Method of equal heights

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The method of equal heights is one of the most precise astronomical methods for determining the geographical latitude and longitude of a position, or its plumb direction .

With a special measuring instrument, at least three stars - depending on the accuracy requirement, 10 to 20 stars - are observed at exactly the same elevation angle by stopping the star passage through the thread network of the measuring telescope . The result is a circle of distance for each star on the celestial sphere , which intersects with all the others at the zenith of the location.

The classic evaluation goes back to the "three height problem" by Carl Friedrich Gauß - which only assumes the constancy of the height, but not its value itself as known. The solution includes about 20 lines of trigonometric and spherical calculations; If the desired accuracy is high (up to 0.1 "), temperatures and other small sources of error must also be analyzed.

A simpler evaluation can be carried out using astronomical stand lines . The transit time for the assumed location is calculated for each star and compared with the measured time. This results in the two local corrections for the geographical coordinates.

For earth measurements , the method using a portable prism astrolab is ideal if the perpendicular direction or deviation from the perpendicular is to be determined on numerous points. With the prism placed on an automatic level, about 10 stars are observed at an elevation angle of 60 °, which results in an accuracy of 0.3 to 0.5 "after just 30 minutes. This makes it one of the most important measuring methods for astro-geodetic geoid determination .

See also

literature

  • Karl Ramsayer : Geodetic Astronomy (= Handbook of Surveying, Volume 2a). 10th, completely revised and restructured edition. JB Metzler-Verlag, Stuttgart 1970
  • Gottfried Gerstbach : Optimization of astrolabe observations. In: Geoscientific Communications Volume 7, pp. 102–140, TU Wien 1975, ISSN  1811-8380
  • Albert Schödlbauer : Geodetic Astronomy: Basics and Concepts. deGruyter-Verlag, Berlin-New York 2000, ISBN 3-11-015148-0