GRS 80

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Definition

GRS 80, or Geodetic Reference System 1980, is a geodetic reference system consisting of a global reference ellipsoid and a gravity field model.

The reference elllipsoid is defined by its semi-major axis (equatorial radius) <math>a</math> and either its semi-minor axis (polar radius) <math>b</math>, aspect ratio <math>(b/a)</math> or flattening <math>f</math>. For GRS80, these are:

Defining geometrical constants 

Semi-major axis = Equatorial Radius <math>=a =</math>6,378,137.00000 m;

Semi-minor axis = Polar Radius <math>=b=</math> 6,356,752.31414 m;

Aspect ratio <math>=b/a=</math> 0.996647189318775;

Flattening <math>=f=</math> 0.003352810681225;

Reciprocal of flattening <math>=1/f=</math>298.2572220972;

Derived geometrical constants 

Quadratic mean radius= 6,372,797.5559 m;

Authalic mean radius= 6,371,007.1810 m;

Radius of a sphere of the same volume <math>=(a^2b)^{1/3}=</math> 6,371,000.7900 m;

Linear eccentricity <math>=(a^2-b^2)^{.5}=</math> 521,854.0097 m;

Polar radius of curvature <math>=a^2/b=</math> 6,399,593.6259 m;

Meridian quadrant = 10,001,965.7293 m;

Defining physical constants 

Geocentric gravitational constant, including mass of the atmosphere <math>GM=</math> 3986005·10⁸ m³/s²;

Dynamical form factor <math>J_2</math> = 108263· 10^-8;

Angular velocity of rotation <math>\omega</math> = 7292115·10^-11 s^-1;

For a complete definition, four independent constants are required. GRS80 chooses as these <math>a, GM, J_2</math> and <math>\omega</math>, making the geometical constant <math>f</math> a derived quantity.

Additional derived physical constants and geodetic formulas are found in the following reference: Geodetic Reference System 1980, Bulletin Géodésique, Vol 54:3, 1980.

The GRS80 reference system is used by the Global Positioning System, in a realization called WGS 84 (World Geodetic System 1984).