KNOWPIA
WELCOME TO KNOWPIA

**Flattening** is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Other terms used are **ellipticity**, or **oblateness**. The usual notation for flattening is f and its definition in terms of the semi-axes of the resulting ellipse or ellipsoid is

The *compression factor* is in each case; for the ellipse, this is also its aspect ratio.

There are three variants of flattening; when it is necessary to avoid confusion, the main flattening is called the **first flattening**.^{[1]}^{[2]}^{[3]} and online web texts^{[4]}^{[5]}

In the following, a is the larger dimension (e.g. semimajor axis), whereas b is the smaller (semiminor axis). All flattenings are zero for a circle (*a* = *b*).

(First) flattening Fundamental. Geodetic reference ellipsoids are specified by giving Second flattening Rarely used. Third flattening Used in geodetic calculations as a small expansion parameter. ^{[6]}

The flattenings are related to other parameters of the ellipse. For example:

where is the eccentricity.

- Astronomy
- Earth flattening
- Earth's rotation
- Eccentricity (mathematics) § Ellipses
- Equatorial bulge
- Gravitational field
- Gravity formula
- Ovality
- Planetology
- Planetary flattening
- Sphericity
- Roundness (object)
- Darwin–Radau equation

**^**Maling, Derek Hylton (1992).*Coordinate Systems and Map Projections*(2nd ed.). Oxford; New York: Pergamon Press. ISBN 0-08-037233-3.**^**Snyder, John P. (1987).*Map Projections: A Working Manual*. U.S. Geological Survey Professional Paper.**1395**. Washington, D.C.: United States Government Printing Office.**^**Torge, W. (2001).*Geodesy*(3rd edition). de Gruyter. ISBN 3-11-017072-8**^**Osborne, P. (2008).*The Mercator Projections Archived 2012-01-18 at the Wayback Machine*Chapter 5.**^**Rapp, Richard H. (1991).*Geometric Geodesy, Part I*. Dept. of Geodetic Science and Surveying, Ohio State Univ., Columbus, Ohio. [1]**^**F. W. Bessel, 1825,*Uber die Berechnung der geographischen Langen und Breiten aus geodatischen Vermessungen*,*Astron.Nachr.*, 4(86), 241–254, doi:10.1002/asna.201011352, translated into English by C. F. F. Karney and R. E. Deakin as*The calculation of longitude and latitude from geodesic measurements*,*Astron. Nachr.*331(8), 852–861 (2010), E-print arXiv:0908.1824, Bibcode:1825AN......4..241B