For the use of coordinates on Wikipedia pages see: Wikipedia:WikiProject Geographical coordinates
Map of Earth showing lines of latitude (horizontally) and longitude (vertically), Eckert VI projection; large version (pdf, 1. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 Latitude, usually denoted symbolically by the Greek letter phi ( Φ) gives the location of a place on Earth (or other planetary body north or south of the Longitude (ˈlɒndʒɪˌtjuːd or ˈlɒŋgɪˌtjuːd symbolized by the Greek character Lambda (λ is the east-west Geographic coordinate measurement 8MB)

A geographic coordinate system enables every location on the earth to be specified, using mainly a spherical coordinate system. In Mathematics, the spherical coordinate system is a Coordinate system for representing geometric figures in three dimensions using three coordinates the radial There are three coordinates: latitude, longitude and geodesic height.

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. "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe An ellipsoid is a type of quadric surface that is a higher dimensional analogue of an Ellipse. [1]

## Latitude and longitude

Latitude phi (φ) and Longitude lambda (λ)

Latitude (abbreviation: Lat. Latitude, usually denoted symbolically by the Greek letter phi ( Φ) gives the location of a place on Earth (or other planetary body north or south of the Latitude, usually denoted symbolically by the Greek letter phi ( Φ) gives the location of a place on Earth (or other planetary body north or south of the 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. The equator (sometimes referred to colloquially as "the Line") is the intersection of the Earth 's surface with the plane perpendicular to the 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. A circle of latitude, on the Earth, is an imaginary East - West circle connecting all locations (not taking into account elevation that share a given The north pole 90° N; the south pole 90° S. The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is subject to the caveats explained below defined as the point in the northern The South Pole, also known as the Geographic South Pole or Terrestrial South Pole, is the southernmost point on the surface of the Earth. The 0° parallel of latitude is designated the equator. The equator is the fundamental plane of all geographic coordinate systems. The fundamental plane in a Spherical coordinate system is a Plane which divides the Sphere into two Hemispheres The Latitude of a The equator divides the globe into the Northern and Southern Hemispheres.

Longitude (abbreviation: Long. Longitude (ˈlɒndʒɪˌtjuːd or ˈlɒŋgɪˌtjuːd symbolized by the Greek character Lambda (λ is the east-west Geographic coordinate measurement 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. This article is about the geographical concept For other uses of the word see Meridian. All meridians are halves of great circles, and are not parallel. They converge at the north and south poles.

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. The Royal Observatory Greenwich (formerly the Royal Greenwich Observatory or RGO) was commissioned in 1675 by King Charles II, with the The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located The Prime Meridian is the meridian (line of Longitude) at which longitude is defined to be 0° 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 antipodes refer to lands and peoples located on the opposite side of the World compared to the speaker The choice of Greenwich is arbitrary, and in other cultures and times in history other locations have been used as the prime meridian. [2]

By combining these two angles, the horizontal position of any location on Earth can be specified.

For example, Baltimore, Maryland (in the USA) has a latitude of 39. The United States of America —commonly referred to as the 3° North, and a longitude of 76. 6° West (39.3° N 76.6° W). So, a vector drawn from the center of the earth to a point 39. 3° north of the equator and 76. 6° west of Greenwich will pass through Baltimore.

### Graticule perspective

This latitude/longitude "webbing" is known as the conjugate graticule.
In defining an ellipse, the vertical diameter is known as the conjugate diameter, and the horizontal diameter——which is perpendicular, or "transverse", to the conjugate——is the transverse diameter. In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a [3] With a sphere or ellipsoid, the conjugate diameter is known as the polar axis and the transverse as the equatorial axis. In Geometry, the semi-minor axis (also semiminor axis) is a Line segment associated with most Conic sections (that is with ellipses and In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae The graticule 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. Perspective (from Latin perspicere to see through in the graphic arts such as drawing is an approximate representation on a flat surface (such as paper of an image as it is perceived 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). Spherical trigonometry is a part of Spherical geometry that deals with Polygons (especially Triangles on the Sphere and explains how to find relations

