Stellar Triangulation
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Stellar triangulation is a method of
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 ...
and of its subdiscipline space geodesy used to measure Earth's geometric shape. Stars were first used for this purpose by the Finnish astronomer Yrjö Väisälä in 1959, who made astrometric photographs of the night sky at two stations together with a lighted balloon probe between them. Even this first step showed the potential of the method, as Väisälä got the azimuth between Helsinki and Turku (a distance of 150 km) with an accuracy of 1″. Soon the method was successfully tested by ballistic rockets and for some special
satellites A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioisotop ...
. Adequate computer programs were written for * the astrometric reduction of the photographic plates, * the
intersection In mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, their i ...
of the "observation planes" containing the stations and the targets, * and the least-squares adjustment of stellar-terrestrial networks with redundancy. The advantages of stellar triangulation were the possibility to cross far distances (terrestrial observations are restricted to approx. 30 km, and even in high mountains to 60 km), and the independency of the Earth's gravity field. The results are azimuths between the stations in the stellar-inertial navigation system, despite of no direct line of sight. In 1960, the first appropriate space probe was launched: Project Echo, a 30 m diameter
balloon satellite A balloon satellite is inflated with gas after it has been put into orbit. It is also occasionally referred to as a "satelloon", which is a trademarked name owned by Gilmore Schjeldahl's G.T. Schjeldahl Company. List of balloon satellites a ...
. By then the whole of Western Europe could be linked together geodetically with accuracies 2–10 times better than by classical
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 ...
. During the late 1960s, a global project was begun by H.H. Schmid (Switzerland) to connect 45 stations all over the continents, with distances of 3000–5000 km. It was finished in 1974 by precise reduction of some 3000 stellar plates and network adjustment of 46 stations (2 additional ones in Germany and the Pacific, but without the areas of Russia and
China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...
). The mean accuracy was between ±5 m (Europe, USA) and 7–10 m (Africa, Antarctica), depending on weather and infrastructure conditions. Combined with Doppler measurements (such as from ''Transit'') the global accuracy was even 3 m. This is more than 20 times better than previously, because the
gravity field In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenome ...
up to 1974 couldn't be calculated better than 100 meters between distant continents. The use of
star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s as a reference system was expanded in the 70s and early 80s for continental networks, but then the laser and electronic distance measurements became better than 2 m and could be carried out automatically. Nowadays some similar techniques are carried out by
interferometry Interferometry is a technique which uses the ''interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber opt ...
with very distant radio
quasar A quasar is an extremely Luminosity, luminous active galactic nucleus (AGN). It is pronounced , and sometimes known as a quasi-stellar object, abbreviated QSO. This emission from a galaxy nucleus is powered by a supermassive black hole with a m ...
s ( VLBI) instead of optical satellite & star observations. The geodetic connection of
radio telescope A radio telescope is a specialized antenna and radio receiver used to detect radio waves from astronomical radio sources in the sky. Radio telescopes are the main observing instrument used in radio astronomy, which studies the radio frequency ...
s is now possible up to mm–cm precision as published periodically by the community. This global project group was founded in 2000 by Harald Schuh (Munich/TU Vienna) and some dozen research projects worldwide, and is now a permanent service of International Union of Geodesy and Geophysics (IUGG) and
International Earth Rotation and Reference Systems Service The International Earth Rotation and Reference Systems Service (IERS), formerly the International Earth Rotation Service, is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation Pa ...
(IERS). The photographic observations as done 1959–1985 are irrelevant now because of their expense, but lead to some renaissance by electro-optical techniques like CCD.


See also

*
Figure of the Earth Figure of the Earth is a Jargon, 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 Spherical Earth, sphere is a well-k ...
* Fundamental station *
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 ...
* Trilateration * Satellite geodesy ** Satellite geodesy#Optical triangulation * PAGEOS satellite * Satellite laser ranging (SLR) *
Stellar parallax Stellar parallax is the apparent shift of position of any nearby star (or other object) against the background of distant objects, and a basis for determining (through trigonometry) the distance of the object. Created by the different orbital p ...
for distances to stars


References

* A.Berroth, W.Hofmann: ''Kosmische Geodäsie''(''Cosmic Geodesy'') (356 p.), G.Braun, Karlsruhe 1960 * Karl Ledersteger: "Astronomische und Physikalische Geodäsie ( Erdmessung)", '' Handbuch der Vermessungskunde'', Wilhelm Jordan, Otto Eggert and Max Kneissl ed., Volume V, (870 S., espec. §§ 2, 5, 13), J.B.Metzler, Stuttgart 1968. * Hellmut Schmid: ''Das Weltnetz der Satelitentriangulation''. Wiss. Mitteilungen
ETH Zurich (colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , ac ...
and ''Journal of Geophysical Research'', 1974. * Klaus Schnädelbach et al.: Western European Satellite Triangulation Programme (WEST), 2nd Experimental Computation. Mitteilungen Geodät.Inst. Graz 11/1, Graz 1972 * Nothnagel, Schlüter, Seeger: Die Geschichte der geodätischen VLBI in Deutschland, Bonn 2000.


External links


NOAA's geodesy photo library
{{DEFAULTSORT:Stellar Triangulation Geodesy Astrometry