Great circle
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A great circle is a circle on the surface of a sphere that has the same diameter as the sphere, dividing the sphere into two equal hemispheres. Equivalently, a great circle on a sphere is a circle on the sphere's surface whose center is the same as the center of the sphere. A great circle is the intersection of a sphere with a plane going through its center. A great circle is the largest circle that can be drawn on a given sphere.
Great circles serve as the analog of "straight lines" in spherical geometry. See also spherical trigonometry and geodesic.
The great circle on the spherical surface is the path with the smallest curvature, and hence an arc (an orthodrome) is the shortest path between two points on the surface. The distance between any two points on a sphere is known as the great circle distance. When intercontinental airline routes are drawn on a flat map (for instance, the Mercator projection), they often look curved. This is because they lie on great circles. A route that would look like a straight line on the map would actually be longer.
On the Earth, the meridians are on great circles, and the equator is a great circle. Other latitude lines are not great circles, because they are smaller than the equator. However they do lie in planes parallel to the equator. This result comes from another principle of great circles: no two circles lying in distinct, parallel planes can be great circles of the same sphere. Only concentric circles of the same radius are cospherical great circles.
Some examples of great circles on the celestial sphere include: the horizon (in the astronomical sense), the celestial equator, and the ecliptic.
Great circle paths are used by ships and aircraft where currents and winds are not a significant factor. For aircraft traveling westerly between continents in the northern hemisphere these paths will extend northward near or into the arctic region, while easterly flights will often fly a more southerly track to take advantage of the jet stream.
FlightPaths.jpg
See also
Resources
- Great Circle -- from MathWorld (http://mathworld.wolfram.com/GreatCircle.html) Great Circle description, figures, and equations. Mathworld, Wolfram Research, Inc. c1999
- Great Circle Mapper (http://gc.kls2.com/) Interactive tool for plotting great circle routes.ca:Cercle màxim
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