### Degrees: a measurement of angle

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

Geographic coordinates were first used by the astronomer and geographer Ptolemy in his Geographia using alphabetic Greek numerals based on sexagesimal (base 60) Babylonian numerals. In Geometry and Trigonometry, an angle (in full plane angle) is the figure formed by two rays sharing a common Endpoint, called Claudius Ptolemaeus ( Greek: Klaúdios Ptolemaîos; after 83 &ndash ca The Geographia or Geography is Ptolemy 's main work besides the Almagest. ʹ the numeral sign redirects here For the accent ´ see Acute accent. Sexagesimal ( base-sixty) is a Numeral system with sixty as the base. Babylonian numerals were written in cuneiform, using a wedge-tipped reed Stylus to make a mark on a soft Clay tablet which would be exposed This was continued by Muslim geographers using alphabetic Abjad numerals and later via Arabic numerals. The Abjad numerals are a decimal Numeral system in which the 28 letters of the Arabic alphabet are assigned numerical values The arabic numerals (often capitalized are the ten Digits (0 1 2 3 4 5 6 7 8 9 which—along with the system In these systems a full circle is divided into 360 degrees and each degree is divided into 60 minutes. This article describes the unit of angle For other meanings see Degree. A minute of arc, arcminute, or MOA is a unit of angular measurement, equal to one sixtieth (1/60 of one degree. Although seconds, thirds, fourths, etc. A minute of arc, arcminute, or MOA is a unit of angular measurement, equal to one sixtieth (1/60 of one degree. were used by Hellenistic and Arabic astronomers, they were not used by geographers who recognized that their geographic coordinates were imprecise. Greek astronomy is the Astronomy of those who wrote in the Greek language in Classical antiquity. Arabic (ar الْعَرَبيّة (informally ar عَرَبيْ) in terms of the number of speakers is the largest living member of the Semitic language Today seconds subdivided decimally are used. A minute of arc, arcminute, or MOA is a unit of angular measurement, equal to one sixtieth (1/60 of one degree. A minute is designated by ′ or "m" and the second is designated by ″ or "s". Seconds can be expressed as a decimal fraction of a minute, and minutes can be expressed as a decimal fraction of a degree. 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. 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. This article describes a concept from Surveying and Geodesy. For other meanings see Datum (disambiguation. Mean sea level (MSL is the average (mean height of the Sea, with reference to a suitable reference surface Each country has defined its own datum. In the United Kingdom the reference point is Newlyn. Newlyn (Lulynn is a town in southwest Cornwall, England, UK. The town forms a small Conurbation with neighbouring Penzance, The distance to the earth's centre can be used both for very deep positions and for positions in space. [1]

## Cartesian coordinates

Every point that is expressed as spherical coordinate can be expressed as a x,y z (Cartesian) coordinate. In Mathematics, the Cartesian coordinate system (also called rectangular coordinate system) is used to determine each point uniquely in a plane 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.

## Shape of the Earth

The earth is not a sphere, but an irregular changing shape approximating to a biaxial ellipsoid. The Earth ellipsoid -- especially the mean Earth ellipsoid -- is the mathematical Figure of the Earth which is used as a Reference frame for computations 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 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 World Geodetic System defines a reference frame for the earth for use in Geodesy and Navigation. The British national grid reference system is a system of geographic grid references commonly used in Great Britain, different from using Latitude and Longitude The military system ED50, used by NATO is different again and gives inaccuracies of about 120m, and 180m. ED 50 ( European Datum 1950) is a geodetic datum which was defined after World War II for the international connection of Geodetic networks [1]

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 a series of layers of equal potential energy within its 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 world's oceans. This is called the Geoid. The geoid is that Equipotential surface which would coincide exactly with the mean ocean surface of the Earth if the oceans were in equilibrium at rest and extended through [1][4]

