A GEOGRAPHIC COORDINATE SYSTEM is a coordinate system used in geography that enables every location on Earth to be specified by a set of numbers, letters or symbols. The coordinates are often chosen such that one of the numbers represents a vertical position , and two or three of the numbers represent a horizontal position . A common choice of coordinates is latitude , longitude and elevation . To specify a location on a two-dimensional map requires a map projection . CONTENTS * 1 History * 2 Geographic(al) latitude and longitude * 3 Measuring height using datums * 3.1 Complexity of the problem * 3.2 Common baselines * 3.3 Datums * 4 Map projection * 4.1 UTM and UPS systems * 4.2 Stereographic coordinate system * 5 Cartesian coordinates * 5.1 Earth-centered, earth-fixed * 5.2 Local east, north, up (ENU) coordinates * 5.3 Local north, east, down (NED) coordinates * 6 Expressing latitude and longitude as linear units * 7 Geostationary coordinates * 8 On other celestial bodies * 9 See also * 10 Notes * 11 References * 12 External links HISTORY Main articles:
History of geodesy
The invention of a geographic coordinate system is generally credited
to
Eratosthenes of Cyrene , who composed his now-lost _
Geography
Ptolemy's 2nd-century _Geography_ used the same prime meridian but
measured latitude from the equator instead. After their work was
translated into Arabic in the 9th century, Al-Khwārizmī 's _Book of
the Description of the Earth _ corrected Marinus' and Ptolemy's errors
regarding the length of the
Mediterranean Sea , causing medieval
Arabic cartography to use a prime meridian around 10° east of
Ptolemy's line. Mathematical cartography resumed in Europe following
Maximus Planudes ' recovery of Ptolemy's text a little before 1300;
the text was translated into
Latin
In 1884, the
United States
GEOGRAPHIC(AL) LATITUDE AND LONGITUDE 0° EQUATOR Main articles:
Latitude
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. 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 . 0° PRIME MERIDIAN The "longitude" (abbreviation: Long., λ , or lambda) of a point on
Earth's surface is the angle east or west of a reference meridian to
another meridian that passes through that point. All meridians are
halves of great ellipses (often called great circles ), which converge
at the north and south poles. The meridian of the British Royal
Observatory in
Greenwich
The combination of these two components specifies the position of any
location on the surface of Earth, without consideration of altitude or
depth. The grid formed by lines of latitude and longitude is known as
a "graticule". The origin/zero point of this system is located in
the
Gulf of Guinea about 625 km (390 mi) south of
Tema ,
Ghana
MEASURING HEIGHT USING DATUMS Main articles: Geodetic datum , Figure of the Earth , and Reference ellipsoid COMPLEXITY OF THE PROBLEM To completely specify a location of a topographical feature on, in, or above Earth, one also has to specify the vertical distance from Earth's center or surface. Earth is not a sphere, but an irregular shape approximating a biaxial ellipsoid . It is nearly spherical, but has an equatorial bulge making the radius at the equator about 0.3% larger than the radius measured through the poles. The shorter axis approximately coincides with the axis of rotation. Though early navigators thought of the sea as a flat surface that could be used as a vertical datum, this is not actually the case. Earth has a series of layers of equal potential energy within its gravitational field . Height is a measurement at right angles to this surface, roughly toward Earth's centre, but local variations make the equipotential layers irregular (though roughly ellipsoidal). The choice of which layer to use for defining height is arbitrary. COMMON BASELINES Common height baselines include * The surface of the datum ellipsoid, resulting in an _ellipsoidal height_ * The mean sea level as described by the gravity geoid , yielding the orthometric height * A vertical datum , yielding a dynamic height relative to a known reference height. Along with the latitude {displaystyle phi } _ and longitude {displaystyle lambda } , the height h {displaystyle h} provides the three-dimensional geodetic coordinates_ or _geographic coordinates_ for a location. DATUMS In order to be unambiguous about the direction of "vertical" and the "surface" above which they are measuring, map-makers choose a reference ellipsoid with a given origin and orientation 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, called a terrestrial reference system or geodetic datum . 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 movement caused by the moon and the tides . This 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
Examples of global datums include World Geodetic System (WGS 84), the default datum used for the Global Positioning System , and the International Terrestrial Reference Frame (ITRF), used for estimating continental drift and crustal deformation . The distance to Earth's centre can be used both for very deep positions and for positions in space. Local datums chosen by a national cartographical organisation include
the
North American Datum , the European
ED50 , and the British OSGB36
. Given a location, the datum provides the latitude
{displaystyle phi } and longitude {displaystyle lambda } .
