Geographic coordinate system

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"Graticule" redirects here and may mean: a wire or cross lines in an optical focusing system.

A geographic coordinate system is a ellipsoidal coordinate system that enables every location on the surface of the Earth to be specified in two coordinates.

The Earth is not a sphere, but an irregular shape approximating an ellipsoid; the challenge is to define a coordinate system that can accurately state each topographical point as an unambiguous tuple of numbers.[1] It is often most convenient to let one of the numbers represent vertical position, and to let two or three of the numbers represent horizontal position.


Geographic Latitude and longitude

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 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 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 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.


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. San Domingo voted against the adoption of that motion, while France and Brazil abstained.[2] 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.[3]



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.[4] With a sphere or ellipsoid, the conjugate diameter is known as the polar axis and the transverse as the equatorial axis. 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. 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


Stereographic coordinate system


Although no longer used in navigation, the stereographic coordinate system is still used in modern times to describe crystallographic orientations in the field of materials science.[citation needed]

Geodetic height


Cartesian coordinates


Shape of the Earth


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.[1][5]

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 tides. The daily movement can be as much as a metre. Continental movement can be up to 10 cm a year, or 10 m in a century. A weather system high-pressure area can cause a sinking of 5 mm. Scandinavia is rising by 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 0.2 cm. These changes are insignificant if a local datum is used, but are significant if the global GPS datum is used.[1][why?]

Expressing latitude and longitude as linear units


The width of one longitudinal degree on 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):


where Earth's average meridional radius <math>\scriptstyle{M_r}\,\!</math> 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 at latitude <math>\scriptstyle{\phi}\,\!</math> by:


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

Longitudinal length equivalents at selected latitudes
Latitude Town Degree Minute Second ±0.0001°
60° Saint Petersburg 55.65 km 0.927 km 15.42m 5.56m
51° 28' 38" N Greenwich 69.29 km 1.155 km 19.24m 6.93m
45° Bordeaux 78.7 km 1.31 km 21.86m 7.87m
30° New Orleans 96.39 km 1.61 km 26.77m 9.63m
Quito 111.3 km 1.855 km 30.92m 11.13m

Datums often encountered



Geostationary coordinates


See also


  1. 1.0 1.1 1.2 1.3 1.4 1.5 A Guide to coordinate systems in Great Britain v1.7 Oct 2007 D00659 accessed 14.4.2008
  3. The French Institut Géographique National (IGN) still displays a latitude and longitude on its maps centred on a meridian that passes through Paris
  4. Haswell, Charles Haynes (1920). Mechanics' and Engineers' Pocket-book of Tables, Rules, and Formulas. Harper & Brothers. Retrieved 2007-04-09. 
  5. DMA Technical Report Geodesy for the Layman, The Defense Mapping Agency, 1983
  6. WGS 84 is the default datum used in most GPS equipment, but other datums can be selected.
  7. Making maps compatible with GPS Government of Ireland 1999. Accessed 15.4.2008



External links

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