Nautical triangle
The nautical triangle or astronomical triangle is an aid in spherical astronomy when it comes to determining the current position of a fixed star or a planet on the imaginary celestial sphere for a certain observation point and a certain point in time . In this task, the right ascension and the declination of the star are known; the azimuth (the cardinal direction) and the height above the horizon are to be calculated .
definition
As nautical triangle taking the spherical triangle (spherical triangle) on the celestial sphere, which is defined by the following corners:
- Zenith (Ze)
- Celestial North Pole (NP)
- Star (St)
The following simple relationships allow an application of the formulas of spherical trigonometry :
- Side length zenith - celestial north pole:
- Side length celestial north pole - star:
- Side length zenith - star:
- Angle of the north celestial pole - zenith - star:
- Angle zenith - north celestial pole - star:
The following terms were used:
Right ascension of the star | |
Declination of the star | |
Sidereal time (depending on the observation time and the geographical longitude of the observation location) | |
Geographical latitude (observation point) | |
Hour angle | |
a | Azimuth (counted from the south) |
H | Height , elevation (above the horizon) |
conversion
Horizontal system in equatorial system
- Given: a, h and φ
- Wanted: τ and δ
Equatorial system in horizontal system
- Given: τ, δ and φ
- Wanted: a and h
Web links
- Nautical Triangle ( Memento from February 7, 2007 in the Internet Archive )