In the United Kingdom there are three common latitude, longitude, and
height systems in use. WGS 84 differs at
Greenwich
The latitude and longitude on a map made against a local datum may not be the same as one obtained from a GPS receiver. Coordinates from the mapping system can sometimes be roughly changed into another datum using a simple translation . For example, to convert from ETRF89 (GPS) to the Irish Grid add 49 metres to the east, and subtract 23.4 metres from the north. 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 (translation, three-dimensional rotation ), and converting back. 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'. Further information: Geographic coordinate conversion MAP PROJECTION Main article: Map projection To establish the position of a geographic location on a map , a map
projection is used to convert geodetic coordinates to two-dimensional
coordinates on a map; it projects the datum ellipsoidal coordinates
and height onto a flat surface of a map. The datum, along with a map
projection applied to a grid of reference locations, establishes a
_grid system_ for plotting locations. Common map projections in
current use include the
Universal Transverse Mercator (UTM), the
Military Grid Reference System (MGRS), the
United States
Map projection formulas depend in the geometry of the projection as well as parameters dependent on the particular location at which the map is projected. The set of parameters can vary based on type of project and the conventions chosen for the projection. For the transverse Mercator projection used in UTM, the parameters associated are the latitude and longitude of the natural origin, the false northing and false easting, and an overall scale factor. Given the parameters associated with particular location or grin, the projection formulas for the transverse Mercator are a complex mix of algebraic and trigonometric functions. :45-54 UTM AND UPS SYSTEMS Main articles: Universal Transverse Mercator and Universal Polar Stereographic The Universal Transverse Mercator (UTM) and Universal Polar Stereographic (UPS) coordinate systems both use a metric-based cartesian grid laid out on a conformally projected surface to locate positions on the surface of the Earth. The UTM system is not a single map projection but a series of sixty, each covering 6-degree bands of longitude. The UPS system is used for the polar regions, which are not covered by the UTM system. STEREOGRAPHIC COORDINATE SYSTEM Further information: Stereographic projection During medieval times, the stereographic coordinate system was used for navigation purposes. The stereographic coordinate system was superseded by the latitude-longitude system. Although no longer used in navigation, the stereographic coordinate system is still used in modern times to describe crystallographic orientations in the fields of crystallography , mineralogy and materials science. CARTESIAN COORDINATES Main article: axes conventions Every point that is expressed in ellipsoidal coordinates can be expressed as an rectilinear x y z (Cartesian ) coordinate. Cartesian coordinates simplify many mathematical calculations. The Cartesian systems of different datums are not equivalent. EARTH-CENTERED, EARTH-FIXED Earth Centered, Earth Fixed coordinates in relation to latitude
and longitude. Main article:
ECEF
The earth-centered earth-fixed (also known as the ECEF, ECF, or conventional terrestrial coordinate system) rotates with the Earth and has its origin at the center of the Earth. The conventional right-handed coordinate system puts: * The origin at the center of mass of the earth, a point close to the Earth's center of figure * The Z axis on the line between the north and south poles, with positive values increasing northward (but does not exactly coincide with the Earth's rotational axis) * The X and Y axes in the plane of the equator * The X axis passing through extending from 180 degrees longitude at the equator (negative) to 0 degrees longitude (prime meridian ) at the equator (positive) * The Y axis passing through extending from 90 degrees west longitude at the equator (negative) to 90 degrees east longitude at the equator (positive) An example is the NGS data for a brass disk near Donner Summit, in California. Given the dimensions of the ellipsoid, the conversion from lat/lon/height-above-ellipsoid coordinates to X-Y-Z is straightforward—calculate the X-Y-Z for the given lat-lon on the surface of the ellipsoid and add the X-Y-Z vector that is perpendicular to the ellipsoid there and has length equal to the point's height above the ellipsoid. The reverse conversion is harder: given X-Y-Z we can immediately get longitude, but no closed formula for latitude and height exists. See "Geodetic system ." Using Bowring's formula in 1976 _Survey Review_ the first iteration gives latitude correct within 10-11 degree as long as the point is within 10000 meters above or 5000 meters below the ellipsoid. LOCAL EAST, NORTH, UP (ENU) COORDINATES Earth Centred Earth Fixed and East, North, Up coordinates. In many targeting and tracking applications the local East, North, Up
