 (GPS) to the Irish Grid by 49m to the east, and subtracting 23.4m from the north. [6] More generally one datum is changed into any other datum using a process called Helmert transformations. This involves, converting the spherical coordinates into Cartesian coordinates and applying a seven parameter transformation (a translation and 3D- rotation), and converting back.[1] It has been suggested that this article or section be merged with Datum. ... It has been suggested that this article or section be merged with Geodetic system. ... The World Geodetic System defines a reference frame for the earth, for use in geodesy and navigation. ... The expression figure of the Earth has various meanings in geodesy according to the way it is used and the precision with which the Earths size and shape is to be defined. ... Look up translate in Wiktionary, the free dictionary. ... Look up translate in Wiktionary, the free dictionary. ... This article is about rotation as a movement of a physical body. ...

In popular GIS software, data projected in latitude/longitude is often specified via a 'Geographic Coordinate System'. For example, data in latitude/longitude with the datum as the North American Datum of 1983 is denoted by 'GCS_North_American_1983'. It has been suggested that this article or section be merged with Geodetic system. ... The North American Datum is the official reference ellipsoid used for the primary geodetic network in North America. ...

## Geostationary coordinates

Geostationary satellites (e.g., television satellites ) are over the equator. So, their position related to Earth is expressed in longitude degrees. Their latitude does not change, and is always zero over the equator. A geostationary orbit (abbreviated GEO) is a circular orbit in the Earths equatorial plane, any point on which revolves about the Earth in the same direction and with the same period as the Earths rotation. ...

A taxi in Kyoto, equipped with GPS navigation system An automotive navigation system is a satellite navigation system designed for use in automobiles. ... GIS redirects here. ... Geographic coordinates consist of latitude and longitude. ... A geocode is a geographical code to identify a point or area at the surface of the earth. ... Geotagging, sometimes referred to as Geocoding, is the process of adding geographical identification metadata to various media such as websites, RSS feeds, or images. ... GPS redirects here. ... The great-circle distance is the shortest distance between any two points on the surface of a sphere measured along a path on the surface of the sphere (as opposed to going through the spheres interior). ... The Mercator projection shows courses of constant bearing as straight lines. ... For the novel by Henry Miller, see Tropic of Cancer (novel). ... World map showing the Tropic of Capricorn For the novel by Henry Miller, see Tropic of Capricorn (novel). ... The UTM Grid The Universal Transverse Mercator (UTM) coordinate system is a grid-based method of specifying locations on the surface of the Earth. ... Pole carrying telephone, electricity and Cable TV equipment. ...

## References

• Portions of this article are from Jason Harris' "Astroinfo" which is distributed with KStars, a desktop planetarium for Linux/KDE. See [1]
1. ^ a b c d e f A Guide to coordinate systems in Great Britain v1.7 Oct 2007 D00659 accessed 14.4.2008
2. ^ The French Institute Géographic Nationale, still displays a latitude and longitude on its maps centred on a meridian that passes through Paris
3. ^ Borrowing from theories of the ancient Babylonians, later expanded by the famous Greek mathematician and geographer Ptolemy, a full circle is divided into 360 degrees.
4. ^ DMA Technical Report Geodesy for the Layman, The Defense Mapping Agency, 1983
6. ^ Making maps compatible with GPS Government of Ireland 1999. Accessed 15.4.2008

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