# World Geodetic System 1984

The World Geodetic System 1984 ( WGS 84 ) is a geodetic reference system as a uniform basis for position information on earth and in near-earth space .

Location of the 50th parallel according to the World Geodetic System 1984 (WGS 84) in Oestrich-Winkel in the Rheingau . According to the Potsdam date assumed for topographic maps in Germany, the 50th parallel is here about 130 meters further south.

## Components

The system consists of:

• a reference ellipsoid whose simplicity is best adapted to the earth's surface, for location information according to geographical longitude and latitude;
• a detailed model for the earth figure deviating from this idealized shape , the so-called geoid ; the current version is the EGM96 ( Earth Gravitational Model 1996 );
• a set of three-dimensional coordinates of the twelve fundamental stations distributed over the earth for the anchoring of the above models in the earth's crust .

## Reference ellipsoid

The values ​​for the size and flattening of the earth as well as its gravitational field are continuously specified. But so that the ellipsoid forms a stable reference, its official parameters are only redefined every several decades. In the WGS84 or GRS 80 they are:

• major semi-axis a = 6,378,137 meters,
• Flattening f = 1 / 298,257,223,563 corresponding to a small semi-axis b  =  a (1− f ) of about 6,356,752 meters,
• Geocentric gravitational constant G · M = 3.986 004 418 · 10 14 m³ / s² (the product can be determined more precisely than the individual factors),
• Speed ​​of rotation = 7.292 115 · 10 −5 rad / s.${\ displaystyle \ omega}$

The parameters of the WGS84 reference ellipsoid roughly correspond to those of the GRS 80 reference ellipsoid .

## Coordinate system

The coordinate system in which the reference ellipsoid, the geoid and the position of the fundamental stations are defined is a Cartesian legal system (Z points to the north pole, X in the direction of 0 ° longitude and latitude, Y to 90 ° east). Its definition follows the specifications of the IERS :

• It is centered on the center of gravity of the earth including atmospheric mass .
• Its length scale is the local one, in the space relativistically curved by the earth's mass .
• The orientation of its axes relative to the earth's crust (reference pole and reference meridian) corresponded to that of the IERS (then BIH ) in epoch 1984.0 .
• The temporal development of its orientation follows the rotation of the earth's crust globally (the movement of the continental plates takes place against each other, without net rotation).

The measurement of the positions of the fundamental stations in relation to one another and their connection to the International Terrestrial Reference Frame (ITRF) of the IERS is carried out regularly via GPS ; The station set G730 corresponds to epoch 1994, the station set G873 to epoch 1997.

This coordinate system corresponds to the EPSG code : 4326.

## Gravity model

The gravitation model WGS84- EGM96 is currently valid . The location dependence of the earth's gravity potential is described by spherical surface functions of the assigned Legendre polynomials . The expansion coefficients C nm and S nm of the series expansion are measured up to degree  n and order  m of 360, a total of more than 130,000 coefficients.

Short-term effects such as tidal effects that cause an altitude shift of up to 50 cm are not taken into account. Long-term changes, for example caused by the continental drift of a few centimeters per year, are noted as corrections to the existing model. The tectonic movements are up to 7 cm per year in places.

## Use of the system

In 2000, 123 coordinate systems were linked to the WGS-84 ellipsoid via a geodetic datum . This considerably simplifies the conversion of position information between the coordinate systems. The standard WGS 84 was adopted for aviation by resolution of the ICAO in 1989. The geographic information systems of various providers also use the system.

According to WGS 84 , for example, the coordinates as latitude and longitude for the city of Oestrich-Winkel in degrees with 50 ° 0 ′ 30.75 ″ N / 8 ° 1 ′ 11.5 ″ E or decimal 50.008542 ° / 8 , 019861 °. The decimal values ​​for points south of the equator and west of the prime meridian are then negative and are approximately −22.9 ° / −43.2 ° for Rio de Janeiro .

## Deviations from other geodetic data

The reference meridian of the IERS runs about 100 meters east of the Royal Observatory Greenwich (at the equator the deviation from the Greenwich prime meridian is less).

The negligible deviation of the defined flattening from that of the originally used GRS-80 ellipsoid ( f ≈ 1 / 298.257 222) corresponds to 0.1 mm in the minor semi-axis and was caused by rounding in the back and forth conversion between flattening and the corresponding coefficient of Spherical surface function.

For G · M , the less precise GRS-80 value of 3.986 005 · 10 14 m³ / s² was used in an earlier version of WGS 84 . This value is hard-coded into millions of GPS receivers and is therefore still used by the GPS control segment to adapt Kepler ellipses to the satellite positions forecast with the newer value, the parameters of which are transmitted to the GPS receivers as ephemeris .

In epoch 1989.0 the ITRS and the ETRS were identical in terms of measurement accuracy. The latter is connected to the Eurasian plate via fundamental stations and moves 2.5 cm per year against the global system.

## literature

• Department of Defense: World Geodetic System 1984. Its definition and relationships with local geodetic systems . US Government, Department of Defense, Rockville, MD, 1991.