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The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.
View from the Swabian Jura to the Alps. 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.
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).
Vincenty relied on formulation of this method given by Rainsford, 1955. Legendre showed that an ellipsoidal geodesic can be exactly mapped to a great circle on the auxiliary sphere by mapping the geographic latitude to reduced latitude and setting the azimuth of the great circle equal to that of the geodesic.
When finally past the Horn, he headed north for the Juan Fernández Islands to take on supplies for his crew, many of whom were sick with scurvy. On reaching the latitude of Juan Fernández, he did not know whether the islands were to the east or west, and spent 10 days sailing first eastwards and then westwards before finally reaching the islands.
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