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;
- 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).