Laplace point
In geodesy, the Laplace point is a special type of surveying point which, through redundant measurement of astronomical azimuths ( Laplace azimuth ), has a direction- stabilizing effect on a large triangular network .
Laplace points are arranged in the classic national survey at intervals of about 100 to 200 km. As a rule, they are marketed using well-founded measuring pillars on which, in addition to measuring the direction and / or distance to the neighboring trigonometric points , a highly precise astronomical azimuth and the deviation from the perpendicular in both components (ξ, η) are observed.
The perpendicular deviation component η in east-west direction can then be determined twice and results in a conditional equation for the precise alignment of the surrounding network points to astronomical north , which was first discovered by Pierre Simon Laplace and named after him the Laplace equation .
The azimuth to one or two of the neighboring network points is measured with a universal instrument (large theodolite , e.g. DKM3-A ) or a passage instrument , while the vertical deviation can also be determined with smaller measuring devices such as a Ni2 astrolabe .
In the 20th century, many states took advantage of the stabilizing effect of Laplace points in their national surveys; It can also be used very economically when large networks have to be broken down into several node networks to reduce the computing time. The subsequent measurement of a Laplace azimuth is also suitable for increasing the accuracy of already completed frame or grid networks , e.g. B. in the European network of the 1950s to 1970s (see ED50 and ED79 ) or in Iran 1978/83 (G.Gerstbach, H.Mayer). In individual states such as Austria and Switzerland, numerous “normal” vertical deviation points were added to Laplace points in the course of the geoid determination between 1975 and 1990. This contains z. B. Austria's basic network on 84,000 km² almost 150 Laplace points (mean point distance <30 km). This results in a very uniform accuracy and is beneficial for a reliable coordinate transformation between terrestrial and satellite determined points.
Also throughout Western Europe that was in the 1950s calculated years nationwide survey network ED50 expanded to about 1,980 to a greater number of Laplace points and now includes almost 500 of them. This corresponds to an average distance between these important control points of 70 to 100 kilometers.
In the course of the European satellite network and in larger networks outside of Europe, Laplace points were also combined with the measurement of high-precision baselines or EDM triangular sides of 10 to 40 km in length up to around 1990 , whereby the accuracy of basic networks could be increased to around 1: 3 million ( 0.3 mm per kilometer). Recently, however, these methods have become superfluous due to the increased accuracy of the GPS method.
See also
Literature and Sources
- Karl Ledersteger : Astronomical and Physical Geodesy . Volume V of the Jordan-Eggert- Kneissl series of books , Handbook of Surveying ; 871 pp., Verlag JB Metzler, Stuttgart 1969.
- BEV : Austria's astro-geodetic work for the ED79. Special issue ÖKIE, Vienna ~ 1981
- WA Magnizki , WW Browar, BP Schimbirew: Textbook Theory of the Figure of the Earth (340p.), Moscow 1961 (Russian) and Verlag für Bauwesen (East Berlin) 1964.