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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
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 ...
Pilots use aeronautical charts based on LCC because a straight line drawn on a Lambert conformal conic projection approximates a great-circle route between endpoints for typical flight distances. The US systems of VFR ( visual flight rules ) sectional charts and terminal area charts are drafted on the LCC with standard parallels at 33°N and 45°N.
The shortest distance between two geographical points is the great-circle distance. In the example (right), the aircraft travelling westward from North America to Japan is following a great-circle route extending northward towards the Arctic region. The apparent curve of the route is a result of distortion when plotted onto a conventional map ...
The map on the right shows, in red, a typical, non-competitive, route for a sailing circumnavigation of the world by the trade winds and the Suez and Panama canals; overlaid in yellow are the points antipodal to all points on the route. It can be seen that the route roughly approximates a great circle, and passes through two pairs of antipodal ...
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 ...
Leif Viking (LN-LMP) from SAS was the first airplane to use the polar route for regular flights. Here Leif Viking becomes christened by Cyd Charisse on 18 November 1954.. Of the commercial airlines, SAS was first: their Douglas DC-6B flights between Los Angeles and Copenhagen, via Kangerlussuaq and Winnipeg, started on November 15, 1954. [4]
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