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Encyclopedia > Great circle

For the Brisbane bus routes known collectively as the Great Circle Line (598 & 599), see the following list of Brisbane Transport routes For the most up-to-date timetable and route inforation, please visit the TransLink website at www. ...

A great circle on a sphere
A great circle on a sphere

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. This was scanned from an old nautic handbook for the Swedish Royal Navy. ... In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, called the centre. ... A sphere is a perfectly symmetrical geometrical object. ... The term hemisphere is used in three different meanings: one-half of the Earth (or other planetary or stellar body; see also New World and Old World) Eastern Hemisphere and Western Hemisphere. ...


Great circles serve as the analog of "straight lines" in spherical geometry. See also spherical trigonometry and geodesic. Spherical geometry is the geometry of the two-dimensional surface of a sphere. ... Right spherical triangle Spherical trigonometry is a part of spherical geometry that deals with polygons (especially triangles) on the sphere and explains how to find relations between the involved angles. ... In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. ...


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. Great circle distance is the shortest distance between any two points on the surface of the Earth measured along a path on the surface of the Earth (as opposed to going through the Earths interior). ... The Mercator projection of the world up to a latitude of 86° N and S The Mercator projection is a cylindrical map projection devised by Gerardus Mercator in 1569. ...


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. On the earth, a meridian is a north-south line between the North Pole and the South Pole. ... The equator is an imaginary circle drawn around a planet at a distance halfway between the poles. ... Latitude, denoted by the Greek letter φ, gives the location of a place on Earth north or south of the Equator. ...


Some examples of great circles on the celestial sphere include: the horizon (in the astronomical sense), the celestial equator, and the ecliptic. In astronomy and navigation, the celestial sphere is an imaginary rotating sphere of gigantic radius, concentric with the Earth. ... Horizon The horizon is the line that separates earth from sky. ... The celestial equator is a great circle on the imaginary celestial sphere, which could be constructed by inflating the Earths equator until it intersects with said sphere. ... The plane of the Ecliptic is well seen in this picture from the 1994 lunar prospecting Clementine spacecraft. ...


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. Jet streams are fast flowing, relatively narrow air currents found in the atmosphere at around 12 km above the surface of the Earth, just under the tropopause. ...

Airline great circle track at top, jet stream track at bottom
Airline great circle track at top, jet stream track at bottom

Great circle and jet stream flight paths as shown on an airliner flight monitor. ... Great circle and jet stream flight paths as shown on an airliner flight monitor. ...

See also

Jet streams are fast flowing, relatively narrow air currents found in the atmosphere at around 12 km above the surface of the Earth, just under the tropopause. ... Lune or Luna is a poetic name for Earths Moon. ... A small circle, of a sphere, is the circle constructed by a plane crossing the sphere not in its middle point. ... The Mercator projection shows courses of constant bearing as straight lines. ... At prayer in Damascus Qibla is an Arabic word referring to the direction that should be faced when a Muslim prays. ... Example of pole-to-pole loxodrome In navigation, a rhumb line (or loxodrome) is a line crossing all meridians at the same angle, i. ...

Resources


  Results from FactBites:
 
Great circle - Wikipedia, the free encyclopedia (429 words)
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.
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.
On the Earth, the meridians are on great circles, and the equator is a great circle.
Great-circle distance - Wikipedia, the free encyclopedia (610 words)
Geodesics on the sphere are the great circles (circles on the sphere whose centers are coincident with the center of the sphere).
Between any two points on a sphere which are not directly opposite each other, there is a unique great circle.
Between two points which are directly opposite each other (called antipodal points) there infinitely many great circles, but all have the same length, equal to half the circumference of the circle, or πr, where r is the radius of the sphere.
  More results at FactBites »


 

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