Astronomical coordinates and deviation from the perpendicular
The Astronomical width must not with the geographical latitude are equated, although that is often done since the expeditions of the 15th century. The two widths differ by the deviation from the perpendicular - i.e. H. by that small angle ξ by which the true perpendicular direction deviates from the theoretical normal to the earth ellipsoid. In formulas, this difference is usually emphasized by the symbol φ ' (or B' ), compared to φ (or B ) for the geographical latitude. As a consequence of the deviation from the perpendicular, the following applies to the astronomical latitude and its counterpart, the astronomical longitude :
- φ '= φ + ξ
- λ '= λ + η / cos φ
The two components of the vertical deviation (ξ, η) are caused by the mass irregularities / gravity anomalies of the earth's body. At a point at sea level , ξ is the angle difference between the true horizon ( geoid ) and the ellipsoidal horizon.
The astronomical latitude is on the one hand a physical fact of the earth's gravitational field , but on the other hand it can be understood geometrically - as an angle between the perpendicular and the celestial equator (see adjacent picture). In contrast, the "geographical" latitude is a physical fiction - that is, an angle that is only defined on an idealized earth ellipsoid and depends on its shape parameters.
In order to take this ambiguity of the term "latitude" into account, it is better to speak of "ellipsoidal" (geodetic) latitude than of "geographical" latitude in geodesy . Because of the flattening of the earth (deviation of the ideal shape of the earth from the spherical shape) there is even a third latitude term in the geosciences, the " geocentric latitude ".
- Astronomical latitude φ, B '
- the angle between the actual perpendicular direction and the equatorial plane ( celestial equator ). The difference to the ellipsoidal latitude is the north-south component ( ξ ) of the vertical deviation .
- Ellipsoidal width φ, β, B
- If an ellipsoid of revolution is used as the earth model , it corresponds to the angle between the equatorial plane and the normal to the ellipsoid . It is also called the geodetic latitude and is used in land surveying and cartography . When determining locations with GPS , one also receives ellipsoidal coordinates (latitude and longitude).
- Geocentric latitude ψ
- the direction to the center of the earth . The perpendicular direction and ellipsoid normal run - except at the equator and at the poles - not through the center of the earth. The geocentric latitude differs from the geodetic or ellipsoidal latitude by up to 0.2 °.
Measurement methods and instruments
The measurement of the astronomical latitude (together with the longitude formerly wrongly called astronomical position determination ) can be done with several methods of astrogeodesy or astrometry . If the coordinates of the observed stars are known, the most accurate methods are (depending on the effort, 0.3 ″ to 0.05 ″ per evening):
- Determination of latitude by measuring zenith distances
- Determination of latitude from horizontal directions
- in the largest digression (maximum north distance) of the star: Embacher method
- in the vertical of a terrestrial target : method of Döllen and Niethammer
- (These 3 methods are favorable, even if astronomical azimuths or the exact orientation of the instrument have to be determined. Otherwise the above and below methods are to be preferred)
- Simultaneous latitude and longitude determination: method of equal heights
- Photographs of the zenith in two opposite directions:
The last three methods can be carried out most quickly today (with modern instruments). If both components of the perpendicular direction (besides B also L) are desired, the method of equal heights with a Ni2 astrolabe is most economical, and most accurate with a Danjon astrolabe .
Suitable measuring instruments for the angle methods are the universal instrument (or a more precise theodolite with a zenith prism ), a transit or passage instrument . The highest precision can be achieved with the zenith telescope - visually about 0.1 ", photographically or photoelectrically even more precise.