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A data set which describes the global average of the Earth's surface curvature is called the mean Earth Ellipsoid. It refers to a theoretical coherence between the geographic latitude and the meridional curvature of the geoid. The latter is close to the mean sea level, and therefore an ideal Earth ellipsoid has the same volume as the geoid.
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).
Legendre (1811, p. 180) pointed out that the equation for s is the same as the equation for the arc on an ellipse with semi-axes b √ 1 + e′ 2 cos 2 α 0 and b. In order to express the equation for λ in terms of σ, we write = ,
This is a list of free and open-source software for geological data handling and interpretation. The list is split into broad categories, depending on the intended use of the software and its scope of functionality. Notice that 'free and open-source' requires that the source code is available and users are given a free software license.
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 inverse problem for earth sections is: given two points, and on the surface of the reference ellipsoid, find the length, , of the short arc of a spheroid section from to and also find the departure and arrival azimuths (angle from true north) of that curve, and . The figure to the right illustrates the notation used here.
Vincenty's goal was to express existing algorithms for geodesics on an ellipsoid in a form that minimized the program length (Vincenty 1975a). His unpublished report (1975b) mentions the use of a Wang 720 desk calculator, which had only a few kilobytes of memory. To obtain good accuracy for long lines, the solution uses the classical solution ...
The slant distance s (chord length) between two points can be reduced to the arc length on the ellipsoid surface S as: [21] = (+) / / where R is evaluated from Earth's azimuthal radius of curvature and h are ellipsoidal heights are each point. The first term on the right-hand side of the equation accounts for the mean elevation and the second ...