is the scientific discipline that deals with the measurement and representation of the earth, its gravitational field and geodynamic phenomena 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, or more usually the geoid-ellipsoid separation, N. It varies globally between. A reference ellipsoid, customarily chosen to be the same size as the geoid, is described by its semi-major axisa and flatteningf. The quantity f = /a, where b is the semi-minor axis, is a purely geometrical one. The mechanical ellipticity of the earth 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 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 in Canberra, Australia, 1979. The GRS 80 reference system was originally used by the World Geodetic System 1984. 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.
Defining features of GRS 80
The reference ellipsoid is usually defined by its semi-major axis and either its semi-minor axis , aspect ratio or flattening, but GRS80 is an exception: For a complete definition, four independent constants are required. GRS80 chooses as these,, and, making the geometrical constant a derived quantity. ; Defining geometrical constants ; Defining physical constants ; Derived geometrical constants ; Derived physical constants The formula giving the eccentricity of the GRS80 spheroid is where and . The equation is solved iteratively to give which gives
