Bessel ellipsoid
Encyclopedia
The Bessel ellipsoid is an important reference ellipsoid
of geodesy
. It is currently used by several countries for their national geodetic surveys, in Europe and on other continents, but will be replaced in the next decades by modern ellipsoids of satellite geodesy
.
The Bessel ellipsoid was derived 1841 by Friedrich Wilhelm Bessel, based on several meridian arc
s and other data of continental geodetic network
s of Europe
, Russia
and the British Survey of India
. It is based on 10 meridional arcs and 38 precise measurements of the astro—geographic latitude
and longitude
(see also astro geodesy
). The dimensions of the ellipsoid axes were defined by logarithm
s in keeping with former calculation
methods.
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 the two axes a, b and the flattening
ƒ = (a − b)/a. As for comparison, the data of the modern World Geodetic System WGS84 are shown, which is mainly used for modern surveys and the GPS
system.
. They were used by almost all national surveys just some surveys in Asia
switching 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 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
networks and about 20% of other continent
s networks were based on the Bessel ellipsoid. In the following decades the American
states switched mainly to the Hayford ellipsoid
1908 ("internat. Ell. 1924") which was also used for the European unification project ED50
sponsored by the USA after World War II. Russia
forced its satellite states in Eastern Europe
to use the Krassowski ellipsoid of about 1940.
As of 2010 the Bessel ellipsoid is the geodetic system for Germany
, for Austria
and Czech Republic
. Partly also in the successive states of Yugoslavia
and some Asian countries: Sumatra
& Borneo
, Belitung
, Okinawa (Japan) and Africa in Eritrea
and Namibia
.
Reference ellipsoid
In geodesy, a reference ellipsoid is a mathematically-defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body....
of geodesy
Geodesy
Geodesy , also named geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, in a three-dimensional time-varying space. Geodesists also study geodynamical phenomena such as crustal...
. It is currently used by several countries for their national geodetic surveys, in Europe and on other continents, but will be replaced in the next decades by modern ellipsoids of satellite geodesy
Satellite geodesy
Satellite geodesy is the measurement of the form and dimensions of the Earth, the location of objects on its surface and the figure of the Earth's gravity field by means of artificial satellite techniques—geodesy by means of artificial satellites...
.
The Bessel ellipsoid was derived 1841 by Friedrich Wilhelm Bessel, based on several meridian arc
Meridian arc
In geodesy, a meridian arc measurement is a highly accurate determination of the distance between two points with the same longitude. Two or more such determinations at different locations then specify the shape of the reference ellipsoid which best approximates the shape of the geoid. This...
s and other data of continental geodetic network
Geodetic network
A geodetic network is a network of triangles which are measured exactly by techniques of terrestrial surveying or by satellite geodesy.In "classical geodesy" this is done by triangulation, based on measurements of angles and of some spare distances; the precise orientation to the geographic north...
s of Europe
Europe
Europe is, by convention, one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally 'divided' from Asia to its east by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways connecting...
, Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
and the British Survey of India
Survey of India
The Survey of India is India's central engineering agency in charge of mapping and surveying. Set up in 1767 to help consolidate the territories of the British East India Company, it is one of the oldest Engineering Departments of the Government of India...
. It is based on 10 meridional arcs and 38 precise measurements of the astro—geographic latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...
and longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
(see also astro geodesy
Astro-geodetic
Astro-geodetic methods are a group of important methods in geodesy, satellite techniques and astrometry.The classical astro-geodetic leveling is a reasonably accurate method to derive the terrestrial geoid, provided a starting point is given...
). The dimensions of the ellipsoid axes were defined by logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
s in keeping with former calculation
Calculation
A calculation is a deliberate process for transforming one or more inputs into one or more results, with variable change.The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm to the vague heuristics of calculating a strategy in a competition...
methods.
The Bessel and GPS ellipsoids
The Bessel ellipsoid fits especially well to the geoidGeoid
The geoid is that equipotential surface which would coincide exactly with the mean ocean surface of the Earth, if the oceans were in equilibrium, at rest , and extended through the continents . According to C.F...
curvature of Europe and Eurasia
Eurasia
Eurasia is a continent or supercontinent comprising the traditional continents of Europe and Asia ; covering about 52,990,000 km2 or about 10.6% of the Earth's surface located primarily in the eastern and northern hemispheres...
. 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
Earth ellipsoid
An Earth ellipsoid is a mathematical figure approximating the shape of the Earth, used as a reference frame for computations in geodesy, astronomy and the geosciences...
derived by satellites.
Below the two axes a, b and the flattening
Flattening
The flattening, ellipticity, or oblateness of an oblate spheroid is a measure of the "squashing" of the spheroid's pole, towards its equator...
ƒ = (a − b)/a. As for comparison, the data of the modern World Geodetic System WGS84 are shown, which is mainly used for modern surveys and the GPS
Global Positioning System
The Global Positioning System is a space-based global navigation satellite system that provides location and time information in all weather, anywhere on or near the Earth, where there is an unobstructed line of sight to four or more GPS satellites...
system.
- Bessel ellipsoid 1841 (defined by log a and ƒ):
- a = 6,377,397.155 m
- ƒ = 1 / 299.1528153513233 (0.003342 773154 ± 0.000005)
- b = 6,356,078.963 m.
- Earth ellipsoid WGS84 (defined directly by a and ƒ):
- a = 6,378,137.0 m
- ƒ = 1 / 298.257223563
- b = 6,356,752.30 m.
Usage
The ellipsoid data published by Bessel (1841) were the best and most modern data mapping the Earth's figureFigure of the Earth
The expression figure of the Earth has various meanings in geodesy according to the way it is used and the precision with which the Earth's size and shape is to be defined. The actual topographic surface is most apparent with its variety of land forms and water areas. This is, in fact, the surface...
