# Grade measurement

An astronomical- geodetic technique is referred to as degree of measurement that was used from the 16th to the 20th century for measuring the earth's shape. The name comes from the precise determination of that distance ( 111-112 km), which is located between two 1 ° different latitudes.

## Methodology and first measurements

The method is based on measuring the curvature of the earth between distant points by their distance ( arc length B) with the angle β between their astronomically determined Lotrichtungen is compared. The quotient B / β gives the average radius of curvature of the earth between these points. Best to select these two locations of Lotrichtungsmessung in north-south direction so that β corresponds to the difference of their latitude.

The principle of the measurement of a degree goes back to the Alexandrian mathematician Eratosthenes and Library Director; he estimated the Earth's circumference around 240 BC from the 7.2 ° different Sun between Alexandria and Syene (now Aswan ). His result of 250,000 stadia met - depending on the exact length of the stadium used - the true value to about 10 percent.

The method was refined by the Arabs under Al- Ma'mun to 1-2 % accuracy in the early Middle Ages. In France, Jean François Fernel received (1497-1558) in 1525 of a 100 -km-long arc of the meridian from Paris to Amiens the local mean radius of the earth (about 6370 km ) already at some kilometer, where the meridian degrees were measured with a measuring wheel.

Later combined with the method of triangulation large triangles to measure precise distances can. They revealed that a locally varying curvature of the earth, ie deviations from the spherical shape. Multiple profiles in the north and in the south of France 1669 should clarify the question of whether the curvature of the earth from the pole increases or decreases towards the poles and the earth flattened or ovoid.

In the 20th century it went from about profile - area networks and on certain regional curvature of the earth through various Geoidstudien and transnational projects. Since the practicality of the Navstar GPS, many surveys but no longer relate to the true earth's shape ( the geoid ), but on an average Erdellipsoid - which of course has problems with the height measurement result.

## French Geodesy Lapland Peru

Because of conflicting results fitted out the Paris Academy of Sciences two major expeditions to Peru (La Condamine ) and Lapland ( Maupertuis ).

The results of these measurements (1735-1740) should define not only the Erdellipsoid also a new international measure of length - with exactly 10,000,000 meters from the equator to the pole.

Various problems with rust and calibration of the scales used (see Toise ), however, led to 1 km shortened Ellipsoidradien ( present data indicate the meridian quadrant with 10,002,249 meters of ).

The Earth flattening ¹ surrendered with f = 0.0046 (instead of 0.00335 ), thus shortening the radius of the earth to the poles ( 6378 ⇒ 6357 km ) or the increasing radius of curvature ( 6335 ⇒ 6400 km ) was first identified:

¹) Cassini's final measurement in 1740 showed flattening f = 0.00329

## Other major meridian arcs in the 18th - 20th century

## Longitude measurements and subsequent cross-linking

The degree of measurement along meridians is easier to implement, because the astronomical work require only width measurements. However, east-west profiles and measurements for longitude are required for accurate continental projects - the first by radio time signals and technical precision chronometers were possible on a large scale:

### International degree and Geodesy

To the international coordination of these major projects was founded in 1862 to German - Austrian initiative, the Central European degree measurement Commission. My longtime head was the Prussian General Johann Jacob Baeyer. It was in 1867 extended to the European level measurement and Figures ( 1919) the precursor to the international geodetic Union IAG, as well as today's geoscience Union IUGG.

Since around 1910 and 1940, respectively, the profiles are no longer observed in the direction of north-south and east-west or evaluated separately, but increasingly connected to large surveying networks. Although the computational complexity of such large-scale area networks and their minimization process increases enormously ( with 2nd to 3rd power of the number of points ), but well worth it due to higher accuracy and homogeneity. The first of these major projects related to the U.S. and Western Europe; for the "Third Reich" returns the initial cross-linking of East and West Europe country surveys.

Since the 1970s and the development of computer networks, this area also be combined with 3D measurements of satellite geodesy. Thus, the classical concept of going " degree measurement" in that the " earth measurement " on.

### Reference and earth ellipsoids

In the national survey, the individual States have until 1850 their own as " geodetic datum " is defined ( reference system ). With the international extension and crosslinking degree of the mentioned measurement profiles developed the ability and the desire to be based on the individual areas of large-scale valid data. The result was a series of so-called reference ellipsoid that the " middle Erdellipsoid " annäherten with increasing extension.

Of the approximately 200 state worldwide surveying networks today are based on 90 % of the data from a dozen more widely ellipsoids, which increases its quality and facilitates international cooperation. The older of these ellipsoids based on the great meridian arcs of the second section, the newer emerged from intercontinental and satellite networks. The most important of these ellipsoids are:

For many Central European countries, the Bessel ellipsoid is important, also, the ellipsoids of John Fillmore Hayford and Krasovsky and GPS survey the WGS 84

The pioneering work of Jean -Baptiste Joseph Delambre based only on local measurements. On the other hand creates the big difference between Everest ( Asia) and Hayford ( America) by the geologically -related geoid curvature of the different continents.