Great circles are the "straight lines" of the sphere in nonEuclidean geometry.
The shortest path between two points on a sphere will lie on a great circle. 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 longitude lines lie on great circles, and the equator is a great circle. Other latitude lines are not great circles, because they are smaller than the equator.
Some examples of great circles on the celestial sphere include: the horizon (in the astronomical sense), the celestial equator, and the ecliptic.
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