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Great-circle navigation or orthodromic navigation (related to orthodromic course; from Ancient Greek ορθός (orthós) 'right angle' and δρόμος (drómos) 'path') is the practice of navigating a vessel (a ship or aircraft) along a great circle.
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 ...
In 1594, John Davis published an 80-page pamphlet called The Seaman's Secrets which, among other things describes great circle sailing. [61] It's said that the explorer Sebastian Cabot had used great circle methods in a crossing of the North Atlantic in 1495. [61]
Identifying the bulk cargo routes that would still offer paying freights, he manned the ships with a smattering of paid experienced officers. Some of the deckhands were apprentices from steamship lines and other adventurous youth who had paid a premium to sail while being trained, some recruited for very modest salaries. The apprentices were ...
The disk bounded by a great circle is called a great disk: it is the intersection of a ball and a plane passing through its center. In higher dimensions, the great circles on the n-sphere are the intersection of the n-sphere with 2-planes that pass through the origin in the Euclidean space R n + 1. Half of a great circle may be called a great ...
But at 60 degrees north the great circle distance is 4,602 km (2,485 nmi) while the rhumb line is 5,000 km (2,700 nmi), a difference of 8.5%. A more extreme case is the air route between New York City and Hong Kong , for which the rhumb line path is 18,000 km (9,700 nmi).
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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.