Great Circle - Earth Geodesics

Earth Geodesics

The Earth is not a perfect sphere, it is an oblate spheroid or ellipsoid (i.e. – slightly compressed at the poles), which means that the shortest distance between two points (a geodesic) is not quite a great circle. The equatorial radius of the earth is about 6378.137 kilometers. The polar radius of the earth is about 6356.752 kilometers (about 21.4 kilometers less). 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 appear as 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 a spherical Earth, the meridians (or lines of longitude) are great circles, as is the equator. Lines of latitude (except for the equator) 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. Since Earth is not a perfect sphere, the equator (which is generally considered a spherical great circle) is about 40,075 km, while a north-south meridian line (which is an ellipse) is almost 40,008 km. The quadratic mean or root mean square of these extremes provides a decent approximation of the average great-circle circumference, about 40041.5 km.

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

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.

For navigational convenience, 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.