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Spherical Distance


The spherical distance between two points P and Q on a sphere is the distance of the shortest path along the surface of the sphere (paths that cut through the interior of the sphere are not allowed) from P to Q, which always lies along a great circle.

For points P and Q on the unit sphere, the spherical distance is given by

 d=cos^(-1)(P·Q),

where P·Q denotes a dot product.


See also

Geodesic, Great Circle, Sphere, Spherical Geometry

This entry contributed by Todd Rowland

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References

Brannan, D. A., Esplen, M. F.; and Gray, J. J. Geometry. Cambridge, England: Cambridge University Press, p. 144, 1999.

Referenced on Wolfram|Alpha

Spherical Distance

Cite this as:

Rowland, Todd. "Spherical Distance." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SphericalDistance.html

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