GRS 80, or Geodetic Reference System 1980, is a geodetic reference system consisting of a global reference ellipsoid and a gravity field model. In Geodesy, a reference ellipsoid is a mathematically-defined surface that approximates the Geoid, the truer Figure of the Earth, or other planetary body

## 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. Geodesy (dʒiːˈɒdɪsi also called geodetics, a branch of Earth sciences, is the scientific discipline that deals EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 Gravitation is a natural Phenomenon by which objects with Mass attract one another Polar motion is the movement of Earth 's rotation axis across its surface Characteristics A tide is a repeated cycle of sea level changes in the following stages Over several hours the water rises or advances up a beach in the flood

The geoid is essentially the figure of the Earth abstracted from its topographic features. The geoid is that Equipotential surface which would coincide exactly with the mean ocean surface of the Earth if the oceans were in equilibrium at rest and extended through 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. In Geodesy, a reference ellipsoid is a mathematically-defined surface that approximates the Geoid, the truer Figure of the Earth, or other planetary body The quantity f = (ab)/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 (GRS80) posited a 6,378,137 m semi-major axis and a 1:298. 257 flattening. This system was adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics (IUGG). The International Union of Geodesy and Geophysics, or IUGG, is a Non-governmental organisation dedicated to the scientific study of the Earth using It is essentially the basis for geodetic positioning by the Global Positioning System and is thus also in extremely widespread use outside the geodetic community.

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 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. In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae In Geometry, the semi-minor axis (also semiminor axis) is a Line segment associated with most Conic sections (that is with ellipses and The aspect ratio of a Shape is the ratio of its longer Dimension to its shorter dimension Ellipticity redirects here For the mathematical topic of ellipticity see Elliptic operator. For GRS80, these are:

Defining geometrical constants
Semi-major axis = Equatorial Radius = a = 6,378,137. Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position 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. The Earth 's shape like that of all major Planets approximates a Sphere. 5559 m;
Authalic mean radius= 6,371,007. The Earth 's shape like that of all major Planets approximates a Sphere. 1810 m;
Radius of a sphere of the same volume = (a2b)1 / 3 = 6,371,000. 7900 m;
Linear eccentricity = (a2b2). 5 = 521,854. 0097 m;
Polar radius of curvature = a2 / b = 6,399,593. 6259 m;
Meridian quadrant = 10,001,965. 7293 m;
Defining physical constants
Geocentric gravitational constant, including mass of the atmosphere GM = 3986005·108 m3/s2;
Dynamical form factor J2 = 108263· 10-8;
Angular velocity of rotation ω = 7292115·10-11 s-1;

For a complete definition, four independent constants are required. Nature, in the broadest sense is equivalent to the natural world, physical universe, material world or material universe. GRS80 chooses as these a, GM, J2 and ω, making the geometrical constant f a derived quantity.

The GRS80 reference system is used by the Global Positioning System, in a realization called WGS 84 (World Geodetic System 1984). Basic concept of GPS operation A GPS receiver calculates its position by carefully timing the signals sent by the constellation of GPS Satellites high above the Earth The World Geodetic System defines a reference frame for the earth for use in Geodesy and Navigation.

## References

• Additional derived physical constants and geodetic formulas are found in the following reference: Geodetic Reference System 1980, Bulletin Géodésique, Vol 54:3, 1980.