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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).
The geometrical separation between it and the reference ellipsoid is called the geoidal undulation, or more usually the geoid-ellipsoid separation, N. It varies globally between ±110 m. A reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial radius) a and flattening f.
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.
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]
The Molodensky transformation converts directly between geodetic coordinate systems of different datums without the intermediate step of converting to geocentric coordinates (ECEF). [24] It requires the three shifts between the datum centers and the differences between the reference ellipsoid semi-major axes and flattening parameters.
A standard datum specification (whether horizontal, vertical, or 3D) consists of several parts: a model for Earth's shape and dimensions, such as a reference ellipsoid or a geoid; an origin at which the ellipsoid/geoid is tied to a known (often monumented) location on or inside Earth (not necessarily at 0 latitude 0 longitude); and multiple ...
The value for the semimajor axis (a) of the WGS 72 Ellipsoid is 6 378 135 m. The adoption of an a-value 10 meters smaller than that for the WGS 66 Ellipsoid was based on several calculations and indicators including a combination of satellite and surface gravity data for position and gravitational field determinations. Sets of satellite derived ...
The Tracker Component Library from the United States Naval Research Laboratory is a free Matlab library with a number of gravitational synthesis routines. The function getEGMGeoidHeight can be used to evaluate the geoid height under the EGM96 and EGM2008 models.