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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.
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).
In setting up a coordinate system, a static terrestrial point called the IERS Reference Pole, or IRP, is used as the origin; the x-axis is in the direction of IRM, the IERS Reference Meridian; the y-axis is in the direction 90 degrees West longitude. x and y are the coordinates of the CEP relative to the IRP.
Example: grid with coordinates (φ,λ,z) where z is the elevation. A standard Geoid surface. The z coordinate is zero for all grid, thus can be omitted, (φ,λ). Ancient standards, before 1687 (the Newton's Principia publication), used a "reference sphere"; in nowadays the Geoid is mathematically abstracted as reference ellipsoid.
A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.
In geometry, a Cartesian coordinate system (UK: / k ɑːr ˈ t iː zj ə n /, US: / k ɑːr ˈ t iː ʒ ə n /) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines ...
Geodetic latitude and geocentric latitude have different definitions. Geodetic latitude is defined as the angle between the equatorial plane and the surface normal at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure).
In all these formulae (h, k) are the center coordinates of the hyperbola, a is the length of the semi-major axis, and b is the length of the semi-minor axis. Note that in the rational forms of these formulae, the points ( −a , 0) and (0 , −a ) , respectively, are not represented by a real value of t , but are the limit of x and y as t tends ...