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Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic ...
An example of an incorrect result is provided by the NGS online utility, which returns a distance that is about 5 km too long. Vincenty suggested a method of accelerating the convergence in such cases (Rapp, 1993).
Klein quartic with 28 geodesics (marked by 7 colors and 4 patterns). In geometry, a geodesic (/ ˌ dʒ iː. ə ˈ d ɛ s ɪ k,-oʊ-,-ˈ d iː s ɪ k,-z ɪ k /) [1] [2] is a curve representing in some sense the locally [a] shortest [b] path between two points in a surface, or more generally in a Riemannian manifold.
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).
The reverse conversion is harder: given X-Y-Z can immediately get longitude, but no closed formula for latitude and height exists. See "Geodetic system." Using Bowring's formula in 1976 Survey Review the first iteration gives latitude correct within 10-11 degree as long as the point is within 10,000 meters above or 5,000 meters below the ellipsoid.
For example, using the surface normal at Paris, ^, results in an arrival point of = 49.007778°, = 2.546842°, which is about 1/8 nm from the arrival point defined above. Using the surface normal at Reykjavik (while still using the departure azimuth and trip distance of the geodesic to Paris) will have you arriving about 347 nm from Paris ...
Adrien-Marie Legendre showed that the distance along a geodesic on a spheroid is the same as the distance along the perimeter of an ellipse. [29] For this reason, the expression for m in terms of β and its inverse given above play a key role in the solution of the geodesic problem with m replaced by s , the distance along the geodesic, and β ...
The geodesic distance between opposite umbilical points is the same regardless of the initial direction of the geodesic. Whereas the closed geodesics on the ellipses X = 0 and Z = 0 are stable (a geodesic initially close to and nearly parallel to the ellipse remains close to the ellipse), the closed geodesic on the ellipse Y = 0 , which goes ...