Great-circle distance is the shortest distance between any two points on the surface of a sphere that is measured along a path on the surface of the sphere. When calculating great-circle distance, the line of measurement does not pass through the sphere's interior. Great-circle distance is very important for trans oceanic voyages.
One example of its usage is when long distance routes are drawn on flat maps (for instance, a Mercator projection). When drawn on flat maps, the routes often look curved. This is the routes lie on great circles. If the route was to be drawn as a straight line, the measured distance would actually be longer than the great-circle distance.
Due to the fact that the Earth is approximately spherical, the equations for great-circle distance are important for finding the shortest distance between two points on the surface of the Earth. Therefore great-circle distance has important applications in navigation, as it can help navigators plan shorter routes and optimize voyage time and fuel efficiency.
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