. They were used by almost all national surveys just some surveys in Asia
Asia
Asia is the world's largest and most populous continent, located primarily in the eastern and northern hemispheres. It covers 8.7% of the Earth's total surface area and with approximately 3.879 billion people, it hosts 60% of the world's current human population...
switching to the Clarke ellipsoid of 1880. After the arrival of the geophysical reduction techniques many projects used other examples such as the Hayford ellipsoid
Hayford ellipsoid
The Hayford ellipsoid is a geodetic reference ellipsoid, named after the US geodesist John Fillmore Hayford , which was introduced in 1910. The Hayford ellipsoid was also referred to as the International ellipsoid 1924 after it had been adopted by the International Union of Geodesy and Geophysics...
of 1910 which was adopted in 1924 by the IAG
IAG
IAG may mean:* IAG – The IATA code for Niagara Falls International Airport* IAg – Immersion Silver plating, a conductor plating technology used for Printed circuit boards...
as the International ellipsoid 1924. All of them are influenced by geophysical effects like vertical deflection
Vertical deflection
The vertical deflection at a point on the earth is a measure of how far the direction of the local gravity field has been shifted by local anomalies such as nearby mountains....
, mean continental density, rock density and the distribution of network data. Every reference ellipsoid deviates from the worldwide data (e.g. of satellite geodesy
Satellite geodesy
Satellite geodesy is the measurement of the form and dimensions of the Earth, the location of objects on its surface and the figure of the Earth's gravity field by means of artificial satellite techniques—geodesy by means of artificial satellites...
) in the same way as the pioneering work of Bessel.
In 1950 about 50% of the European triangulation
Triangulation
In trigonometry and geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly...
networks and about 20% of other continent
Continent
A continent is one of several very large landmasses on Earth. They are generally identified by convention rather than any strict criteria, with seven regions commonly regarded as continents—they are : Asia, Africa, North America, South America, Antarctica, Europe, and Australia.Plate tectonics is...
s networks were based on the Bessel ellipsoid. In the following decades the American
Americas
The Americas, or America , are lands in the Western hemisphere, also known as the New World. In English, the plural form the Americas is often used to refer to the landmasses of North America and South America with their associated islands and regions, while the singular form America is primarily...
states switched mainly to the Hayford ellipsoid
Hayford ellipsoid
The Hayford ellipsoid is a geodetic reference ellipsoid, named after the US geodesist John Fillmore Hayford , which was introduced in 1910. The Hayford ellipsoid was also referred to as the International ellipsoid 1924 after it had been adopted by the International Union of Geodesy and Geophysics...
1908 ("internat. Ell. 1924") which was also used for the European unification project ED50
ED50
ED 50 is a geodetic datum which was defined after World War II for the international connection of geodetic networks....
sponsored by the USA after World War II. Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
forced its satellite states in Eastern Europe
Eastern Europe
Eastern Europe is the eastern part of Europe. The term has widely disparate geopolitical, geographical, cultural and socioeconomic readings, which makes it highly context-dependent and even volatile, and there are "almost as many definitions of Eastern Europe as there are scholars of the region"...
to use the Krassowski ellipsoid of about 1940.
As of 2010 the Bessel ellipsoid is the geodetic system for Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
, for Austria
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
and Czech Republic
Czech Republic
The Czech Republic is a landlocked country in Central Europe. The country is bordered by Poland to the northeast, Slovakia to the east, Austria to the south, and Germany to the west and northwest....
. Partly also in the successive states of Yugoslavia
Yugoslavia
Yugoslavia refers to three political entities that existed successively on the western part of the Balkans during most of the 20th century....
and some Asian countries: Sumatra
Sumatra
Sumatra is an island in western Indonesia, westernmost of the Sunda Islands. It is the largest island entirely in Indonesia , and the sixth largest island in the world at 473,481 km2 with a population of 50,365,538...
& Borneo
Borneo
Borneo is the third largest island in the world and is located north of Java Island, Indonesia, at the geographic centre of Maritime Southeast Asia....
, Belitung
Belitung
Belitung, , is an island on the east coast of Sumatra, Indonesia in the Java Sea. The island is known for its pepper and for its tin. It was in the possession of the British from 1812 until the British ceded control of the island to the Dutch in the Anglo-Dutch Treaty of 1824...
, Okinawa (Japan) and Africa in Eritrea
Eritrea
Eritrea , officially the State of Eritrea, is a country in the Horn of Africa. Eritrea derives it's name from the Greek word Erethria, meaning 'red land'. The capital is Asmara. It is bordered by Sudan in the west, Ethiopia in the south, and Djibouti in the southeast...
and Namibia
Namibia
Namibia, officially the Republic of Namibia , is a country in southern Africa whose western border is the Atlantic Ocean. It shares land borders with Angola and Zambia to the north, Botswana to the east and South Africa to the south and east. It gained independence from South Africa on 21 March...
.
See also
- GeodesyGeodesyGeodesy , also named geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, in a three-dimensional time-varying space. Geodesists also study geodynamical phenomena such as crustal...
, WGS 72, WGS 84 - Gauss–Krüger coordinate system, Helmert transformationHelmert transformationThe Helmert transformation is a transformation method within a three-dimensional space...
- worldwide Ellipsoids (website in german)
- http://www.gpsy.com/gpsinfo/geotoutm/index.htmlConversion of Longitude and Latitude degrees into UTMUTMUTM is a three-letter abbreviation with multiple meanings, as described below* Ultrasonic Thickness Measurement, using propagation of ultrasound waves to determine the thickness of metals...
coordinates]