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.[n 1] 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.[1]
To specify a location on a two-dimensional map requires a map
projection.[2]
Contents
1 History
2 Geographic latitude and longitude
3 Measuring height using datums
3.1 Complexity of the problem
3.2 Common baselines
3.3 Datums
4
Map

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

Geostationary coordinates
8 On other celestial bodies
9 See also
10 Notes
11 References
12 External links
History[edit]
Main articles: History of geodesy, history of longitude, and history
of prime meridians
The invention of a geographic coordinate system is generally credited
to
Eratosthenes

Eratosthenes of Cyrene, who composed his now-lost
Geography

Geography at the
Library of Alexandria

Library of Alexandria in the 3rd century BC.[3] A century later,
Hipparchus of
Nicaea

Nicaea improved on this system by determining latitude
from stellar measurements rather than solar altitude and determining
longitude by timings of lunar eclipses, rather than dead reckoning. In
the 1st or 2nd century,
Marinus of Tyre compiled an extensive
gazetteer and mathematically-plotted world map using coordinates
measured east from a prime meridian at the westernmost known land,
designated the Fortunate Isles, off the coast of western Africa around
the Canary or Cape Verde Islands, and measured north or south of the
island of
Rhodes

Rhodes off Asia Minor.
Ptolemy

Ptolemy credited him with the full
adoption of longitude and latitude, rather than measuring latitude in
terms of the length of the midsummer day.[4]
Ptolemy's 2nd-century
Geography

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,[n 2] 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

Latin at Florence by
Jacobus Angelus

Jacobus Angelus around
1407.
In 1884, the
United States

United States hosted the International Meridian
Conference, attended by representatives from twenty-five nations.
Twenty-two of them agreed to adopt the longitude of the Royal
Observatory in
Greenwich, England

Greenwich, England as the zero-reference line. The
Dominican Republic

Dominican Republic voted against the motion, while France and Brazil
abstained.[5] France adopted
Greenwich Mean Time

Greenwich Mean Time in place of local
determinations by the
Paris Observatory

Paris Observatory in 1911.
Geographic latitude and longitude[edit]
0°
Equator
Main articles:
Latitude

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.[n 3] 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, in south-east London, England, is the
international prime meridian, although some organizations—such as
the French Institut Géographique National—continue to use other
meridians for internal purposes. The prime meridian determines the
proper Eastern and Western Hemispheres, although maps often divide
these hemispheres further west in order to keep the
Old World

Old World on a
single side. The antipodal meridian of
Greenwich

Greenwich is both 180°W and
180°E. This is not to be conflated with the International Date Line,
which diverges from it in several places for political reasons,
including between far eastern Russia and the far western Aleutian
Islands.
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".[6] The origin/zero point of this system is located in
the
Gulf of Guinea
.jpg/500px-Gulf_of_Guinea_(English).jpg)
Gulf of Guinea about 625 km (390 mi) south of Tema,
Ghana.
Measuring height using datums[edit]
Main articles: Geodetic datum, Figure of the Earth, and Reference
ellipsoid
Complexity of the problem[edit]
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[edit]
Common height baselines include[2]
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[1][7]
A vertical datum, yielding a dynamic height relative to a known
reference height.
Along with the latitude
ϕ
displaystyle phi
and longitude
λ
displaystyle lambda
, the height
h
displaystyle h
provides the three-dimensional geodetic coordinates or geographic
coordinates for a location.[8]
Datums[edit]
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

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
.svg/440px-Highlands_and_Islands_(Scottish_Parliament_electoral_region).svg.png)
Scotland is rising by only 0.2 cm. These changes are
insignificant if a local datum is used, but are statistically
significant if a global datum is used.[1]
Examples of global datums include
World Geodetic System

World Geodetic System (WGS 84), the
default datum used for the Global Positioning System,[n 4] and the
International Terrestrial Reference Frame

International Terrestrial Reference Frame (ITRF), used for estimating
continental drift and crustal deformation.[9] The distance to Earth's
centre can be used both for very deep positions and for positions in
space.[1]
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
ϕ
displaystyle phi
and longitude
λ
displaystyle lambda
. In the United Kingdom there are three common latitude, longitude,
and height systems in use. WGS 84 differs at
Greenwich

Greenwich from the one
used on published maps
OSGB36

OSGB36 by approximately 112m. The military
system ED50, used by NATO, differs from about 120m to 180m.[1]
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.[10] 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.[1]
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

North American Datum of 1983 is
denoted by 'GCS North American 1983'.
Further information: Geographic coordinate conversion
Map

Map projection[edit]
Main article:
Map

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

Universal Transverse Mercator (UTM), the Military Grid
Reference System (MGRS), the
United States

