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 and its definition in terms of the
semi-axes and of the resulting ellipse or ellipsoid is
The compression factor is in each case; for the ellipse, this is also its
aspect ratio.
Definitions
There are three variants: the flattening [1] sometimes called the first flattening,[2] as well as two other "flattenings" and each sometimes called the second flattening,[3] sometimes only given a symbol,[4] or sometimes called the second flattening and third flattening, respectively.[5]
In the following, is the larger dimension (e.g. semimajor axis), whereas is the smaller (semiminor axis). All flattenings are zero for a circle (a = b).
^For example, is called the second flattening in: Taff, Laurence G. (1980).
An Astronomical Glossary (Technical report). MIT Lincoln Lab. p. 84. However, is called the second flattening in: Hooijberg, Maarten (1997). Practical Geodesy: Using Computers. Springer. p. 41.
doi:
10.1007/978-3-642-60584-0_3.
^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