Stellar triangulation

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 photographs 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 programs were written for

• the astrometric reduction of the photographic plates,
• the intersection of the "observation planes" containing the stations and the targets,
• and the adjustment of stellar-terrestric networks with redundancy.

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 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. 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 ±5 m (Europe, USA) and 7–10 m (Africa, Antarctica), depending of weather and infrastructure conditions. Combined with Doppler measurements the global accuracy was even 3 m. 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 continents.

The use of stars as a reference system was expanded in the 70s and early 80s for continental networks, but then the laser and electronic measurements became better than 2 m and could be carried out automatically. Nowadays some similar techniques are carried out by interferometry with very distant radio quasars 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 IVS 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 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.

See also

• Figure of the Earth
• Triangulation
• Trilateration
• Satellite geodesy
• PAGEOS satellite
• fundamental station
• Satellite laser ranging (SLR)

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 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.