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TheEarth-centered, Earth-fixed coordinate system (acronymECEF), also known as thegeocentric coordinate system, is acartesianspatial reference system that represents locations in the vicinity of the Earth (including itssurface, interior,atmosphere, and surrounding outer space) asX,Y, andZ measurements from itscenter of mass.[1][2] Its most common use is in tracking the orbits ofsatellites and insatellite navigation systems for measuring locations on the surface of the Earth, but it is also used in applications such as trackingcrustal motion.
The distance from a given point of interest to the center of Earth is called thegeocentric distance,R = (X2 +Y2 +Z2)0.5, which is a generalization of thegeocentric radius,R0, not restricted to points on thereference ellipsoid surface.Thegeocentric altitude is a type of altitude defined as the difference between the two aforementioned quantities:h′ =R −R0;[3] it is not to be confused for thegeodetic altitude.
Conversions between ECEF and geodetic coordinates (latitude and longitude) are discussed atgeographic coordinate conversion.
As with anyspatial reference system, ECEF consists of an abstractcoordinate system (in this case, a conventional three-dimensional right-handed system), and ageodetic datum that binds the coordinate system to actual locations on the Earth.[4] The ECEF that is used for theGlobal Positioning System (GPS) is the geocentricWGS 84, which currently includes its own ellipsoid definition.[5] Other local datums such asNAD 83 may also be used. Due to differences between datums, the ECEF coordinates for a location will be different for different datums, although the differences between most modern datums is relatively small, within a few meters.
The ECEF coordinate system has the following parameters:
An example is theNGS 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 can immediately get longitude, but no closed formula for latitude and height exists. See "Geodetic system." Using Bowring's formula in 1976Survey Review the first iteration gives latitude correct within 10-11 degree as long as the point is within 10,000 meters above or 5,000 meters below the ellipsoid.
Geocentric coordinates can be used for locatingastronomical objects in theSolar System inthree dimensions along theCartesian X, Y, and Z axes. They are differentiated fromtopocentric coordinates, which use the observer's location as the reference point for bearings in altitude andazimuth.
Fornearby stars, astronomers useheliocentric coordinates, with the center of theSun as the origin. Theplane of reference can be aligned with the Earth'scelestial equator, theecliptic, or theMilky Way'sgalactic equator. These 3Dcelestial coordinate systems add actual distance as the Z axis to theequatorial,ecliptic, andgalactic coordinate systems used inspherical astronomy.
