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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.
latitude of the points; U 1 = arctan( (1 − ƒ) tan Φ 1), U 2 = arctan( (1 − ƒ) tan Φ 2) reduced latitude (latitude on the auxiliary sphere) L 1, L 2: longitude of the points; L = L 2 − L 1: difference in longitude of two points; λ: Difference in longitude of the points on the auxiliary sphere; α 1, α 2: forward azimuths at the ...
Informally, specifying a geographic location usually means giving the location's latitude and longitude. The numerical values for latitude and longitude can occur in a number of different units or formats: [2] sexagesimal degree: degrees, minutes, and seconds : 40° 26′ 46″ N 79° 58′ 56″ W
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.
A contour plot of the hours of daylight as a function of latitude and day of the year, using the most accurate models described in this article. It can be seen that the area of constant day and constant night reach up to the polar circles (here labeled "Anta. c." and "Arct. c."), which is a consequence of the earth's inclination.
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.
As with latitude and longitude, the values are bounded by ±90° and ±180° respectively. Positive latitudes are north of the equator, negative latitudes are south of the equator. Positive longitudes are east of the Prime Meridian; negative longitudes are west of the Prime Meridian. Latitude and longitude are usually expressed in that sequence ...