# Bessel ellipsoid > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Bessel_ellipsoid > Markdown URL: https://mediated.wiki/source/Bessel_ellipsoid.md > Source: https://en.wikipedia.org/wiki/Bessel_ellipsoid > Source revision: 1275628638 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) Reference ellipsoid in geodesy This article needs more citations. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Bessel ellipsoid" – news · newspapers · books · scholar · JSTOR (February 2022) (Learn how and when to remove this message) The **Bessel ellipsoid** (or **Bessel 1841**) is an important [reference ellipsoid](/source/Reference_ellipsoid) of [geodesy](/source/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](/source/Satellite_geodesy). The Bessel ellipsoid was derived in 1841 by [Friedrich Wilhelm Bessel](/source/Friedrich_Wilhelm_Bessel), based on several [arc measurements](/source/Arc_measurements) and other data of continental [geodetic networks](/source/Geodetic_network) of [Europe](/source/Europe), Russia and the British [Survey of India](/source/Survey_of_India). It is based on 10 [meridian arcs](/source/Meridian_arc) and 38 precise measurements of the [astronomic latitude](/source/Astronomic_latitude) and [longitude](/source/Longitude) (see also [astro geodesy](/source/Astro-geodetic)). The dimensions of the [Earth ellipsoid](/source/Earth_ellipsoid) axes were defined by [logarithms](/source/Logarithm) in keeping with former [calculation](/source/Calculation) methods. ## The Bessel and GPS ellipsoids The Bessel ellipsoid fits especially well to the [geoid](/source/Geoid) curvature of Europe and [Eurasia](/source/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](/source/Earth_ellipsoid) derived by satellites. Below there are the two axes a, b and the [flattening](/source/Flattening) *f* = (*a* − *b*)/*a*. For comparison, the data of the modern *World Geodetic System* [WGS84](/source/WGS84) are shown, which is mainly used for modern surveys and the [GPS](/source/Global_Positioning_System) system. - Bessel ellipsoid 1841 (defined by log a and f): - a = 6377397.155 m - f = 1 / 299.15281285[1][2][3] - b = 6356078.962822 m. - Earth ellipsoid WGS84 (defined directly by a and f): - a = 6378137.0 m - f = 1 / 298.257223563 - b = 6356752.30 m. ## Usage The ellipsoid data published by Bessel (1841) were then the best and most modern data mapping the [Earth's figure](/source/Figure_of_the_Earth). They were used by almost all national surveys. Some surveys in [Asia](/source/Asia) switched to the [Clarke ellipsoid](/source/Clarke_ellipsoid) of 1880. After the arrival of the [geophysical](/source/Geophysical) reduction techniques many projects used other examples such as the [Hayford ellipsoid](/source/Hayford_ellipsoid) of 1910 which was adopted in 1924 by the [International Association of Geodesy](/source/International_Association_of_Geodesy) (IAG) as the [International ellipsoid](/source/International_ellipsoid) 1924. All of them are influenced by geophysical effects like [vertical deflection](/source/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](/source/Satellite_geodesy)) in the same way as the pioneering work of Bessel. In 1950 about 50% of the European [triangulation](/source/Triangulation) networks and about 20% of other [continents](/source/Continent) networks were based on the Bessel ellipsoid. In the following decades the [American](/source/Americas) states switched mainly to the [Hayford ellipsoid](/source/Hayford_ellipsoid) 1908 ("internat. Ell. 1924") which was also used for the European unification project [ED50](/source/ED50) sponsored by the United States after World War II. The Soviet Union forced its satellite states in [Eastern Europe](/source/Eastern_Europe) to use the [Krasovsky ellipsoid](/source/Krasovsky_ellipsoid) of about 1940. As of 2010 the Bessel ellipsoid is the geodetic system for Germany, for Austria and the [Czech Republic](/source/Czech_Republic). It is also used partly in the successor states of [Yugoslavia](/source/Yugoslavia) and some Asian countries: [Sumatra](/source/Sumatra) and [Borneo](/source/Borneo), [Belitung](/source/Belitung). In Africa it is the geodetic system for [Eritrea](/source/Eritrea) and [Namibia](/source/Namibia). ## See also - [Gauss–Krüger coordinate system](/source/Gauss%E2%80%93Kr%C3%BCger_coordinate_system) – Adaptation of the standard Mercator projectionPages displaying short descriptions of redirect targets - [Geodesy](/source/Geodesy) – Science of measuring the shape, orientation, and gravity of Earth - [Hayford ellipsoid](/source/Hayford_ellipsoid) – Earth-approximating ellipsoid introduced in 1910 - [Helmert transformation](/source/Helmert_transformation) – Transformation method within a three-dimensional space - [WGS 72](/source/WGS_72) – Geodetic reference systemPages displaying short descriptions of redirect targets - [WGS 84](/source/WGS_84) – Geodetic reference systemPages displaying short descriptions of redirect targets ## References 1. **[^](#cite_ref-1)** Bessel, Friedrich Wilhelm (1841-12-01). ["Über einen Fehler in der Berechnung der französischen Gradmessung und seineh Einfluß auf die Bestimmung der Figur der Erde. Von Herrn Geh. Rath und Ritter Bessel"](https://ui.adsabs.harvard.edu/abs/1841AN.....19...97B). *Astronomische Nachrichten*. **19** (7): 216. [Bibcode](/source/Bibcode_(identifier)):[1841AN.....19...97B](https://ui.adsabs.harvard.edu/abs/1841AN.....19...97B). [doi](/source/Doi_(identifier)):[10.1002/asna.18420190702](https://doi.org/10.1002%2Fasna.18420190702). [ISSN](/source/ISSN_(identifier)) [0004-6337](https://search.worldcat.org/issn/0004-6337). 1. **[^](#cite_ref-2)** Viik, T, *F. W. Bessel and Geodesy*, vol. Struve Geodetic Arc, 2006 International Conference, The Struve Arc Extension in Space and Time, Haparanda and Pajala, Sweden, 13–15 August 2006, pp. 8–10 1. **[^](#cite_ref-3)** ["Formulas and constants for the calculation of the Swiss conformal cylindrical projection and for the transformation between coordinate systems"](https://www.swisstopo.admin.ch/content/swisstopo-internet/en/topics/survey/reference-systems/switzerland/_jcr_content/contentPar/tabs/items/dokumente_publikatio/tabPar/downloadlist/downloadItems/517_1459343190376.download/refsys_e.pdf) (PDF). *swisstopo*. 2016. p. 5. [Archived](https://web.archive.org/web/20191205124728/https://www.swisstopo.admin.ch/content/swisstopo-internet/en/topics/survey/reference-systems/switzerland/_jcr_content/contentPar/tabs/items/dokumente_publikatio/tabPar/downloadlist/downloadItems/517_1459343190376.download/refsys_e.pdf) (PDF) from the original on 2019-12-05. Retrieved 2021-09-25. ## External links - [Conversion of Longitude and Latitude degrees into Universal Transverse Mercator coordinate system coordinates](http://www.gpsy.com/gpsinfo/geotoutm/index.html) --- Adapted from the Wikipedia article [Bessel ellipsoid](https://en.wikipedia.org/wiki/Bessel_ellipsoid) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Bessel_ellipsoid?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.