Eccentricity
The eccentricity of a conic section is a parameter that encodes the type of shape and is defined in terms of semimajor a and semiminor axes b as follows.
The eccentricity can also be interpreted as the fraction of the distance along the semimajor axis at which the focus lies,
| e=c/a, |
(1)
|
where c is the distance from the center of the conic section to the focus.
The term "eccentricity" is also used in geodesy to refer to one of a number of similar quantities characterizing a spheroid. Given a spheroid with equatorial radius a and polar semi-axis b, this (first) eccentricity, commonly denoted e (Snyder 1987, p. 13; Karney 2023) but sometimes also as epsilon (Beyer 1987, p. 131), is defined as
| [画像: e^2=(a^2-b^2)/(a^2). ] |
(2)
|
As a result of the definition, the eccentricity e is positive for an oblate spheroid and purely imaginary for a prolate spheroid. Additional (second and third) eccentricities are defined as
| [画像: e^('2)=(a^2-b^2)/(b^2) ] |
(3)
|
and
(Karney 2023).
See also
Circle, Conic Section, Eccentric Anomaly, Ellipse, Ellipticity, Flattening, Focal Parameter, Focus, Graph Eccentricity, Hyperbola, Parabola, Semimajor Axis, Semiminor Axis, SpheroidExplore with Wolfram|Alpha
References
Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, 1987.Karney, C. F. F. "On Auxiliary latitudes." 21 May 2023. https://arxiv.org/abs/2212.05818.Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, 1987.Referenced on Wolfram|Alpha
EccentricityCite this as:
Weisstein, Eric W. "Eccentricity." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Eccentricity.html