Flatness

The flatness , F , of a Planet is a measurement of sound “ellipticity”; a Sphère has a flatness of 0, whereas a infinitely thin disc has a flatness of 1.

A planet in rotation has a tendency natural to be flattened, the Effet centrifuges creating a “equatorial pad”. Mathematically, flatness is given by:

$f= \ mbox {worm} (O \! \ varepsilon) =2 \ sin \ left (\ frac {O \! \ varepsilon} {2} \ right) ^2=1- \ cos (O \! \ varepsilon) = \ frac {a-b} {has} \ approx \ frac {3 \ pi} {2GT^ {2} \ rho}; \, \!$

where

a \, \!

and

b \, \!

is the rays equatorial and polar of planet, respectively, and

o \! \ varepsilon \, \!

is the angular eccentricity . The approximation, in the case of validates a fluid planet of uniform Densité, is function of the constant of universal gravitation,

G

, of the Period of rotation

T

and of the density

\ rho

.
There is also the second flatness, f' (sometimes indicated as a " N "), that is the tangente² of half-angle:

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

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