# Geographic coordinate system

The **geographic coordinate system** (**GCS**) is a

^{[1]}It is the simplest, oldest and most widely used of the various spatial reference systems that are in use, and forms the basis for most others. Although latitude and longitude form a coordinate tuple like a cartesian coordinate system, the geographic coordinate system is not cartesian because the measurements are angles and are not on a planar surface.

^{[2]}

^{[self-published source?}

A full GCS specification, such as those listed in the

^{[3]}

## History

The

^{[5]}

Ptolemy's 2nd-century

In 1884, the

^{[6]}France adopted Greenwich Mean Time in place of local determinations by the Paris Observatory

## Latitude and longitude

The "latitude" (abbreviation: Lat., φ, or phi) of 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.^{[note 2]} Lines joining points of the same latitude trace circles on the surface of Earth called parallels, as they are parallel to the Equator and to each other. 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.

The "longitude" (abbreviation: Long.,

The combination of these two components specifies the position of any location on the surface of Earth, without consideration of altitude or depth. The visual grid on a map formed by lines of latitude and longitude is known as a *graticule*.^{[7]} The origin/zero point of this system is located in the Gulf of Guinea about 625 km (390 mi) south of Tema, Ghana, a location often facetiously called Null Island.

## Geodetic datum

In order to be unambiguous about the direction of "vertical" and the "horizontal" surface above which they are measuring, map-makers choose a

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. Points on the Earth's surface move relative to each other due to continental plate motion, subsidence, and diurnal

^{[8]}

Examples of global datums include

^{[10]}The distance to Earth's center can be used both for very deep positions and for positions in space.

^{[8]}

Local datums chosen by a national cartographical organization include the

^{[8]}

The latitude and longitude on a map made against a local datum may not be the same as one obtained from a GPS receiver. Converting coordinates from one datum to another requires a datum transformation such as a Helmert transformation, although in certain situations a simple translation may be sufficient.^{[11]}

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 North American Datum of 1983 is denoted by 'GCS North American 1983'.

## Length of a degree

On the GRS80 or WGS84 spheroid at sea level at the Equator, one latitudinal second measures 30.715 meters, one latitudinal minute is 1843 meters and one latitudinal degree is 110.6 kilometers. 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 meters, a longitudinal minute is 1855 meters and a longitudinal degree is 111.3 kilometers. At 30° a longitudinal second is 26.76 meters, at Greenwich (51°28′38″N) 19.22 meters, and at 60° it is 15.42 meters.

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

^{[12]}

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

^{[12]}

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

where Earth's average meridional radius is 6,367,449 m. Since the Earth is an oblate spheroid, not spherical, that result can be off by several tenths of a percent; a better approximation of a longitudinal degree at latitude is

where Earth's equatorial radius equals *6,378,137 m* and ; for the GRS80 and WGS84 spheroids, b/a calculates to be 0.99664719. ( is known as the reduced (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 meter of each other if the two points are one degree of longitude apart.

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 alphanumeric strings or words:

- the Maidenhead Locator System, popular with radio operators.
- the World Geographic Reference System (GEOREF), developed for global military operations, replaced by the current Global Area Reference System (GARS).
- Open Location Code or "Plus Codes", developed by Google and released into the public domain.
- Geohash, a public domain system based on the Morton Z-order curve.
- 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.
- Military Grid Reference System is the geocoordinate standard used by NATO militaries for locating points on Earth.

## 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
- ISO 6709, standard representation of geographic point location by coordinates
- Linear referencing
- Primary direction – Celestial coordinate system
- Planetary 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*. ICA Commission on Map Projections.

## Notes

- circumference of the Earth, causing their degree measurements to overstate its length west from Rhodes or Alexandria, respectively.
**^**Alternative versions of latitude and longitude include geocentric coordinates, which measure with respect to Earth's center; geodetic coordinates, which model Earth as an ellipsoid; and geographic coordinates, which measure with respect to a plumb line at the location for which coordinates are given.**^**WGS 84 is the default datum used in most GPS equipment, but other datums can be selected.

**
**

## References

- ISBN 978-1-259-92964-9.
**^**Taylor, Chuck. "Locating a Point On the Earth". Archived from the original on 3 March 2016. Retrieved 4 March 2014.**^**"Using the EPSG geodetic parameter dataset, Guidance Note 7-1".*EPSG Geodetic Parameter Dataset*. Geomatic Solutions. Retrieved 15 December 2021.**^**McPhail, Cameron (2011),*Reconstructing Eratosthenes' Map of the World*(PDF), Dunedin: University of Otago, pp. 20–24.- ISBN 9780199874453.
**^**Greenwich 2000 Limited (9 June 2011). "The International Meridian Conference". Wwp.millennium-dome.com. Archived from the original on 6 August 2012. Retrieved 31 October 2012.- ISBN 9780784475706.
- ^
^{a}^{b}^{c}*A guide to coordinate systems in Great Britain*(PDF), D00659 v3.6, Ordnance Survey, 2020, archived (PDF) from the original on 2 April 2020, retrieved 17 December 2021 **^**"WGS 84: EPSG Projection -- Spatial Reference".*spatialreference.org*. Retrieved 5 May 2020.- ISBN 978-0-9717647-3-6.
**^**"Making maps compatible with GPS". Government of Ireland 1999. Archived from the original on 21 July 2011. Retrieved 15 April 2008.- ^
^{a}^{b}[1] Geographic Information Systems - Stackexchange

**
**### Sources

*Portions of this article are from Jason Harris' "Astroinfo" which is distributed with KStars, a desktop planetarium for Linux/KDE. See The KDE Education Project - KStars*

## External links

- Media related to Geographic coordinate systemat Wikimedia Commons