Large circle
In Geometry, a large circle is a Cercle traced on the surface of a Sphère which has same the Diamètre as it and divides it into two equal hemisphere S. In an equivalent way, a large circle is a circle on the sphere having the same center as it, as well as the intersection of this sphere with all plan passing by its center.
A large circle is the largest circle which one can trace on a sphere.
Geodetic
The large circles are the Géodésique S of a sphere, i.e. the ways having smallest curve and the arcs of large circles are consequently the shortest ways connecting two points to the surface of a sphere. The shortest distance between these two points is in addition given by the Distance of the large circle.The large circles are the equivalent of the right S in spherical Géométrie.
Cartography
On Ground, the Meridian S and the equator are large circles (the parallel S are however not).On the celestial Sphere, the horizon, the ecliptic and the celestial equator are also large circles.
On the surface of the Earth, the shortest way between two points is thus an arc of large circle: the Orthodromy. On a Planisphere, this way appears generally curved; a right route on a chart planes would actually be much longer. The orthodromic routes are employed by the ships or the planes for the oceanic or intercontinental crossings, particularly with the high latitudes. A plane accomplishing a transcontinental flight towards the west in the northern Hemisphere generally flies over the areas Arctique S, while such a flight towards the east often takes a way more from the south in order to draw advantage from the Courant-jet.
See too
- spherical Geometry
- Hemisphere (geography)
- Fibration of Hopf
- Road (navigation)
Simple: Great circle Zh-min-nan: Tōa-îⁿ
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