Stellar triangulation is a method of

geodesy Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), Earth rotation, orientation in space, and Earth's gravity, gravity. The field also incorporates studies of how these properti ...

and of its subdiscipline

space geodesy Space geodesy is geodesy by means of sources external to Earth, mainly artificial satellites (in satellite geodesy) but also quasars (in very-long-baseline interferometry, VLBI), visible stars (in stellar triangulation), and the retroreflectors o ...

used to measure Earth's geometric shape. Stars were first used for this purpose by the Finnish astronomer

Yrjö Väisälä Yrjö Väisälä (; 6 September 1891 – 21 July 1971) was a Finnish astronomer and physicist. His main contributions were in the field of optics. He was also active in geodetics, astronomy and optical metrology. He had an affectionate nick ...

in 1959, who made

astrometric Astrometry is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It provides the kinematics and physical origin of the Solar System and this galaxy, the Milky Way. Histor ...

photographs of the night sky at two stations together with a lighted

balloon A balloon is a flexible bag that can be inflated with a gas, such as helium, hydrogen, nitrous oxide, oxygen, and air. For special tasks, balloons can be filled with smoke, liquid water, granular media (e.g. sand, flour or rice), or li ...

probe between them. Even this first step showed the potential of the method, as Väisälä got the

azimuth An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north. Mathematicall ...

between

Helsinki Helsinki ( or ; ; sv, Helsingfors, ) is the Capital city, capital, primate city, primate, and List of cities and towns in Finland, most populous city of Finland. Located on the shore of the Gulf of Finland, it is the seat of the region of U ...

and

Turku Turku ( ; ; sv, Åbo, ) is a city and former capital on the southwest coast of Finland at the mouth of the Aura River, in the region of Finland Proper (''Varsinais-Suomi'') and the former Turku and Pori Province (''Turun ja Porin lääni''; ...

(a distance of 150 km) with an accuracy of 1″. Soon the method was successfully tested by

ballistic Ballistics may refer to: Science * Ballistics, the science that deals with the motion, behavior, and effects of projectiles ** Forensic ballistics, the science of analyzing firearm usage in crimes ** Internal ballistics, the study of the proce ...

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 program A computer program is a sequence or set of instructions in a programming language for a computer to execute. Computer programs are one component of software, which also includes documentation and other intangible components. A computer progra ...

s 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, thei ...

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 The line of sight, also known as visual axis or sightline (also sight line), is an imaginary line between a viewer/observer/spectator's eye(s) and a subject of interest, or their relative direction. The subject may be any definable object taken n ...

. In 1960, the first appropriate

space probe A space probe is an artificial satellite that travels through space to collect scientific data. A space probe may orbit Earth; approach the Moon; travel through interplanetary space; flyby, orbit, or land or fly on other planetary bodies; or ...

was launched:

Project Echo Project Echo was the first passive communications satellite experiment. Each of the two American spacecraft, launched in 1960 and 1964, were metalized balloon satellites acting as passive reflectors of microwave signals. Communication sign ...

, 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 Western Europe is the western region of Europe. The region's countries and territories vary depending on context. The concept of "the West" appeared in Europe in juxtaposition to "the East" and originally applied to the ancient Mediterranean ...

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 ...

. During the late 1960s, a global project was begun by

H.H. Schmid HH may refer to: Organizations * Happy Hippie Foundation, a non-profit organization founded by Miley Cyrus * Hartmann House Preparatory School, an independent preparatory school in Harare, Zimbabwe * Heirs Holdings, a Nigerian conglomerate with ...

(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, officially the Federal Republic of Germany (FRG),, is a country in Central Europe. It is the most populous member state of the European Union. Germany lies between the Baltic and North Sea to the north and the Alps to the sou ...

and the Pacific, but without the areas of

Russia Russia (, , ), or the Russian Federation, is a transcontinental country spanning Eastern Europe and Northern Asia. It is the largest country in the world, with its internationally recognised territory covering , and encompassing one-eigh ...

and China). 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

continent A continent is any of several large landmasses. Generally identified by convention rather than any strict criteria, up to seven geographical regions are commonly regarded as continents. Ordered from largest in area to smallest, these seven ...

s. The use of

star A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth make ...

s as a reference system was expanded in the 70s and early 80s for continental networks, but then the

laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The firs ...

and

electronic Electronic may refer to: *Electronics, the science of how to control electric energy in semiconductor * ''Electronics'' (magazine), a defunct American trade journal *Electronic storage, the storage of data using an electronic device *Electronic co ...

distance measurement Length measurement, distance measurement, or range measurement (ranging) refers to the many ways in which length, distance, or range can be measured. The most commonly used approaches are the rulers, followed by transit-time methods and the in ...

s 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 o ...

with very distant radio

quasar A quasar is an extremely 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 mass rangin ...

s (

VLBI Very-long-baseline interferometry (VLBI) is a type of astronomical interferometry used in radio astronomy. In VLBI a signal from an astronomical radio source, such as a quasar, is collected at multiple radio telescopes on Earth or in space. T ...

) instead of optical satellite & star observations. The geodetic connection of radio telescopes 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 The International Union of Geodesy and Geophysics (IUGG; french: Union géodésique et géophysique internationale, UGGI) is an international non-governmental organization dedicated to the scientific study of Earth and its space environment usi ...

(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 P ...

(IERS). The photographic observations as done 1959–1985 are irrelevant now because of their expense, but lead to some

renaissance The Renaissance ( , ) , from , with the same meanings. is a period in European history marking the transition from the Middle Ages to modernity and covering the 15th and 16th centuries, characterized by an effort to revive and surpass id ...

by electro-optical techniques like CCD.

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 Paul Hermann Otto Eggert (born 4 February 1874 in Tilsit, d. January 20, 1944 in Gdańsk) was a German surveyor and professor of Gdańsk University of Technology (). He was also dean of the Faculty of Civil Engineering from 1909 to 1910 and from 1 ...

and Max Kneissl ed., Volume V, (870 S., espec. §§ 2, 5, 13), J.B.Metzler, Stuttgart 1968. *

Hellmut Schmid Hellmut H. Schmid (12 September 1914 – 27 April 1998) was Professor of geodesy and photogrammetry on the ETH Zürich (Switzerland), where he emerited in 1985. In the 1950s, he worked on research projects of space exploration in the United States ...

: ''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 , a ...

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

in Deutschland, Bonn 2000.

External links

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

See also

References

External links