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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. This arc is the shortest path ...
Its arc length is the great-circle distance between the points (the intrinsic distance on a sphere), and is proportional to the measure of the central angle formed by the two points and the center of the sphere. 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 ...
The distance along the great circle will then be s 12 = ... where R is the assumed radius of the Earth and σ 12 is expressed in radians. Using the mean Earth radius, ...
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.
Any great circle s (blue) passing through the poles is secondary to g. In mathematics, two points of a sphere (or n-sphere, including a circle) are called antipodal or diametrically opposite if they are the endpoints of a diameter, a straight line segment between two points on a sphere and passing through its center. [1]
The point can be illustrated with an east–west passage over 90 degrees of longitude along the equator, for which the great circle and rhumb line distances are the same, at 10,000 kilometres (5,400 nautical miles). At 20 degrees north the great circle distance is 9,254 km (4,997 nmi) while the rhumb line distance is 9,397 km (5,074 nmi), about ...
Angular distance or angular separation is the measure of the angle between the orientation of two straight lines, ... meaning hence ... Great-circle distance;
(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 ...