(ENU)
Cartesian coordinate system is far more intuitive and practical
than
ECEF
LOCAL NORTH, EAST, DOWN (NED) COORDINATES ALSO KNOWN AS LOCAL TANGENT PLANE (LTP). In an airplane, most objects of interest are below the aircraft, so it is sensible to define down as a positive number. The North, East, Down (NED) coordinates allow this as an alternative to the ENU local tangent plane. By convention, the north axis is labeled x {displaystyle xprime } , the east y {displaystyle yprime } and the down z {displaystyle zprime } . To avoid confusion between x {displaystyle x} and x {displaystyle xprime } , etc. in this web page we will restrict the local coordinate frame to ENU. EXPRESSING LATITUDE AND LONGITUDE AS LINEAR UNITS Main articles: Length of a degree of latitude and Length of a degree of longitude _ This section DOES NOT CITE ANY SOURCES . Please help improve this section by adding citations to reliable sources . Unsourced material may be challenged and removed . (May 2015)_ _(Learn how and when to remove this template message )_ On the GRS80 or
WGS84
On the
WGS84
Similarly, the length in meters of a degree of longitude can be calculated as 111412.84 cos 93.5 cos 3 + 0.118 cos 5 {displaystyle 111412.84,cos varphi -93.5,cos 3varphi +0.118,cos 5varphi } (Those coefficients can be improved, but as they stand the distance they give is correct within a centimeter.) An alternative method to estimate the length of a longitudinal degree at latitude {displaystyle scriptstyle {varphi },!} is to assume a spherical Earth (to get the width per minute and second, divide by 60 and 3600, respectively): 180 M r cos {displaystyle {frac {pi }{180}}M_{r}cos varphi !} where Earth\'s average meridional radius M r {displaystyle scriptstyle {M_{r}},!} is 6,367,449 m. Since the Earth is not spherical that result can be off by several tenths of a percent; a better approximation of a longitudinal degree at latitude {displaystyle scriptstyle {varphi },!} is 180 a cos {displaystyle {frac {pi }{180}}acos beta ,!} where Earth's equatorial radius a {displaystyle a} _ equals
6,378,137 m_ and tan = b a tan {displaystyle
scriptstyle {tan beta ={frac {b}{a}}tan varphi },!} ; for the GRS80
and
WGS84
Longitudinal length equivalents at selected latitudes LATITUDE CITY DEGREE MINUTE SECOND ±0.0001° 60°
Saint Petersburg
51° 28′ 38″ N
Greenwich
45° Bordeaux 78.85 km 1.31 km 21.90 m 7.89 m 30°
New Orleans
0° Quito 111.3 km 1.855 km 30.92 m 11.13 m GEOSTATIONARY COORDINATES Geostationary satellites (e.g., television satellites) are over the equator at a specific point on Earth, so their position related to Earth is expressed in longitude degrees only. Their latitude is always zero (or approximately so), that is, over the equator. ON OTHER CELESTIAL BODIES Similar coordinate systems are defined for other celestial bodies such as: * A similarly well-defined system based on the reference ellipsoid
for
Mars
SEE ALSO * Atlas portal * Decimal degrees * Geodetic datum * Geographic coordinate conversion * Geographic information system * Geographical distance * Linear referencing * Map projection * Spatial reference systems NOTES * ^ In specialized works, "geographic coordinates" are
distinguished from other similar coordinate systems, such as
geocentric coordinates and geodetic coordinates. See, for example,
Sean E. Urban and P. Kenneth Seidelmann, _Explanatory Supplement to
the Astronomical Almanac, 3rd. ed., (Mill Valley CA: University
Science Books, 2013) p. 20–23._
* ^ The pair had accurate absolute distances within the
Mediterranean but underestimated the circumference of the earth ,
causing their degree measurements to overstate its length west from
Rhodes
REFERENCES * ^ _A_ _B_ _C_ _D_ _E_ _F_ _A guide to coordinate systems in Great
Britain_ (PDF), D00659 v2.3, Ordnance Survey, Mar 2015, retrieved
2015-06-22
* ^ _A_ _B_ _C_ Taylor, Chuck. "Locating a Point On the Earth".
Retrieved 4 March 2014.
* ^ McPhail, Cameron (2011), _Reconstructing Eratosthenes\'
Map
* ^ DMA Technical Report Geodesy for the Layman, The Defense Mapping Agency, 1983 * ^ Kwok, Geodetic Survey Section Lands Department Hong Kong. "Geodetic Datum Transformation, p.24" (PDF). Geodetic Survey Section Lands Department Hong Kong. Retrieved 4 March 2014. * ^ Bolstad, Paul. _GIS Fundamentals, 4th Edition_ (PDF). Atlas books. p. 89. 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. * ^ "Grids and Reference Systems". National Geospatial-Intelligence Agenc. Retrieved 4 March 2014. * ^ _A_ _B_ "Geomatics Guidance Note Number 7, part 2 Coordinate Conversions and Transformations including Formulas" (PDF). International Association of Oil and Gas Producers (OGP). pp. 9–10. Retrieved 5 March 2014. * ^ Note on the BIRD ACS Reference Frames Archived 18 July 2011 at the Wayback Machine . * ^ _A_ _B_ Geographic Information Systems - Stackexchange * _Portions of this article are from Jason Harris' "Astroinfo" which
is distributed with
KStars , a desktop planetarium for
Linux
EXTERNAL LINKS _ Wikidata has the |