GRS 80

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[edit] 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 ellipsoid is defined by its semi-major axis (equatorial radius) $a$ and either its semi-minor axis (polar radius) $b$ , aspect ratio $(b / a)$ or flattening $f$ . For GRS80, these are:

Defining geometrical constants

Semi-major axis = Equatorial Radius

= a =

6,378,137.00000 m;

Semi-minor axis = Polar Radius

= b =

6,356,752.31414 m;

Aspect ratio

= b / a =

0.996647189318775;

Flattening

= f =

0.003352810681225;

Reciprocal of flattening

= 1 / f =

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

= (a 2 b) 1 / 3 =

6,371,000.7900 m;

Linear eccentricity

= (a 2 - b 2) .5 =

521,854.0097 m;

Polar radius of curvature

= a 2 / b =

6,399,593.6259 m;

Meridian quadrant = 10,001,965.7293 m;

Defining physical constants

Geocentric gravitational constant, including mass of the atmosphere

G M =

3986005·10⁸ m³/s²;

Dynamical form factor

J 2

= 108263· 10^-8;

Angular velocity of rotation

ω

= 7292115·10^-11 s^-1;

For a complete definition, four independent constants are required. GRS80 chooses as these $a, G M, J 2$ and $ω$ , making the geometical constant $f$ 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).