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d is the distance between the two points along a great circle of the sphere (see spherical distance), r is the radius of the sphere. The haversine formula allows the haversine of θ to be computed directly from the latitude (represented by φ) and longitude (represented by λ) of the two points:
Great Circle Calculator deriving (initial) course and distance between two points. Great Circle Distance Graphical tool for drawing great circles over maps. Also shows distance and azimuth in a table. Google assistance program for orthodromic navigation
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
The shortest distance between two points in plane is a Cartesian straight line. The Pythagorean theorem is used to calculate the distance between points in a plane. Even over short distances, the accuracy of geographic distance calculations which assume a flat Earth depend on the method by which the latitude and longitude coordinates have been ...
A meridian of the map is a great circle on the globe but the continuous scale variation means ruler measurement alone cannot yield the true distance between distant points on the meridian. However, if the map is marked with an accurate and finely spaced latitude scale from which the latitude may be read directly—as is the case for the ...
The straight-line distance between the central point on the map to any other point is the same as the straight-line 3D distance through the globe between the two points. c. 150 BC: Stereographic: Azimuthal Conformal Hipparchos* Map is infinite in extent with outer hemisphere inflating severely, so it is often used as two hemispheres.
A two-point equidistant projection of Eurasia. If the length of the line segment connecting two projected points on the plane is proportional to the geodesic (shortest surface) distance between the two unprojected points on the globe, then we say that distance has been preserved between those two points.
On a Mercator projection map, any rhumb line is a straight line; a rhumb line can be drawn on such a map between any two points on Earth without going off the edge of the map. But theoretically a loxodrome can extend beyond the right edge of the map, where it then continues at the left edge with the same slope (assuming that the map covers ...
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