Editing Geodetic Reference System 1980 (section)

==Derived quantities==

; Derived geometrical constants (all rounded)
:Flattening = <math>f</math> = 0.003 352 810 681 183 637 418;
:Reciprocal of flattening = <math>1/f</math> = 298.257 222 100 882 711 243;
:Semi-minor axis = Polar Radius = <math>b</math> = 6 356 752.314 140 347 m;
:Aspect ratio = <math>b/a</math> = 0.996 647 189 318 816 363;
:[[Earth radius#Mean radius: R1|Mean radius]] as defined by the [[International Union of Geodesy and Geophysics]] (IUGG): <math>R_1 = (2a+b)/3</math> = 6 371 008.7714 m;
:[[Earth radius#Authalic radius|Authalic mean radius]] = <math>R_2</math> = 6 371 007.1809 m;
:Radius of a sphere of the same volume = <math>R_3 = (a^2b)^{1/3}</math> = 6 371 000.7900 m;
:Linear eccentricity = <math>c = \sqrt{a^2-b^2}</math> = 521 854.0097 m;
:[[Eccentricity (mathematics)|Eccentricity]] of elliptical section through poles = <math>e = \frac{\sqrt{a^2-b^2}}{a}</math> = 0.081 819 191 0428;
:Polar radius of curvature = <math>a^2/b</math> = 6 399 593.6259 m;
:Equatorial radius of curvature for a meridian = <math>b^2/a</math> = 6 335 439.3271 m;
:Meridian quadrant = 10 001 965.7292 m;

; Derived physical constants (rounded)
:Period of rotation ([[sidereal day]]) = <math>2\pi/\omega</math> = 86 164.100 637 s

The formula giving the eccentricity of the GRS80 spheroid is:<ref name=Moritz1980/>

:<math>e^2  =  \frac {a^2 - b^2}{a^2} = 3J_2 + \frac4{15} \frac{\omega^2 a^3}{GM} \frac{e^3}{2q_0},</math>

where

:<math> 2q_0 = \left(1 + \frac3{e'^2}\right) \arctan e' - \frac3{e'}</math>

and <math>e' = \frac{e}{\sqrt{1 - e^2}} </math> (so <math>\arctan e' = \arcsin e</math>).  The equation is solved iteratively to give

:<math>e^2 = 0.00669\,43800\,22903\,41574\,95749\,48586\,28930\,62124\,43890\,\ldots</math>

which gives

:<math>f = 1/298.25722\,21008\,82711\,24316\,28366\,\ldots.</math>