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. The weather is a set of all the phenomena occurring in a given Atmosphere at a given Time. Scandinavia is rising by 1 cm a year as a result of the recession of the last ice age, but neighbouring Scotland is only rising by 0. Terminology and usage As a cultural term "Scandinavia" has no official definition and is subject to usage by those who identify with the culture in question as well An ice age is a period of long-term reduction in the Temperature of the Earth 's surface and atmosphere resulting in an expansion of continental Ice sheets Scotland ( Gaelic: Alba) is a Country in northwest Europethat occupies the northern third of the island of Great Britain. 2 cm. These changes are insignificant if a local datum is used. Wikipedia uses the global GPS datum so these changes are significant. [1]

## Expressing latitude and longitude as linear units

On a spherical surface at sea level, one latitudinal second measures 30. Mean sea level (MSL is the average (mean height of the Sea, with reference to a suitable reference surface 82 metres and one latitudinal minute 1849 metres, and one latitudinal degree is 110. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International 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. This article is about the geographical concept For other uses of the word see Meridian. A geographical pole, or geographic 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 equator at sea level, one longitudinal second measures 30. The equator (sometimes referred to colloquially as "the Line") is the intersection of the Earth 's surface with the plane perpendicular to the 92 metres ,a longitudinal minute 1855 metres and a longitudinal degree111. 3 kilometres. [5]

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. The Earth 's shape like that of all major Planets approximates a Sphere. 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:

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

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
LatitudeTownDegreeMinuteSecondDecimal degree at 4 dp
60Saint Petersburg55. Saint Petersburg ( tr: Sankt-Peterburg,) is a city and a federal subject of Russia located on the Neva River 65km0. 927km15. 42m5. 56m
51° 28' 38" NGreenwich69. Greenwich ( ˈɡrɛnɪtʃ GREN-itch /ˈɡrɛnɪdʒ/ GREN-idge or /ˈɡrɪnɪdʒ/ GRIN-idge is a district in south-east London, 29km1. 155km19. 24m6. 93m
45Bordeaux78. ( Gascon: Bordèu) is a port city in southwest France, with one million inhabitants in its metropolitan area at a 2008 estimate 7km1. 31km21. 86m7. 87m
30New Orleans96. New Orleans (nʲuːˈɔrliənz nʲuːˈɔrlənz French: La Nouvelle-Orléans) is a major United States port city and the largest city in Louisiana 39km1. 61km26. 77m9. 63m
0Quito111. Quito, officially San Francisco de Quito, is the Capital of Ecuador in northwestern South America. 3km1. 855km30. 92m11. 13m

## 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. Geodetic systems or geodetic data are used in Geodesy, Navigation, Surveying by Cartographers and Satellite navigation systems The World Geodetic System defines a reference frame for the earth for use in Geodesy and Navigation. 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. The expression figure of the Earth has various meanings in Geodesy according to the way it is used and the precision with which the Earth's size and shape is to be defined Translation is the interpreting of the meaning of a text and the subsequent production of an equivalent text likewise called a " 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. The Helmert transformation (named after Friedrich Robert Helmert, 1843&ndash1917 also called a seven-parameter transformation) is a transformation method within This involves, converting the spherical coordinates into Cartesian coordinates and applying a seven parameter transformation (a translation and 3D- rotation), and converting back. Translation is the interpreting of the meaning of a text and the subsequent production of an equivalent text likewise called a " translation A rotation is a movement of an object in a circular motion A two- Dimensional object rotates around a center (or point) of rotation [1]

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'. This article describes a concept from Surveying and Geodesy. For other meanings see Datum (disambiguation. The North American Datum is the official datum used for the primary Geodetic network in North America

## Geostationary coordinates

Geostationary satellites (e. A geostationary orbit (GEO is a Geosynchronous orbit directly above the Earth 's Equator (0° Latitude) with a period equal to the Earth's 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.