Geodetic Reference System 1980
The Geodetic Reference System 1980 (GRS 80) is a geodetic reference system consisting of a global reference ellipsoid and a normal gravity model. Background. Geodesy is the scientific discipline that deals with the measurement and representation of the earth, its gravitational field and geodynamic phenomena (polar motion, earth tides, and crustal motion) in three-dimensional, time-varying space. The geoid is essentially the figure of the Earth abstracted from its topographic features. It is an idealized equilibrium surface of sea water, the mean sea level surface in the absence of currents, air pressure variations etc. and  continued under the continental masses. The geoid, unlike the ellipsoid, is irregular and too complicated to serve as the computational surface on which to solve geometrical problems like point positioning. 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 . 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". The quantity "f" = ("a"−"b")/"a", where "b" is the semi-minor axis (polar radius), is a purely  geometrical one. The mechanical ellipticity of the earth (dynamical flattening, symbol "J") is determined to high precision by observation of satellite orbit perturbations. Its relationship with the geometric flattening is indirect. The relationship depends on the internal density distribution. The 1980 Geodetic Reference System (GRS 80) posited a semi-major axis and a flattening. This system was adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics (IUGG) in Canberra, Australia, 1979. The GRS 80 reference system was originally used by the World Geodetic System 1984 (WGS 84). The reference ellipsoid of WGS 84 now differs  slightly due to later refinements. The numerous other systems which have been used by diverse countries for their maps and charts are gradually dropping out of use as more and more countries move to global, geocentric reference systems using the GRS80 reference ellipsoid. Definition. The reference ellipsoid is usually defined by its semi-major axis (equatorial radius) formula_1 and either its semi-minor axis (polar radius) formula_2, aspect ratio formula_3 or flattening formula_4, but GRS80 is an exception: For a complete definition, "four" independent constants are required. GRS80 chooses as these formula_1, formula_6, formula_7 and formula_8, making the geometrical constant  formula_4 a derived quantity. Derived quantities. The formula giving the eccentricity of the GRS80 spheroid is: where and formula_28 (so formula_29). The equation is solved iteratively to give which gives