United States National Grid (USNG), the
Global Area Reference System

Global Area Reference System (GARS) and the World Geographic Reference
System (GEOREF).[11] Coordinates on a map are usually in terms
northing N and easting E offsets relative to a specified origin.
Map projection

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.[12] 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.[12]:45-54
UTM and UPS systems[edit]
Main articles:
Universal Transverse Mercator

Universal Transverse Mercator and Universal Polar
Stereographic
The
Universal Transverse Mercator

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[edit]
Further information: Stereographic projection
During medieval times, the stereographic coordinate system was used
for navigation purposes.[citation needed] 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.[citation needed]
Cartesian coordinates[edit]
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.[2]
Earth-centered, earth-fixed[edit]
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)[13]
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[edit]
Earth Centred Earth Fixed and East, North, Up coordinates.
In many targeting and tracking applications the local East, North, Up
(ENU)
Cartesian coordinate

Cartesian coordinate system is far more intuitive and practical
than
ECEF

ECEF or Geodetic coordinates. The local ENU coordinates are
formed from a plane tangent to the Earth's surface fixed to a specific
location and hence it is sometimes known as a "Local Tangent" or
"local geodetic" plane. By convention the east axis is labeled
x
displaystyle x
, the north
y
displaystyle y
and the up
z
displaystyle z
.
Local north, east, down (NED) coordinates[edit]
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[edit]
Main articles:
Length of a degree of latitude

Length of a degree of latitude and Length of a degree
of longitude
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On the GRS80 or
WGS84

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

WGS84 spheroid, the length in meters of a degree of latitude at
latitude φ (that is, the distance along a north–south line from
latitude (φ − 0.5) degrees to (φ + 0.5) degrees) is about
111132.92
−
559.82
cos
2
φ
+
1.175
cos
4
φ
−
0.0023
cos
6
φ
displaystyle 111132.92-559.82,cos 2varphi +1.175,cos 4varphi
-0.0023,cos 6varphi
[14]
Similarly, the length in meters of a degree of longitude can be
calculated as
111412.84
cos
φ
−
93.5
cos
3
φ
+
0.118
cos
5
φ
displaystyle 111412.84,cos varphi -93.5,cos 3varphi +0.118,cos
5varphi
[14]
(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
φ
displaystyle scriptstyle varphi ,!
is to assume a spherical Earth (to get the width per minute and
second, divide by 60 and 3600, respectively):
π
180
M
r
cos
φ
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
φ
displaystyle scriptstyle varphi ,!
is
π
180
a
cos
β
displaystyle frac pi 180 acos beta ,!
where Earth's equatorial radius
a
displaystyle a
equals 6,378,137 m and
tan
β
=
b
a
tan
φ
displaystyle scriptstyle tan beta = frac b a tan varphi ,!
; for the GRS80 and
WGS84

WGS84 spheroids, b/a calculates to be 0.99664719.
(
β
displaystyle scriptstyle beta ,!
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.
Longitudinal length equivalents at selected latitudes
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
Geostationary

Geostationary coordinates[edit]
Geostationary

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[edit]
Similar coordinate systems are defined for other celestial bodies such
as:
A similarly well-defined system based on the reference ellipsoid for
Mars.
Selenographic coordinates

Selenographic coordinates for the Moon
See also[edit]
Atlas portal
Decimal degrees
Geodetic datum
Geographic coordinate conversion
Geographic information system
Geographical distance
Linear referencing
Map

Map projection
Spatial reference systems
Notes[edit]
^ 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

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[edit]
^ 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

Map of the
World (PDF), Dunedin: University of Otago, pp. 20–24 .
^ Evans, James (1998), The History and Practice of Ancient Astronomy,
Oxford: Oxford University Press, pp. 102–103,
ISBN 9780199874453 .
^
Greenwich

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.
^ American Society of Civil Engineers (1994-01-01). Glossary of the
Mapping Sciences. ASCE Publications. p. 224.
ISBN 9780784475706.
^ 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, 5th Edition (PDF). Atlas books.
p. 102. 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. Archived
from the original (PDF) on 6 March 2014. Retrieved 5 March 2014.
^ Note on the BIRD ACS Reference Frames Archived 18 July 2011 at the
Wayback Machine.
^ a b [1] Geographic Information Systems - Stackexchange
Portions of this article are from Jason Harris' "Astroinfo" which is
distributed with KStars, a desktop planetarium for Linux/KDE. See The
KDE

KDE Education Project - KStars
External links[edit]
Wikidata

Wikidata has the property: coordinate location (P625) (see talk; uses)
Media related to
Geographic coordinate system

Geographic coordinate system at Wikimedia Commons
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