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 .

Nautical triangle

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: ${\ displaystyle 90 ^ {\ circ} - \ varphi}$
Side length celestial north pole - star: ${\ displaystyle 90 ^ {\ circ} - \ delta}$
Side length zenith - star: ${\ displaystyle 90 ^ {\ circ} -h}$
Angle of the north celestial pole - zenith - star: ${\ displaystyle 180 ^ {\ circ} -a}$
Angle zenith - north celestial pole - star: ${\ displaystyle \ tau}$

The following terms were used:

${\ displaystyle \ alpha}$	Right ascension of the star
${\ displaystyle \ delta}$	Declination of the star
${\ displaystyle \ theta}$	Sidereal time (depending on the observation time and the geographical longitude of the observation location)
${\ displaystyle \ varphi}$	Geographical latitude (observation point)
${\ displaystyle \ tau = \ theta - \ alpha}$	Hour angle
a	Azimuth (counted from the south)
H	Height , elevation (above the horizon)