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Concept# Bessel ellipsoid

Summary

The Bessel ellipsoid (or Bessel 1841) is an important reference ellipsoid of geodesy. It is currently used by several countries for their national geodetic surveys, but will be replaced in the next decades by modern ellipsoids of satellite geodesy.
The Bessel ellipsoid was derived in 1841 by Friedrich Wilhelm Bessel, based on several arc measurements and other data of continental geodetic networks of Europe, Russia and the British Survey of India. It is based on 10 meridian arcs and 38 precise measurements of the astronomic latitude and longitude (see also astro geodesy). The dimensions of the Earth ellipsoid axes were defined by logarithms in keeping with former calculation methods.
The Bessel ellipsoid fits especially well to the geoid curvature of Europe and Eurasia. Therefore, it is optimal for National survey networks in these regions, although its axes are about 700 m shorter than that of the mean Earth ellipsoid derived by satellites.
Below there are the two axes a, b and the flattening f = (a − b)/a. For comparison, the data of the modern World Geodetic System WGS84 are shown, which is mainly used for modern surveys and the GPS system.
Bessel ellipsoid 1841 (defined by log a and f):
a = 6377397.155m
f = 1 / 299.15281285
b = 6356078.962822m.
Earth ellipsoid WGS84 (defined directly by a and f):
a = 6378137.0m
f = 1 / 298.257223563
b = 6356752.30m.
The ellipsoid data published by Bessel (1841) were then the best and most modern data mapping the Earth's figure. They were used by almost all national surveys. Some surveys in Asia switched to the Clarke ellipsoid of 1880. After the arrival of the geophysical reduction techniques many projects used other examples such as the Hayford ellipsoid of 1910 which was adopted in 1924 by the International Association of Geodesy (IAG) as the International ellipsoid 1924. All of them are influenced by geophysical effects like vertical deflection, mean continental density, rock density and the distribution of network data. Every reference ellipsoid deviates from the worldwide data (e.

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Earth ellipsoid

An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations. It is a spheroid (an ellipsoid of revolution) whose minor axis (shorter diameter), which connects the geographical North Pole and South Pole, is approximately aligned with the Earth's axis of rotation.

Meridian arc

In geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length. The purpose of measuring meridian arcs is to determine a figure of the Earth. One or more measurements of meridian arcs can be used to infer the shape of the reference ellipsoid that best approximates the geoid in the region of the measurements.

Arc measurement

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