Astronomical baseline
An astronomical position line is a geometric location for one's own position (geographic latitude and longitude), which is determined in nautical science and on expeditions by measuring the elevation angle of stars.
Starting from an approximate (cast) location on the globe , each measured star defines a circular base line. By measuring according to two stars you get the true location at their intersection, by measuring further stars you get a control.
principle
Of the three spatial coordinates of a location, the height is usually given by the position on the sea or earth surface. The determination of the location is reduced to two dimensions on the globe (more precisely: the earth ellipsoid ), i.e. H. on the determination of the geographical latitude and longitude . Because of these two location unknowns, at least two height measurements to stars are required.
Every measurement defines a geometric location as a circle on the earth's surface, the center of which is the “image point” of the star (the point where the star is exactly at the zenith ). The radius of the circle corresponds to the observed zenith distance (90 ° elevation angle). Because this circle usually has a radius of thousands of kilometers, it can be replaced in the vicinity of the location with its tangent, the so-called base line . The location along this line is initially unknown. The measurement of a second star gives a further base line; where it intersects the first is your own location.
Application in nautical science
The measurement is made with a marine sextant , the timekeeping with a chronometer or a digital stopwatch . For geodesy see below.
In seafaring practice, one assumes an estimated ( cast ) location for which one calculates the elevation angle of two or three stars. The comparison with the measured height of each star then shows by how much one has to move the position towards or away from it because of the curvature of the earth . The actual location lies at the intersection of two such lines and is often determined graphically - directly on the nautical chart . A third star serves as a control or to increase accuracy.
In its nautical form, the method goes back to Captain Thomas Sumner (1807–1876), who discovered it by chance in 1837 (when comparing different "target heights" of stars) on a trip from the USA to Scotland. He did not publish his findings until six years later, but it soon became the standard method of astronavigation at sea. Beginners manage around 2–5 ', while a trained observer can achieve accuracies of 0.5 to 1 ' , which corresponds to around 1 km in position.
Astrogeodesy and Earth Measurement
The Geodetic Astronomy the method used for. B. on expeditions or for quick location and geoid determination . The measuring instrument is a theodolite with a diagonal prism and a digital stopwatch that is synchronized with a precise time signal (telephone or radio signal) .
- With multiple measurements of the stars and arithmetical (instead of graphical) evaluation, ± 1 to 5 " can be achieved. Small systematic errors in the elevation angles are ineffective if at least three stars are measured. With around 5 stars, the accuracy increases to at least 1".
The determination of the location is most accurate if all star measurements are made at the same zenith distance . For this method of equal heights , which goes back to Gauss, rapid methods with field-compatible prism astrolabies were developed between 1955 and 1980 and used throughout Europe for the targeted cm-geoid . For example, the Ni2 astrolabe from Zeiss combines an optical 60 ° prism with an automatic level . From 15–20 star passages , the astronomical latitude and longitude can be determined to ± 0.2 "in about 1 hour. CCD zenith cameras have also been used for this purpose for about 10 years .
special cases
Another special case of the astro stand line is the so-called midday altitude for determining latitude at sea. From some solar measurements around noon, the largest value h max is selected , which corresponds exactly to the highest level of the sun in the south. The geographical latitude B then follows by means of the sun declination δ directly (without a second base line) from the formula B = 90 ° - h max + δ .
Similar to the altitude lines to stars, measurements to earth satellites can also be evaluated. In the early years of satellite geodesy , this included a. Time of flight and direction measurements. The former have become the standard for GPS location today; For the latter, G. Gerstbach developed a method in 1973 that determined the exact position of a satellite station by adjusting numerous directional residuals .
See also
literature
- Albrecht-Vierow: Textbook of Navigation. 11th edition (revised by B. Soeken and H. Hansen), 430 p. +6 plates, Decker's Verlag, Berlin 1925
- Karl Ramsayer : Geodetic Astronomy (= Handbook of Surveying. Vol. 2a). 10th, completely revised and restructured edition. JB Metzler-Verlag, Stuttgart 1970.
- Thomas H. Sumner - A New and Accurate Method of Finding a Ship's Position at Sea, by Projection on Mercator's Chart , Thomas Groom & Company of Boston, July 1843
- Gottfried Gerstbach: Absolute Positioning by Satellite Sumner Lines . Intercosmos Symposium, Budapest 1973
- Bobby Schenk: Astronavigation. Bielefeld: Delius Klasing 2000, ISBN 3-7688-0259-0