Stellar triangulation
Encyclopedia
Stellar triangulation is a method of geodesy
which uses cosmic instead of terrestrial targets. It was first done by the Finnish geodesist Väisälä
in 1959, who made astrometric photograph
s of the sky at two stations together with a balloon
probe between them.
Even this first step showed the potential of the method, because 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. Adequate computer program
s were written for
The advantage of stellar triangulation is 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 system, despite of no direct line of sight
.
In 1960 the first appropriate space probe
was launched - the 30 m diameter balloon satellite
(Project Echo). By then the whole of Western Europe
could be linked together geodetically with accuracies 2-10 times better than by classical triangulation
.
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
). The mean accuracy was between ± 5m (Europe, USA) and 7–10 m (Africa, Antarctica), depending of weather and infrastructure conditions. Combined with Doppler
measurements the global accuracy was even 3m. This is more than 20 times better than previously, because the gravity field
up to 1974 couldn't be calculated better than 100 meters between distant continent
s.
The use of star
s as a reference system wars expanded in the 70s and early 80s for continental networks - but then the laser
and electronic
measurements became better than 2m and could be carried out automatically. Nowadays some similar techniques are carried out by interferometry
with very distant radio quasar
s instead of optical satellite & star observations. The geodetic connection of radio telescope
s is now possible up to mm...cm precision as published periodically by the IVS community. This global project group was founded in 2000 by Harald Schuh (H. Schuh) (Munich/ TU Vienna) and some dozen research projects worldwide, and is now a permanent
service of IUGG
and 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
.
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...
which uses cosmic instead of terrestrial targets. It was first done by the Finnish geodesist Väisälä
Yrjö Väisälä
Yrjö Väisälä was a Finnish astronomer and physicist.His main contributions were in the field of optics, but he was also very active in geodetics, astronomy and optical metrology...
in 1959, who made astrometric photograph
Photograph
A photograph is an image created by light falling on a light-sensitive surface, usually photographic film or an electronic imager such as a CCD or a CMOS chip. Most photographs are created using a camera, which uses a lens to focus the scene's visible wavelengths of light into a reproduction of...
s of the sky at two stations together with a balloon
Balloon
A balloon is an inflatable flexible bag filled with a gas, such as helium, hydrogen, nitrous oxide, oxygen, or air. Modern balloons can be made from materials such as rubber, latex, polychloroprene, or a nylon fabric, while some early balloons were made of dried animal bladders, such as the pig...
probe between them.
Even this first step showed the potential of the method, because Väisälä got the azimuth between Helsinki
Helsinki
Helsinki is the capital and largest city in Finland. It is in the region of Uusimaa, located in southern Finland, on the shore of the Gulf of Finland, an arm of the Baltic Sea. The population of the city of Helsinki is , making it by far the most populous municipality in Finland. Helsinki is...
and Turku
Turku
Turku is a city situated on the southwest coast of Finland at the mouth of the Aura River. It is located in the region of Finland Proper. It is believed that Turku came into existence during the end of the 13th century which makes it the oldest city in Finland...
(a distance of 150 km) with an accuracy of 1". Soon the method was successfully tested by ballistic
External ballistics
External ballistics is the part of the science of ballistics that deals with the behaviour of a non-powered projectile in flight. External ballistics is frequently associated with firearms, and deals with the behaviour of the bullet after it exits the barrel and before it hits the target.-Forces...
rockets and for some special satellites. Adequate computer program
Computer program
A computer program is a sequence of instructions written to perform a specified task with a computer. A computer requires programs to function, typically executing the program's instructions in a central processor. The program has an executable form that the computer can use directly to execute...
s were written for
- the astrometric reduction of the photographic plates,
- the intersectionIntersection (set theory)In mathematics, the intersection of two sets A and B is the set that contains all elements of A that also belong to B , but no other elements....
of the "observation planes" containing the stations and the targets, - and the adjustmentAdjustmentAdjustment means regulating, adapting or settling in a variety of contexts:...
of stellar-terrestric networks with redundancyData redundancyData redundancy occurs in database systems which have a field that is repeated in two or more tables. For instance, in case when customer data is duplicated and attached with each product bought then redundancy of data is a known source of inconsistency, since customer might appear with different...
.
The advantage of stellar triangulation is 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 system, despite of no direct line of sight
Line-of-sight propagation
Line-of-sight propagation refers to electro-magnetic radiation or acoustic wave propagation. Electromagnetic transmission includes light emissions traveling in a straight line...
.
