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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 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.
d is the distance between the two points along a great circle of the sphere (see spherical distance), r is the radius of the sphere. The haversine formula allows the haversine of θ to be computed directly from the latitude (represented by φ) and longitude (represented by λ) of the two points:
The WGS 84 meridian of zero longitude is the IERS Reference Meridian, [8] 5.3 arc seconds or 102 metres (335 ft) east of the Greenwich meridian at the latitude of the Royal Observatory. [ 9 ] [ 10 ] (This is related to the fact that the local gravity field at Greenwich does not point exactly through the Earth's center of mass, but rather ...
The length of one minute of latitude is 1.853 km (1.151 statute miles) (1.00 nautical miles), while the length of 1 second of latitude is 30.8 m or 101 feet (see nautical mile). Meridian distance on the ellipsoid
Given the difficulties of astronomical measures of longitude in classical times, most if not all of Ptolemy's values would have been obtained from distance measures and converted to longitude using the 500 value. [8] Ancient Hindu astronomers were aware of the method of determining longitude from lunar eclipses, assuming a spherical Earth.
On the ellipsoid the exact distance between parallels at φ 1 and φ 2 is m(φ 1) − m(φ 2). For WGS84 an approximate expression for the distance Δm between the two parallels at ±0.5° from the circle at latitude φ is given by = ()
Latitude and longitude should be displayed by sexagesimal fractions (i.e. minutes and seconds). When minutes and seconds are less than ten, leading zeroes should be shown. Degree, minutes and seconds should be followed by the symbols ° ( U+00B0 ), ′ ( U+2032 ), and ″ ( U+2033 ), without spaces between the number and symbol.