The Bessel ellipsoid (or Bessel 1841) is an important

reference 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 ...

geodesy Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivale ...

. 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 Arc measurement, sometimes degree measurement (german: Gradmessung), is the astrogeodetic technique of determining of the radius of Earth – more specifically, the local Earth radius of curvature of the figure of the Earth – by relating the ...

and other data of continental geodetic networks of Europe, Russia and the British

Survey of India The Survey of India is India's central engineering agency in charge of Cartography, mapping and surveying.

. It is based on 10

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 de ...

s and 38 precise measurements of the

astronomic latitude In geography, latitude is a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pole ...

and longitude (see also astro geodesy). The dimensions of the Earth ellipsoid axes were defined by logarithms in keeping with former

calculation A calculation is a deliberate mathematical process that transforms one or more inputs into one or more outputs or ''results''. The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm, to th ...

methods.

The Bessel and GPS ellipsoids

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, despite of the fact that its axes are about 700 m shorter than that of the mean Earth ellipsoid derived by satellites. Below there are the two axes , and the flattening . For comparison, the data of the modern ''World Geodetic System'' WGS84 are shown, which is mainly used for modern surveys and the

GPS The Global Positioning System (GPS), originally Navstar GPS, is a Radionavigation-satellite service, satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of t ...

system. * Bessel ellipsoid 1841 (defined by log and ): ** = ** = 1 / ** = . * Earth ellipsoid WGS84 (defined directly by and ): ** = ** = 1 / ** = .

Usage

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 Col Alexander Ross Clarke FRS FRSE (1828–1914) was a British geodesist, primarily remembered for his calculation of the Principal Triangulation of Britain (1858), the calculation of the Figure of the Earth (1858, 1860, 1866, 1880) and one ...

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.g. of satellite geodesy) in the same way as the pioneering work of Bessel. In 1950 about 50% of the European

triangulation In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle me ...

networks and about 20% of other continents networks were based on the Bessel ellipsoid. In the following decades the

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...

states switched mainly to the Hayford ellipsoid 1908 ("internat. Ell. 1924") which was also used for the European unification project ED50 sponsored by the United States after World War II. The Soviet Union forced its satellite states in Eastern Europe to use the

Krasovsky ellipsoid The SK-42 reference system also known as the Krasovsky 1940 ellipsoid, is a coordinate system established in the Soviet Union in 1942 as ''Systema koordinat'' (russian: Система координат 1942 года), and provides parameters which ...

of about 1940. As of 2010 the Bessel ellipsoid is the geodetic system for Germany, for Austria and the Czech Republic. It is also used partly in the successor states of Yugoslavia and some Asian countries:

Sumatra Sumatra is one of the Sunda Islands of western Indonesia. It is the largest island that is fully within Indonesian territory, as well as the sixth-largest island in the world at 473,481 km2 (182,812 mi.2), not including adjacent i ...

and Borneo, Belitung, Okinawa (Japan). In Africa it is the geodetic system for

Eritrea Eritrea ( ; ti, ኤርትራ, Ertra, ; ar, إرتريا, ʾIritriyā), officially the State of Eritrea, is a country in the Horn of Africa region of Eastern Africa, with its capital and largest city at Asmara. It is bordered by Ethiopia ...

and Namibia.

References

{{reflist

External links

UTM">Conversion of Longitude and Latitude degrees into UTM
coordinates Geodesy

The Bessel and GPS ellipsoids

Usage

See also

References

External links