Bessel ellipsoid

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The Bessel ellipsoid (also Bessel 1841 ) is a reference ellipsoid for Europe. Friedrich Wilhelm Bessel derived it in 1841 from the data of large-scale surveys in Europe , Russia , India and South America.

The Bessel ellipsoid

Bessel processed the data from the Prussian degree measurements he carried out himself with those of nine other degree measurements carried out worldwide: the French, English, Hanoverian, Danish, Swedish and Russian degree measurements as well as the degree measurements of the Paris Academy in South America (Peru / Ecuador ) and the two East Indian profiles.

According to Ledersteger, the total length of the measuring arcs is 50 ° 34 ', which corresponds to about 5,700 kilometers. Through his careful data processing, Bessel was able to achieve a very good approximation of the value known today for the earth figure . In accordance with the computing technology of the time, Bessel gave the results (dimensions of the ellipsoid) not only numerically in the Toise unit of length, which was common at the time, but also as logarithms .

Bessel determined the values ​​for his reference ellipsoid (converted into today's units):

 Equatorial half- axis a = 6,377,397.155 m, polar half-axis b = 6,356,078.963 m, flattening of the earth  f = 1: 299.152815

In accordance with the computing technology of the time, Bessel gave the results (dimensions of the ellipsoid) not only numerically in the Toise unit of length, which was common at the time, but also as logarithms .

Compared to the currently used earth ellipsoid , which is known to the nearest decimeter, its axes a (equatorial) and b (polar) are around 700 meters shorter. The exact values ​​compared to others, for example the World Geodetic System WGS84 from 1984 used for GPS surveying , can be found in this table .

use

When it was published in 1841, the Bessel ellipsoid was the most accurate and was used as a basis for practically all newer surveying networks over the next few decades . It was not until Clarke's ellipsoids around 1880 or after the advent of geophysical calculation methods (including Hayford around 1920) that some states switched to newer ellipsoids. However, these are only regionally adapted to the curvature of the earth and therefore, like Bessel's pioneering work, deviate from the ellipsoids of our time derived from satellite data worldwide .

The Bessel ellipsoid adapts itself particularly well to the geoid and the mean curvature of the earth in Eurasia thanks to its data base and has therefore been used as the basis for many national surveys , e.g. B. in Germany (since 1989 also back in East Germany), in Austria , in Switzerland and in the Czech Republic as well as in the successor states of Yugoslavia . But it is also used outside of Europe, namely in Indonesia ( Sumatra , Kalimantan ( Borneo ), Bangka , Belitung ) and Japan ( Okinawa , Mean Solu), as well as in Eritrea and Namibia .

Around 1950 about half of the triangulations in Europe and about 20% on other continents were based on the Bessel ellipsoid; The reference ellipsoids by Hayford 1908 ("internat. Ell. 1924", especially for America and ED50 ) and by Krassowski (above all eastern half of Europe) were also strongly represented .

See also

literature

  • Karl Ledersteger : Astronomical and Physical Geodesy ( Earth Measurement ) , Chapters 12 (Degree measurements) and 36 (Land Surveying). Jordan-Eggert-Kneissl Volume V, Handbook of Surveying, Verlag JB Metzler, Stuttgart 1969

Individual evidence

  1. ↑ About an error in the calculation of the French degree measurement and its influence on the determination of the figure of the earth. From Herr Geheimen Rath and Ritter Bessel. Astronomical News Volume 19, No. 438 (1842) 97-116.

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