In 1960 the first appropriate space probe
Space probe
A robotic spacecraft is a spacecraft with no humans on board, that is usually under telerobotic control. A robotic spacecraft designed to make scientific research measurements is often called a space probe. Many space missions are more suited to telerobotic rather than crewed operation, due to...
was launched - the 30 m diameter balloon satellite
Balloon satellite
A balloon satellite is a satellite that is inflated with gas after it has been put into orbit.-List of Balloon Satellites:...
(Project Echo). By then the whole of Western Europe
Western Europe
Western Europe is a loose term for the collection of countries in the western most region of the European continents, though this definition is context-dependent and carries cultural and political connotations. One definition describes Western Europe as a geographic entity—the region lying in the...
could be linked together geodetically with accuracies 2-10 times better than by classical 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...
.
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
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...
and the Pacific, but without the areas of 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 China
China
Chinese civilization may refer to:* China for more general discussion of the country.* Chinese culture* Greater China, the transnational community of ethnic Chinese.* History of China* Sinosphere, the area historically affected by Chinese culture...
). The mean accuracy was between ± 5m (Europe, USA) and 7–10 m (Africa, Antarctica), depending of weather and infrastructure conditions. Combined with Doppler
Doppler effect
The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...
measurements the global accuracy was even 3m. This is more than 20 times better than previously, because the gravity field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...
up to 1974 couldn't be calculated better than 100 meters between distant 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.
The use of star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
s as a reference system wars expanded in the 70s and early 80s for continental networks - but then the laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...
and electronic
Electronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...
measurements became better than 2m and could be carried out automatically. Nowadays some similar techniques are carried out by interferometry
Interferometry
Interferometry refers to a family of techniques in which electromagnetic waves are superimposed in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy,...
with very distant radio quasar
Quasar
A quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...
s instead of optical satellite & star observations. The geodetic connection of radio telescope
Radio telescope
A radio telescope is a form of directional radio antenna used in radio astronomy. The same types of antennas are also used in tracking and collecting data from satellites and space probes...
s is now possible up to mm...cm precision as published periodically by the IVS community. This global project group was founded in 2000 by Harald Schuh (H. Schuh) (Munich/ TU Vienna) and some dozen research projects worldwide, and is now a permanent
Permanent
The permanent of a square matrix in linear algebra, is a function of the matrix similar to the determinant. The permanent, as well as the determinant, is a polynomial in the entries of the matrix...
service of IUGG
International Union of Geodesy and Geophysics
The International Union of Geodesy and Geophysics is a non-governmental organisation dedicated to the scientific study of the Earth using geophysical and geodesic techniques. The IUGG was established in 1919. Some areas within its scope are environmental preservation, reduction of the effects of...
and IERS
International Earth Rotation and Reference Systems Service
The International Earth Rotation and Reference Systems Service , formerly the International Earth Rotation Service, is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation Parameter and International Celestial Reference System ...
.
The photographic observations as done 1959 - 1985 are irrelevant now because of their expense, but lead to some renaissance
Renaissance
The Renaissance was a cultural movement that spanned roughly the 14th to the 17th century, beginning in Italy in the Late Middle Ages and later spreading to the rest of Europe. The term is also used more loosely to refer to the historical era, but since the changes of the Renaissance were not...
by electro-optical techniques like CCD
Charge-coupled device
A charge-coupled device is a device for the movement of electrical charge, usually from within the device to an area where the charge can be manipulated, for example conversion into a digital value. This is achieved by "shifting" the signals between stages within the device one at a time...
.
See also
- Figure of the EarthFigure of the EarthThe 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...
- TriangulationTriangulationIn 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...
- TrilaterationTrilaterationIn geometry, trilateration is the process of determinating absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres or triangles. In addition to its interest as a geometric problem, trilateration does have practical applications in surveying and...
- Satellite geodesySatellite geodesySatellite 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...
- PAGEOSPAGEOSPAGEOS was a balloon satellite which was launched by the NASA in June 1966. Pageos had a diameter of exactly , consisted of a thick mylar plastic film coated with vapour deposited aluminium enclosing a volume of and was used for the Weltnetz der Satellitentriangulation -- a global cooperation...
satellite - fundamental stationFundamental stationA fundamental point is the geometric origin of a geodetic network and defines the geodetic datum of a national survey.Some fundamental stations are an astronomical or satellite geodetic observatory...
- Satellite laser rangingSatellite laser rangingIn satellite laser ranging a global network of observation stations measure the round trip time of flight of ultrashort pulses of light to satellites equipped with retroreflectors...
(SLR)