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A systematic solution for the paths of geodesics was given by Legendre (1806) and Oriani (1806) (and subsequent papers in 1808 and 1810). The full solution for the direct problem (complete with computational tables and a worked out example) is given by Bessel (1825). During the 18th century geodesics were typically referred to as "shortest lines".
EGM96 is a composite solution, consisting of: [6] a combination solution to degree and order 70, a block diagonal solution from degree 71 to 359, and the quadrature solution at degree 360. PGM2000A is an EGM96 derivative model that incorporates normal equations for the dynamic ocean topography implied by the POCM4B ocean general circulation model.
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.
In geodesy, a reference ellipsoid is a mathematically defined surface that approximates the geoid, which is the truer, imperfect figure of the Earth, or other planetary body, as opposed to a perfect, smooth, and unaltered sphere, which factors in the undulations of the bodies' gravity due to variations in the composition and density of the ...
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.
The geoid is often expressed as a geoid undulation or geoidal height above a given reference ellipsoid, which is a slightly flattened sphere whose equatorial bulge is caused by the planet's rotation. Generally the geoidal height rises where the Earth's material is locally more dense and exerts greater gravitational force than the surrounding areas.
A college student just solved a seemingly paradoxical math problem—and the answer came from an incredibly unlikely place. Skip to main content. 24/7 Help. For premium support please call: 800 ...
So, in the role of Geoid, the "globe" covered by a DGG can be any of the following objects: The topographical surface of the Earth, when each cell of the grid has its surface-position coordinates and the elevation in relation to the standard Geoid. Example: grid with coordinates (φ,λ,z) where z is the elevation. A standard Geoid surface.