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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 ...
Geographic coordinate conversion has applications in cartography, surveying, navigation and geographic information systems. In geodesy, geographic coordinate conversion is defined as translation among different coordinate formats or map projections all referenced to the same geodetic datum. [1]
The equator is divided into 360 degrees of longitude, so each degree at the equator represents 111,319.5 metres (365,221 ft). As one moves away from the equator towards a pole, however, one degree of longitude is multiplied by the cosine of the latitude, decreasing the distance, approaching zero at the pole.
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.
Rectangular, distance-based coordinate systems have long been recognized for their practical utility for land measurement and geolocation over local areas. In the United States, the Public Land Survey System (PLSS), created in 1785 in order to survey land newly ceded to the nation, introduced a rectangular coordinate system to improve on the ...
These are the defining dimensions for NAD 27, but Clarke actually defined his 1866 spheroid as a = 20,926,062 British feet, b = 20,855,121 British feet. The conversion to meters uses Clarke's 1865 inch-meter ratio of 39.370432. The length of a foot or meter at the time could not practically be benchmarked to better than about 0.02 mm. [11]
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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).