Ellipsoid Geodesic

An ellipsoid can be specified parametrically by


The geodesic parameters are then


When the coordinates of a point are on the quadric


and expressed in terms of the parameters p and q of the confocal quadrics passing through that point (in other words, having a+p, b+p, c+p, and a+q, b+q, c+q for the squares of their semimajor axes), then the equation of a geodesic can be expressed in the form


with theta an arbitrary constant, and the arc length element ds is given by


where upper and lower signs are taken together.

See also

Great Circle, Oblate Spheroid Geodesic

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Ellipsoid Geodesic

Cite this as:

Weisstein, Eric W. "Ellipsoid Geodesic." From MathWorld--A Wolfram Web Resource.

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