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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 ...
The formulas involved can be complex and in some cases, such as in the ECEF to geodetic conversion above, the conversion has no closed-form solution and approximate methods must be used. References such as the DMA Technical Manual 8358.1 [15] and the USGS paper Map Projections: A Working Manual [16] contain formulas for conversion of map ...
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods that assume a spherical Earth, such ...
The rectifying latitude, μ, is the meridian distance scaled so that its value at the poles is equal to 90 degrees or π / 2 radians: = where the meridian distance from the equator to a latitude ϕ is (see Meridian arc)
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.
Bowring gave formulas for meridian distance (the distance from the equator to the given latitude along a north–south line on the spheroid) that seem to be correct within 0.001 millimeter on earth-size spheroids. [2] The symbol n is the same as in the Redfearn formulas = + =
However, it differs from global latitude/longitude in that it divides earth into 60 zones and projects each to the plane as a basis for its coordinates. Specifying a location means specifying the zone and the x, y coordinate in that plane. The projection from spheroid to a UTM zone is some parameterization of the transverse Mercator projection ...
The length of a degree of longitude (east–west distance) depends only on the radius of a circle of latitude. For a sphere of radius a that radius at latitude φ is a cos φ , and the length of a one-degree (or π / 180 radian ) arc along a circle of latitude is