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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).
A coordinate system conversion is a conversion from one coordinate system to another, with both coordinate systems based on the same geodetic datum. Common conversion tasks include conversion between geodetic and earth-centered, earth-fixed coordinates and conversion from one type of map projection to another.
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.
The datum of that system was based on the Bessel ellipsoid, with an accurate determination of the geodetic coordinates at the central premises of the National Observatory of Athens 37° 58' 20.1" N - 23° 42' 58.5"E with current Google Earth TM coordinates:37° 58' 20.20" N - 23° 43' 05.36"E and supplemented by an accurately measured azimuth ...
The coordinate origin of WGS 84 is meant to be located at the Earth's center of mass; the uncertainty is believed to be less than 2 cm. [7] Handheld GPS receiver at the Royal Observatory, Greenwich, indicating that the Greenwich meridian is 0.089 arcminutes (or 5.34 arcseconds) west of the WGS 84 datum (the IERS Reference Meridian)
A geodetic datum or geodetic system (also: geodetic reference datum, geodetic reference system, or geodetic reference frame, or terrestrial reference frame) is a global datum reference or reference frame for unambiguously representing the position of locations on Earth by means of either geodetic coordinates (and related vertical coordinates) or geocentric coordinates. [1]
A geographic coordinate system (GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on Earth as latitude and longitude. [1] It is the simplest, oldest and most widely used type of the various spatial reference systems that are in use, and forms the basis for most others.
Formulas for the Web Mercator are fundamentally the same as for the standard spherical Mercator, but before applying zoom, the "world coordinates" are adjusted such that the upper left corner is (0, 0) and the lower right corner is ( , ): [7] = ⌊ (+) ⌋ = ⌊ ( [ (+)]) ⌋ where is the longitude in radians and is geodetic latitude in radians.