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View of the ocean with two ships: one in the foreground and one to the left of it on the horizon. Historically, the distance to the visible horizon has long been vital to survival and successful navigation, especially at sea, because it determined an observer's maximum range of vision and thus of communication, with all the obvious consequences for safety and the transmission of information ...
Navigation that follows the shortest distance between two points, i.e., that which follows a great circle. Such routes yield the shortest distance between two points on the globe. [16] To calculate the bearing and distance between two points it is necessary to solve a spherical triangle whose vertices are the origin, the destination, and the ...
The distance along the great circle will then be s 12 = Rσ 12, where R is the assumed radius of the Earth and σ 12 is expressed in radians. Using the mean Earth radius , R = R 1 ≈ 6,371 km (3,959 mi) yields results for the distance s 12 which are within 1% of the geodesic length for the WGS84 ellipsoid; see Geodesics on an ellipsoid for ...
By knowing which point on the rotating Earth a celestial object is above and measuring its height above the observer's horizon, the navigator can determine his distance from that subpoint. A nautical almanac and a marine chronometer are used to compute the subpoint on Earth a celestial body is over, and a sextant is used to measure the body's ...
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 1.5% further. 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%.
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