The flattening, ellipticity, or oblateness of an oblate spheroid is a measure of the "squashing" of the spheroid's pole, towards its equator. If a is the distance from the spheroid center to the equator and b the distance from the center to the pole then

$\mathrm{flattening} = \frac {a - b}{a}$

## Definition of flattening

### First order

The first, primary flattening, ƒ, is the versine of the spheroid's angular eccentricity α, equalling the relative difference between its equatorial radius, a, and its polar radius, b:

$f=\mathrm{ver}(\alpha)=2\sin^2\left(\frac{\alpha}{2}\right)=1-\cos(\alpha)=\frac{a-b}{a};\,\!$

### Second and third orders

There is also a second flattening, f' ,

$f'=\frac{2\sin^2(\alpha/2)}{1-2\sin^2(\alpha/2)}=\frac{a-b}{b}$

and a third flattening,[1][2] f' ' (sometimes denoted as "n" – a notation first used in 1837 by Friedrich Bessel on calculation of meridian arc length[3] – that is the squared half-angle tangent of α:

$f''=n=\tan^2\left(\frac{\alpha}{2}\right)=\frac{1-\cos(\alpha)}{1+\cos(\alpha)}=\frac{a-b}{a+b};\,\!$

## First order flattening of planets

• The flattening of the Earth in WGS-84 is 1:298.257223563 (which corresponds to a radius difference of 21.385 km (13 mi) of the Earth radius 6378.137 – 6356.752 km) and would not be realized visually from space, since the difference represents only 0.335 %.
• The flattening of Jupiter (1:16) and Saturn (nearly 1:10), in contrast, can be seen even in a small telescope;
• Conversely, that of the Sun is less than 1:1000 and that of the Moon barely 1:900.

The amount of flattening depends on

and in detail on