Great-circle distance

Great-circle distance is the length of the shortest path between two points on a sphere when travel is restricted to its surface. The path lies along a great circle, whose plane passes through the sphere’s center.

Central angle: An angle whose vertex is the center of a circle or sphere and whose sides extend to its surface. The distance equals the sphere’s radius multiplied by the central angle in radians.
Great circle: A circle on a sphere formed by intersecting it with a plane through its center. Every shortest surface path between non-antipodal points follows an arc of a great circle.
Orthodromic navigation: Navigation along a great-circle route, which gives the shortest surface path between two locations on a sphere. It uses great-circle distance to identify the shortest route across the globe.
Rhumb line: A path on a sphere that crosses every meridian at the same angle. Unlike a great-circle route, it maintains a constant compass bearing but is usually longer.
Haversine formula: A formula that computes the great-circle distance between two points from their latitudes and longitudes. It evaluates the central angle from geographic coordinates using trigonometric functions.
Geodesic: A locally shortest path between points on a curved surface or within a curved space. A great-circle arc is a geodesic on a sphere.
Geodesy: The science of measuring Earth’s shape, orientation, gravity field, and positions on its surface. Geodesy supplies Earth models and coordinate systems for geographic distance calculations.
Geodesic distance: The length of a shortest path between two points on a specified curved surface. Great-circle distance is geodesic distance specifically on a sphere.
Spherical law of cosines: A relation among the sides and angles of a spherical triangle, analogous to the planar law of cosines. Its side-angle form gives the central angle between two surface points.
Antipodal points: Two points on a sphere lying at opposite ends of a diameter through its center. Every great-circle route between antipodal points has the same shortest length.

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