great circle

A great circle divides the sphere in two equal hemispheres

A great circle of a sphere is a circle that runs along the surface of that sphere so as to cut it into two equal halves, as distinct from a small circle. The great circle therefore has both the same circumference and the same center as the sphere. It is the largest circle that can be drawn on a given sphere.

Great circles serve as the analogue of "straight lines" in spherical geometry. See also spherical trigonometry and geodesic.

The great circle, also known as the Riemannian circle, is the path with the smallest curvature, and hence, an arc (or an orthodrome) of a great circle is the shortest path between two points on the surface. The distance between any two points on a sphere is therefore known as the great-circle distance. The great-circle route is the shortest path between two points across the surface of a sphere

Earth geodesics

See also Geodesy

An oblate spheroid

Strictly speaking the Earth is not a perfect sphere (it's an oblate spheroid or ellipsoid - i.e., slightly squashed at the poles), which means that the shortest distance between two points (a geodesic) is not quite a great circle. Nevertheless, the sphere model can be considered a first approximation.

When long distance aviation or nautical 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. An exception is the gnomonic projection, in which all straight lines represent great circles.

On the Earth, the meridians are on great circles, and the equator is a great circle. Other lines of latitude are not great circles, because they are smaller than the equator; their centers are not at the center of the Earth -- they are small circles instead. Great circles on Earth are roughly 40,000 km in length, though the Earth is not a perfect sphere; for instance, the equator is 40,075 km.

Some examples of great circles on the celestial sphere include the celestial horizon, the celestial equator, and the ecliptic.

Airline routes between San Francisco and Tokyo following the most direct great circle (top), but following the jet stream (bottom) when heading eastwards

Great circle routes are used by ships and aircraft where currents and winds are not a significant factor. Flight lengths can therefore often be approximated to the great-circle distance between two airports. For aircraft travelling west between continents in the northern hemisphere these paths will extend northward near or into the Arctic region, however easterly flights will often fly a more southerly track to take advantage of the jet stream.

If one were to travel along a great circle, it would be difficult to steer manually as the heading would constantly be changing (except in the case of due north, south, or along the equator). Thus, Great Circle routes are often broken into a series of shorter rhumb lines which allow the use of constant headings between waypoints along the Great Circle.

See also

• Geodesic
• Rhumb line
• Small circle

External links

• Great Circle – from MathWorld Great Circle description, figures, and equations. Mathworld, Wolfram Research, Inc. c1999
• Great Circle Mapper Interactive tool for plotting great circle routes.
• Blue Marble Mapper Draws Great Circle routes between airports using the NASA Blue Marble as the base map.
• Great Circle Calculator deriving (initial) course and distance between two points.
• Great Circle Distance Graphical tool for drawing great circles over maps. Also shows distance and azimuth in a table.
• Great Circles on Mercator's Chart by John Snyder with additional contributions by Jeff Bryant, Pratik Desai, and Carl Woll, Wolfram Demonstrations Project.