GRS 80 - Defining Features of GRS 80

Defining Features of GRS 80

The reference ellipsoid is usually defined by its semi-major axis (equatorial radius) and either its semi-minor axis (polar radius), aspect ratio or flattening, but GRS80 is an exception: For a complete definition, four independent constants are required. GRS80 chooses as these, and, making the geometrical constant a derived quantity.

Defining geometrical constants

Semi-major axis = Equatorial Radius 6 378 137 m;

Defining physical constants

Geocentric gravitational constant, including mass of the atmosphere 3986005·108 m3/s2;

Dynamical form factor = 108 263· 10−8;

Angular velocity of rotation = 7 292 115·10−11 s−1;

Derived geometrical constants (all rounded)

Flattening 0.003 352 810 681 225;

Reciprocal of flattening 298.257 222 101;

Semi-minor axis = Polar Radius 6 356 752.314 14 m;

Aspect ratio 0.996 647 189 318 816;

Mean radius as defined by the International Union of Geodesy and Geophysics (IUGG): R₁= (2a+b)/3 = 6 371 008.7714 m;

Authalic mean radius= 6 371 007.1810 m;

Radius of a sphere of the same volume 6 371 000.7900 m;

Linear eccentricity 521 854.0097 m;

Eccentricity of elliptical section through poles 0.081 819 191 0435;

Polar radius of curvature 6 399 593.6259 m;

Equatorial radius of curvature for a meridian 6 335 439.3271 m;

Meridian quadrant = 10 001 965.7293 m;

The formula giving the flattening/eccentricity of the GRS80 spheroid is iterative; plugging in the defined constants gives

where exactly.

Replace with and with and iterate to get ; a rounded value comes out

0.00669 43800 22903 41574 95749 48586 28930 62124 43890

from which a rounded value of calculates to be the reciprocal of

298.25722 21008 82711 24316 28366