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Geodesy, also called geodetics, is the scientific discipline that deals with the measurement and representation of the earth, its gravitational field and geodynamic phenomena (polar motion, earth tides, and crustal motion) in three-dimensional, time-varying space.
The geoid is essentially the figure of the Earth abstracted from its topographic features. It is an idealized equilibrium surface of sea water, the mean sea level surface in the absence of currents, air pressure variations etc. and continued under the continental masses. The geoid, unlike the ellipsoid, is irregular and too complicated to serve as the computational surface on which to solve geometrical problems like point positioning. The geometrical separation between it and the reference ellipsoid is called the geoidal undulation. It varies globally between ±110 m.
A reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial radius) a and flattening f. The quantity f = (a−b)/a, where b is the semi-minor axis (polar radius), is a purely geometrical one. The mechanical ellipticity of the earth (dynamical flattening, symbol J2) is determined to high precision by observation of satellite orbit perturbations. Its relationship with the geometric flattening is indirect. The relationship depends on the internal density distribution, or, in simplest terms, the degree of central concentration of mass.
The 1980 Geodetic Reference System (GRS 80) posited a 6 378 137m semi-major axis and a 1/298.257 222 101 flattening. This system was adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics (IUGG).
The numerous other systems which have been used by diverse countries for their maps and charts are gradually dropping out of use as more and more countries move to global, geocentric reference systems using the GRS80 reference ellipsoid.
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.
- Semi-major axis = Equatorial Radius = = 6 378 137 m;
- 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
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
Insert non-formatted text here==References==
- Additional derived physical constants and geodetic formulas are found in the following reference: Geodetic Reference System 1980, Bulletin Géodésique, Vol 54:3, 1980. Republished (with corrections) in Moritz, H., 2000, \Geodetic Reference System 1980," J. Geod., 74(1), pp. 128-162, doi:10.1007/S001900050278.
- p395, p398 of Bulletin Geodesique for 1980
- Jason Tiscione's Big Calculator
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