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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.
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown.. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them.
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 ...
Computes the great circle distance between two points, specified by the latitude and longitude, using the haversine formula. Template parameters [Edit template data] Parameter Description Type Status Latitude 1 lat1 1 Latitude of point 1 in decimal degrees Default 0 Number required Longitude 1 long1 2 Longitude of point 1 in decimal degrees Default 0 Number required Latitude 2 lat2 3 Latitude ...
The spherical excess of a spherical quadrangle bounded by the equator, the two meridians of longitudes and , and the great-circle arc between two points with longitude and latitude (,) and (,) is = (+) ().
If a navigator begins at P 1 = (φ 1,λ 1) and plans to travel the great circle to a point at point P 2 = (φ 2,λ 2) (see Fig. 1, φ is the latitude, positive northward, and λ is the longitude, positive eastward), the initial and final courses α 1 and α 2 are given by formulas for solving a spherical triangle
Studies show that keeping your head at the appropriate height—about 2 inches (or 5 centimeters) off the bed—helps air flow into the lungs and stabilizes your respiratory function. However ...
With this information it is possible using the haversine formula to calculate the latitude where the position line crosses the assumed longitude. The formula is: The formula is: h a v ( M Z D ) = h a v ( T Z D ) − h a v ( L H A ) c o s ( L a t ) c o s ( D e c ) {\displaystyle hav(MZD)=hav(TZD)-hav(LHA)cos(Lat)cos(Dec)}