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.
The great circle on the spherical surface is the path with the smallest curvature, and hence 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.
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.
Airline great circle track at top, jet stream track at bottom
Equivalently, a greatcircle on a sphere is a circle on the sphere's surface whose center is the same as the center of the sphere.
The greatcircle 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 greatcircles, and the equator is a greatcircle.
Geodesics on the sphere are the greatcircles (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 greatcircle.
Between two points which are directly opposite each other (called antipodal points) there infinitely many greatcircles, but all have the same length, equal to half the circumference of the circle, or πr, where r is the radius of the sphere.
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