Earth-centered, Earth-fixed coordinate system

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The ECEF coordinates (x, y, z) shown in relation to latitude and longitude Ecef coordinates.svg
The ECEF coordinates (x, y, z) shown in relation to latitude and longitude

The Earth-centered, Earth-fixed coordinate system (acronym ECEF), also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth (including its surface, interior, atmosphere, and surrounding outer space) as X, Y, and Z measurements from its center of mass. [1] [2] 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.

Contents

The distance from a given point of interest to the center of Earth is called the geocentric distance, R = (X2 + Y2 + Z2)0.5, which is a generalization of the geocentric radius , R0, not restricted to points on the reference ellipsoid surface. The geocentric altitude is a type of altitude defined as the difference between the two aforementioned quantities: h = RR0; [3] it is not to be confused for the geodetic altitude .

Conversions between ECEF and geodetic coordinates (latitude and longitude) are discussed at geographic coordinate conversion.

Structure

As with any spatial reference system, ECEF consists of an abstract coordinate system (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. [4] The ECEF that is used for the Global Positioning System (GPS) is the geocentric WGS 84, which currently includes its own ellipsoid definition. [5] Other local datums such as NAD 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 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 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 10,000 meters above or 5,000 meters below the ellipsoid.

In astronomy

Geocentric coordinates can be used for locating astronomical objects in the Solar System in three dimensions 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 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, ecliptic, and galactic coordinate systems used in spherical astronomy.

An example of Earth-centered frame
Animation of IRNSS orbit - Earth fixed - polar view.gif
Polar view, Earth-centered, Earth fixed
  •    Earth
  •    IRNSS-1B
  •    IRNSS-1C
  •    IRNSS-1E
  •    IRNSS-1F
  •    IRNSS-1G
  •    IRNSS-1I
(IRNSS are geosynchronous satellites)

See also

Related Research Articles

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In geography, latitude is a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pole, with 0° at the Equator. Lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude and longitude are used together as a coordinate pair to specify a location on the surface of the Earth.

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The geographic coordinate system (GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on the Earth as latitude and longitude. It is the simplest, oldest and most widely used of the various spatial reference systems that are in use, and forms the basis for most others. Although latitude and longitude form a coordinate tuple like a cartesian coordinate system, the geographic coordinate system is not cartesian because the measurements are angles and are not on a planar surface.

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<span class="mw-page-title-main">World Geodetic System</span> Geodetic reference system

The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS. The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also describes the associated Earth Gravitational Model (EGM) and World Magnetic Model (WMM). The standard is published and maintained by the United States National Geospatial-Intelligence Agency.

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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 conversion: format change of geographic coordinates, conversion of coordinate systems, or transformation to different geodetic datums. Geographic coordinate conversion has applications in cartography, surveying, navigation and geographic information systems.

<span class="mw-page-title-main">Geodetic datum</span> Reference frame for measuring location

A geodetic datum or geodetic system is a global datum reference or reference frame for precisely representing the position of locations on Earth or other planetary bodies by means of geodetic coordinates. Datums are crucial to any technology or technique based on spatial location, including geodesy, navigation, surveying, geographic information systems, remote sensing, and cartography. A horizontal datum is used to measure a location across the Earth's surface, in latitude and longitude or another coordinate system; a vertical datum is used to measure the elevation or depth relative to a standard origin, such as mean sea level (MSL). Since the rise of the global positioning system (GPS), the ellipsoid and datum WGS 84 it uses has supplanted most others in many applications. The WGS 84 is intended for global use, unlike most earlier datums.

<span class="mw-page-title-main">European Terrestrial Reference System 1989</span> Geodetic reference frame fixed to the Eurasian Plate

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<span class="mw-page-title-main">Spatial reference system</span> System to specify locations on Earth

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<span class="mw-page-title-main">North American Datum</span> Reference frame for geodesy on the continent

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<span class="mw-page-title-main">Earth ellipsoid</span> Geometric figure which approximates the Earths shape

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<span class="mw-page-title-main">Geodetic coordinates</span> Geographic coordinate system

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<span class="mw-page-title-main">Hellenic Geodetic Reference System 1987</span>

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<span class="mw-page-title-main">Web Mercator projection</span> Mercator variant map projection

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References

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  5. National Geospatial Intelligence Agency. "World Geodetic System 1984 datasheet" (PDF). United Nations Office for Outer Space Affairs. United Nations. Retrieved December 16, 2021.
  6. Snay, Richard A.; Soler, Tomás (December 1999). "Modern Terrestrial Reference Systems (Part 1)" (PDF). Professional Surveyor.
  7. "Polar motion". Archived from the original on June 13, 2011. Retrieved December 7, 2010.