Definitions

# Great circle

A great circle is a circle on the surface of a sphere that has the same circumference as the sphere, dividing the sphere into two equal hemispheres. Equivalently, a great circle is a circle on a sphere's surface whose center is the same as the center of the sphere. A great circle is the largest circle that can be drawn on a given sphere. The diameter of a great circle is same as the diameter of the sphere.

A great circle can be demonstrated by tightly stretching a piece of sewing thread across the surface of a globe between the start and finish points of the intended journey.

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

The great circle on the spherical surface is also known as the Riemannian circle, and 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. The great-circle route is the shortest path between two points on a sphere; however, if one were to travel along such a route, it would be difficult to manually steer 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.

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 horizon (in the astronomical sense), the celestial equator, and the ecliptic.

Great circle routes 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. The area of a great circle is a quarter of the surface area of the sphere it belongs to.