Geodetic Reference System 1980

TheGeodetic Reference System 1980(GRS80) consists of a globalreference ellipsoidand anormal gravitymodel.^[1]^[2]^[3]The GRS80 gravity model has been followed by the newer more accurateEarth Gravitational Models,but theGRS80 reference ellipsoidis still the most accurate in use forcoordinate reference systems,e.g. for the internationalITRS,the EuropeanETRS89and (with a 0,1 mm rounding error) forWGS 84used for the AmericanGlobal Navigation Satellite System(GPS).

Background

Geodesyis the scientific discipline that deals with the measurement and representation of theearth,itsgravitationalfield and geodynamic phenomena (polar motion,earthtides,and crustal motion) in three-dimensional, time-varying space.

Thegeoidis 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 geoidalundulation,or more usually the geoid-ellipsoid separation,N.It varies globally between±110 m.

Areference ellipsoid,customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial radius)aand flatteningf.The quantityf= (a−b)/a,wherebis the semi-minor axis (polar radius), is a purely geometrical one. The mechanical ellipticity of the earth (dynamical flattening, symbolJ₂) 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 a6378137msemi-major axis and a1⁄298.257222101flattening. 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 theWorld Geodetic System 1984(WGS 84). The reference ellipsoid of WGS 84 now differs slightly due to later refinements.^{[citation needed]}

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.

Definition

The reference ellipsoid is usually defined by itssemi-major axis(equatorial radius) $a$ and either itssemi-minor axis(polar radius) $b$ ,aspect ratio $(b/a)$ orflattening $f$ ,but GRS80 is an exception:fourindependent constants are required for a complete definition. GRS80 chooses as these $a$ , $GM$ , $J_{2}$ and $\omega$ ,making the geometrical constant $f$ a derived quantity.

Defininggeometrical constants: Semi-major axis = Equatorial Radius = $a=6\,378\,137\,\mathrm {m}$ ;

Definingphysical constants: Geocentric gravitational constantdetermined from thegravitational constantand theearth masswith 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 quantities

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 = $b/a$ = 0.996 647 189 318 816 363;; Mean radiusas defined by theInternational Union of Geodesy and Geophysics(IUGG): $R_{1}=(2a+b)/3$ = 6 371 008.7714 m;; Authalic mean radius= $R_{2}$ = 6 371 007.1809 m;; Radius of a sphere of the same volume = $R_{3}=(a^{2}b)^{1/3}$ = 6 371 000.7900 m;; Linear eccentricity = $c={\sqrt {a^{2}-b^{2}}}$ = 521 854.0097 m;; Eccentricityof elliptical section through poles = $e={\frac {\sqrt {a^{2}-b^{2}}}{a}}$ = 0.081 819 191 0428;; 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 = 10 001 965.7292 m;