Flattening
The (first) flattening f of a spheroid, also called oblateness or ellipticity, is defined as
| f=(a-c)/a |
(1)
|
where c is the polar radius and a is the equatorial radius.
It is related to the eccentricity e by
f = 1-sqrt(1-e^2)
(2)
e = sqrt(f(2-f))
(3)
(Snyder 1987, p. 13).
A so-called second and third flattening may be defined as
| f^'=(a-c)/c |
(4)
|
and
| n=(a-c)/(a+c) |
(5)
|
(Karney).
See also
Oblate Spheroid, Prolate Spheroid, SpheroidExplore with Wolfram|Alpha
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References
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
FlatteningCite this as:
Weisstein, Eric W. "Flattening." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Flattening.html