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where = and the coordinates are relative to the standard geodetic reference system extended into space with origin in the center of the reference ellipsoid and with z-axis in the direction of the polar axis.
The separation between the geoid and the reference ellipsoid is called the undulation of the geoid, symbol . The geoid, or mathematical mean sea surface, is defined not only on the seas, but also under land; it is the equilibrium water surface that would result, would sea water be allowed to move freely (e.g., through tunnels) under the land.
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.
It provides a raster of 2.5′×2.5′ and an accuracy approaching 10 cm. 1'×1' is also available [7] in non-float but lossless PGM, [5] [8] but original .gsb files are better. [9] Indeed, some libraries like GeographicLib use uncompressed PGM, but it is not original float data as was present in .gsb format.
The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations.
For the geoid determination (mean sea level) and for exact transformation of elevations. The global geoidal undulations amount to 50–100 m, and their regional values to 10–50 m. They are adequate to the integrals of VD components ξ,η and therefore can be calculated with cm accuracy over distances of many kilometers.
Convert from geodetic coordinates to geocentric coordinates: Calculation of x, y and z relative to the reference ellipsoid of surveying 7-parameter transformation (where x , y and z almost always change by a few hundred metres at most, and distances by a few mm per km).
The geoid undulation (also known as geoid height or geoid anomaly), N, is the height of the geoid relative to a given ellipsoid of reference. N = h − H {\displaystyle N=h-H} The undulation is not standardized, as different countries use different mean sea levels as reference, but most commonly refers to the EGM96 geoid.