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
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
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
0° Equator Main articles:
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
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.
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
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)
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:
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
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
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
A similarly well-defined system based on the reference ellipsoid for
Mars.
See also[edit] Atlas portal Decimal degrees
Geodetic datum
Geographic coordinate conversion
Geographic information system
Geographical distance
Linear referencing
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
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'
Portions of this article are from Jason Harris' "Astroinfo" which is
distributed with KStars, a desktop planetarium for Linux/KDE. See The
External links[edit]
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