Embacher method

The Embacher method is a method of geodetic astronomy for the precise determination of azimuth and latitude .

It was developed in the 1950s by Wilhelm Embacher ( TH Vienna and University of Innsbruck ) and has the special feature of not requiring an exact time system .

Northern pairs of stars are observed in maximum azimuth ( greatest digression ), where they move exactly vertically down or up. The measured azimuth difference is a function of geographical latitude and declination and is used to determine latitude, while the vertical star passages themselves result in the azimuth of the terrestrial target to be subsequently measured .

calculation

Celestial coordinates in astronomical coordinate systems : The spherical triangle to be considered has the corner points North Pole (blue) in the northern hemisphere . Zenith (black) and star (purple). the azimuth in the horizontal system is measured from the meridian (black) and in the equatorial system the declination (red) is measured from the equatorial plane and the hourly angle (cyan) is also measured from the meridian. The geographical latitude of the observation site is identical to the pole height . ${\displaystyle a}$ ${\displaystyle \delta }$ ${\displaystyle \tau }$ ${\displaystyle \phi }$

The formulas required for the method are so simple that it is astonishing how late their usefulness was discovered.

Since the astronomical triangle ( pole - zenith - star ) becomes right-angled for the moment of greatest digression , the spherical formulas are considerably simplified. If the azimuth of the star is designated with , its declination with , its hour angle with and the geographical latitude of the location with , then the sine or tangent rate is reduced to ${\displaystyle a}$ ${\displaystyle \delta }$ ${\displaystyle \tau }$ ${\displaystyle \phi }$

${\displaystyle \sin a={\frac {\cos \delta }{\cos \phi }}}$ (positive in the east, negative in the west)

${\displaystyle \cos \tau ={\frac {\tan \phi }{\tan \delta }}}$ (Hour angle in the fourth or first quadrant)

Therefore, if you measure the azimuth difference of two stars that digress in the east or west within a few minutes, the latitude is obtained by a small transformation of the first formula (using and ), from which the two star azimuths and can be calculated. ${\displaystyle \Delta a=a_{2}-a_{1}}$ ${\displaystyle \phi }$ ${\displaystyle \Delta _{1}}$ ${\displaystyle \Delta _{2}}$ ${\displaystyle a_{1}}$ ${\displaystyle a_{2}}$

This means that the exact orientation of the horizontal circle is known on the measuring instrument (star azimuth minus circular reading), so that the terrestrial target measured in front of or after the stars can be corrected by this amount, which results in its sought azimuth.

literature

• Wilhelm Embacher: New proposals for geographic location determination , Österreichische Zeitschrift für Vermessungswesen, year 1952, pages 3 to 13, 50-58 and 82 to 88, Vienna, 1952.

Web links

• Department of Geometry and Surveying - History , University of Innsbruck
• Em. O. Univ.Prof. Dipl.-Ing. Dr. Wilhelm Embacher †