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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 great circle is the largest circle that can be drawn on any given sphere. Any diameter of any great circle coincides with a diameter of the sphere, and therefore every great circle is concentric with the sphere and shares the same radius. Any other circle of the sphere is called a small circle, and is the intersection of the sphere with a ...
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 ...
Description. Illustration of great-circle distance.svg. English: 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 depicted. 日本語: 2点（P,Q）間の大円距離 (赤線部)。. u,vは対蹠点. Date.
Consider the great circle that contains the side BC. This great circle is defined by the intersection of a diametral plane with the surface. Draw the normal to that plane at the centre: it intersects the surface at two points and the point that is on the same side of the plane as A is (conventionally) termed the pole of A and it is denoted by A'.
(The distance AB along the parallel is (a cos φ) λ. The length of the chord AB is 2(a cos φ) sin λ / 2 . This chord subtends an angle at the centre equal to 2arcsin(cos φ sin λ / 2 ) and the great circle distance between A and B is 2a arcsin(cos φ sin λ / 2 ).) In the extreme case where the longitudinal separation ...
This shows that a great circle is, with respect to distance measurement on the surface of the sphere, a circle: the locus of points all at a specific distance from a center. Each point is associated with a unique great circle, called the polar circle of the point, which is the great circle on the plane through the centre of the sphere and ...
A diagram illustrating the great-circle distance (in cyan) and the straight-line distance (in red) between two points P and Q on a sphere. To see the utility of different notions of distance, consider the surface of the Earth as a set of points.