GRS 80

Fundamentals

Concepts

Technologies

Standards (History)

NGVD 29	Sea Level Datum 1929
OSGB36	Ordnance Survey Great Britain 1936
SK-42	Systema Koordinat 1942 goda
ED50	European Datum 1950
SAD69	South American Datum 1969
GRS 80	Geodetic Reference System 1980
NAD 83	North American Datum 1983
WGS 84	World Geodetic System 1984
NAVD 88	N. American Vertical Datum 1988
ETRS89	European Terrestrial Reference System 1989
GCJ-02	Chinese encrypted datum 2002

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

Geodesy

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.

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) in Canberra, Australia, 1979.

The GRS 80 reference system was originally used by the World Geodetic System 1984 (WGS 84). The reference ellipsoid of WGS 84 now differs slightly due to later refinements.

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) $a$ and either its semi-minor axis (polar radius) $b$ , aspect ratio $(b/a)$ or flattening $f$ , but GRS80 is an exception: For a complete definition, four independent constants are required. GRS80 chooses as these $a$ , $GM$ , $J_{2}$ and $\omega$ , making the geometrical constant $f$ a derived quantity.

Defining geometrical constants

Semi-major axis = Equatorial Radius =

a=6\,378\,137\,\mathrm {m}

;

Defining physical constants

Geocentric gravitational constant, including mass of the atmosphere

GM=3986005\times 10^{8}\,\mathrm {m^{3}/s^{2}}

;

Dynamical form factor

J_{2}=108\,263\times 10^{-8}

;

Angular velocity of rotation

\omega =7\,292\,115\times 10^{-11}\,\mathrm {s^{-1}}

;

Derived geometrical constants (all rounded)

Flattening =

f

= 0.003 352 810 681 183 637 418;

Reciprocal of flattening =

1/f

= 298.257 222 100 882 711 243;

Semi-minor axis = Polar Radius =

b

= 6 356 752.314 140 347 m;

Aspect ratio =

b/a

= 0.996 647 189 318 816 362;

Mean radius as defined by the International Union of Geodesy and Geophysics (IUGG):

R_{1}=(2a+b)/3

= 6 371 008.7714 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 =

{\sqrt {a^{2}-b^{2}}}

= 521 854.0097 m;

Eccentricity of elliptical section through poles =

{\sqrt {a^{2}-b^{2}}}/a

= 0.081 819 191 0435;

Polar radius of curvature =

a^{2}/b

= 6 399 593.6259 m;

Equatorial radius of curvature for a meridian =

b^{2}/a

= 6 335 439.3271 m;

Meridian quadrant = 10 001 965.7293 m;

The formula giving the eccentricity of the GRS80 spheroid is^[1]

$e^{2}={\frac {a^{2}-b^{2}}{a^{2}}}=3J_{2}+{\frac {4}{15}}{\frac {\omega ^{2}a^{3}}{GM}}{\frac {e^{3}}{2q_{0}}},$

where

$2q_{0}=\left(1+{\frac {3}{e'^{2}}}\right)\arctan e'-{\frac {3}{e'}}$

and $e'=e/{\sqrt {1-e^{2}}}$ (so arctan e' = arcsin e). The equation is solved iteratively to give

$e^{2}=0.00669\,43800\,22903\,41574\,95749\,48586\,28930\,62124\,43890\,\ldots$

which gives

$f=1/298.25722\,21008\,82711\,24316\,28366\,\ldots .$

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

External links

GRS 80 Specification

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