The Earth-centered, Earth-fixed coordinate system (acronym ECEF), also known as the geocentric coordinate system, is a

cartesian Cartesian means of or relating to the French philosopher René Descartes—from his Latinized name ''Cartesius''. It may refer to: Mathematics *Cartesian closed category, a closed category in category theory *Cartesian coordinate system, modern ...

spatial reference system that represents locations in the vicinity of the Earth (including its surface, interior,

atmosphere An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A s ...

, and surrounding outer space) as ''X'', ''Y'', and ''Z'' measurements from its

center of mass In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may ...

. Its most common use is in tracking the orbits of satellites and in satellite navigation systems for measuring locations on the surface of the Earth, but it is also used in applications such as tracking crustal motion. The distance from a given point of interest to the center of Earth is called the geocentric distance, , which is a generalization of the ''

geocentric radius Earth radius (denoted as ''R''🜨 or R_E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly (equatorial radius, denot ...

'', , not restricted to points on the

reference ellipsoid An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations ...

surface. The geocentric altitude is a type of altitude defined as the difference between the two aforementioned quantities: ; it is not to be confused for the ''

geodetic altitude Geodetic coordinates are a type of curvilinear orthogonal coordinate system used in geodesy based on a ''reference ellipsoid''. They include geodetic latitude (north/south) , ''longitude'' (east/west) , and ellipsoidal height (also known as geod ...

''. Conversions between ECEF and geodetic coordinates (latitude and longitude) are discussed at

geographic coordinate conversion In geodesy, conversion among different geographic coordinate systems is made necessary by the different geographic coordinate systems in use across the world and over time. Coordinate conversion is composed of a number of different types of convers ...

Structure

As with any spatial reference system, ECEF consists of an abstract

coordinate system In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sig ...

(in this case, a conventional three-dimensional right-handed system), and a geodetic datum that binds the coordinate system to actual locations on the Earth. The ECEF that is used for the

Global Positioning System The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sy ...

(GPS) is the geocentric WGS 84, which currently includes its own ellipsoid definition. Other local datums such as

NAD 83 The North American Datum (NAD) is the horizontal datum now used to define the geodetic network in North America. A datum is a formal description of the shape of the Earth along with an "anchor" point for the coordinate system. In surveying, ca ...

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: * The ''origin'' at the center of the chosen ellipsoid. In WGS 84, this is

of the Earth. * The ''Z axis'' is the line between the North and South Poles, with positive values increasing northward. In WGS 84, this is the international reference pole (IRP), which does not exactly coincide with the Earth's rotational axis The slight "wobbling" of the rotational axis is known as polar motion, and can actually be measured against an ECEF. * The ''X axis'' is in the plane of the

equator The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can als ...

, passing through the origin and extending from 180° longitude (negative) to the prime meridian (positive); in WGS 84, this is the IERS Reference Meridian. * The ''Y axis'' is also in the plane of the equator, passing through extending from 90°W longitude (negative) to 90°E longitude (positive) An example is th
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 A geodetic datum or geodetic system (also: geodetic reference datum, geodetic reference system, or geodetic reference frame) is a global datum reference or reference frame for precisely representing the position of locations on Earth or other plan ...

." Using Bowring's formula in 1976 ''Survey Review'' the first iteration gives latitude correct within 10 degree as long as the point is within 10,000 meters above or 5,000 meters below the ellipsoid.

In astronomy

Geocentric coordinates can be used for locating

astronomical object An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often us ...

s in the Solar System in

three dimensions Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informal ...

along the Cartesian X, Y, and Z axes. They are differentiated from topocentric coordinates, which use the observer's location as the reference point for bearings in altitude and azimuth. For nearby stars, astronomers use

heliocentric Heliocentrism (also known as the Heliocentric model) is the astronomical model in which the Earth and planets revolve around the Sun at the center of the universe. Historically, heliocentrism was opposed to geocentrism, which placed the Earth at ...

coordinates, with the center of the Sun as the origin. The plane of reference can be aligned with the Earth's celestial equator, the ecliptic, or the Milky Way's galactic equator. These 3D celestial coordinate systems add actual distance as the Z axis to the

equatorial Equatorial may refer to something related to: *Earth's equator **the tropics, the Earth's equatorial region **tropical climate *the Celestial equator ** equatorial orbit **equatorial coordinate system ** equatorial mount, of telescopes * equatorial ...

, ecliptic, and galactic coordinate systems used in

spherical astronomy Spherical astronomy, or positional astronomy, is a branch of observational astronomy used to locate astronomical objects on the celestial sphere, as seen at a particular date, time, and location on Earth. It relies on the mathematical methods of ...

References

External links

ECEF datum transformation
Notes on converting ECEF coordinates to WGS-84 datum
Datum Transformations of GPS Positions Application Note
Clearer notes on converting ECEF coordinates to WGS-84 datum

orientation of the coordinate system and additional information
GeographicLib
includes a utility CartConvert which converts between geodetic and geocentric (ECEF) or local Cartesian (ENU) coordinates. This provides accurate results for all inputs including points close to the center of the earth.
EPSG:4978
{{DEFAULTSORT:Ecef Global Positioning System

Structure

In astronomy

See also

References

External links