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 Satellite geodesy is geodesy by means of artificial satellites—the measurement of the form and dimensions of Earth, the location of objects on its surface and the figure of the Earth's gravity field by means of artificial satellite techniques ...

. The Bessel ellipsoid was derived in 1841 by

Friedrich Wilhelm Bessel Friedrich Wilhelm Bessel (; 22 July 1784 – 17 March 1846) was a German astronomer, mathematician, physicist, and geodesist. He was the first astronomer who determined reliable values for the distance from the sun to another star by the method ...

, based on several arc measurements and other data of continental

geodetic network A geodetic control network (also geodetic network, reference network, control point network, or control network) is a network, often of triangles, which are measured precisely by techniques of terrestrial surveying or by satellite geodesy. A ...

s of

Europe Europe is a large peninsula conventionally considered a continent in its own right because of its great physical size and the weight of its history and traditions. Europe is also considered a subcontinent of Eurasia and it is located entirel ...

, Russia and the British Survey of India. It is based on 10 meridian arcs 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 pol ...

and

longitude Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lette ...

(see also astro geodesy). The dimensions of the

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 ...

axes were defined by

logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of ...

s in keeping with former calculation methods.

The Bessel and GPS ellipsoids

The Bessel ellipsoid fits especially well to the

geoid The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended ...

curvature of Europe and

Eurasia Eurasia (, ) is the largest continental area on Earth, comprising all of Europe and Asia. Primarily in the Northern and Eastern Hemispheres, it spans from the British Isles and the Iberian Peninsula in the west to the Japanese archipelago ...

. 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

derived by satellites. Below there are the two axes , and the

flattening Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution ( spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening i ...

. For comparison, the data of the modern ''World Geodetic System''

WGS84 The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS. The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also describ ...

are shown, which is mainly used for modern surveys and the

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

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 Figure of the Earth is a term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. A sphere is a well-known historical approxima ...

. They were used by almost all national surveys. Some surveys in

Asia Asia (, ) is one of the world's most notable geographical regions, which is either considered a continent in its own right or a subcontinent of Eurasia, which shares the continental landmass of Afro-Eurasia with Africa. Asia covers an are ...

switched to the Clarke ellipsoid of 1880. After the arrival of the

geophysical Geophysics () is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. The term ''geophysics'' some ...

reduction techniques many projects used other examples such as the

Hayford ellipsoid The Hayford ellipsoid is a geodetic reference ellipsoid, named after the US geodesist John Fillmore Hayford (1868–1925), which was introduced in 1910. The Hayford ellipsoid was also referred to as the International ellipsoid 1924 after it had be ...

of 1910 which was adopted in 1924 by the

International Association of Geodesy The International Association of Geodesy (IAG) is a constituent association of the International Union of Geodesy and Geophysics. Overview The precursors to the IAG were arc measurement campaigns. The IAG was founded in 1862 as the ''Mitteleuro ...

(IAG) as the

International ellipsoid The Hayford ellipsoid is a geodetic reference ellipsoid, named after the US geodesist John Fillmore Hayford (1868–1925), which was introduced in 1910. The Hayford ellipsoid was also referred to as the International ellipsoid 1924 after it had b ...

1924. All of them are influenced by geophysical effects like

vertical deflection The vertical deflection (VD) or deflection of the vertical (DoV), also known as deflection of the plumb line and astro-geodetic deflection, is a measure of how far the gravity direction at a given point of interest is rotated by local mass anom ...

, mean continental density, rock density and the distribution of network data. Every reference ellipsoid deviates from the worldwide data (e.g. of

) in the same way as the pioneering work of Bessel. In 1950 about 50% of the European triangulation networks and about 20% of other

continent A continent is any of several large landmasses. Generally identified by convention rather than any strict criteria, up to seven geographical regions In geography, regions, otherwise referred to as zones, lands or territories, are areas t ...

s networks were based on the Bessel ellipsoid. In the following decades the American states switched mainly to the

1908 ("internat. Ell. 1924") which was also used for the European unification project

ED50 ED50 ("European Datum 1950", EPSG:4230) is a geodetic datum which was defined after World War II for the international connection of geodetic networks. Background Some of the important battles of World War II were fought on the borders of Ger ...

sponsored by the United States after World War II. The Soviet Union forced its satellite states in

Eastern Europe Eastern Europe is a subregion of the European continent. As a largely ambiguous term, it has a wide range of geopolitical, geographical, ethnic, cultural, and socio-economic connotations. The vast majority of the region is covered by Russia, whic ...

to use the Krasovsky ellipsoid of about 1940. As of 2010 the Bessel ellipsoid is the geodetic system for Germany, for Austria and the

Czech Republic The Czech Republic, or simply Czechia, is a landlocked country in Central Europe. Historically known as Bohemia, it is bordered by Austria to the south, Germany to the west, Poland to the northeast, and Slovakia to the southeast. The ...

. It is also used partly in the successor states of

Yugoslavia Yugoslavia (; sh-Latn-Cyrl, separator=" / ", Jugoslavija, Југославија ; sl, Jugoslavija ; mk, Југославија ;; rup, Iugoslavia; hu, Jugoszlávia; rue, label=Pannonian Rusyn, Югославия, translit=Juhoslavija ...

and some Asian countries: Sumatra and

Borneo Borneo (; id, Kalimantan) is the third-largest island in the world and the largest in Asia. At the geographic centre of Maritime Southeast Asia, in relation to major Indonesian islands, it is located north of Java, west of Sulawesi, and ea ...

Belitung Belitung ( Belitung Malay: ''Belitong'', formerly Billiton) is an island on the east coast of Sumatra, Indonesia in the Java Sea. It covers , and had a population of 309,097 at the 2020 Census. Administratively, it forms two regencies ( Beli ...

Okinawa is a prefecture of Japan. Okinawa Prefecture is the southernmost and westernmost prefecture of Japan, has a population of 1,457,162 (as of 2 February 2020) and a geographic area of 2,281 km2 (880 sq mi). Naha is the capital and largest city ...

(Japan). In Africa it is the geodetic system for Eritrea and

Namibia Namibia (, ), officially the Republic of Namibia, is a country in Southern Africa. Its western border is the Atlantic Ocean. It shares land borders with Zambia and Angola to the north, Botswana to the east and South Africa to the south and ea ...

References

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External links

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

The Bessel and GPS ellipsoids

Usage

See also

References

External links