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Ellipticity

Given a spheroid with equatorial radius a and polar radius c, the ellipticity is defined by

e={sqrt((a^2-c^2)/(a^2)) c<a (oblate spheroid); sqrt((c^2-a^2)/(c^2)) c>a (prolate spheroid).
(1)

It is defined analogously to eccentricity and is commonly denoted using the symbols e (Snyder 1987, p. 13) or epsilon (Beyer 1987).

It is related to the flattening f by

f=1-sqrt(1-e^2)
(2)
e=sqrt(f(2-f))
(3)

(Snyder 1987, p. 13).

See also

Flattening, Oblate Spheroid, Prolate Spheroid, Spheroid

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References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, 1987.Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, 1987.

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Ellipticity

Cite this as:

Weisstein, Eric W. "Ellipticity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Ellipticity.html

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