# astronomical triangle

## astronomical triangle

A spherical triangle on the celestial sphere formed by the intersection of the great circles joining a celestial body, S, the observer's zenith, Z, and the north (or south) celestial pole, P (see illustration). The relationships between the angles and sides of a spherical triangle are used for transformation between equatorial and horizontal coordinate systems: the angle at S (q) is the parallactic angle; that at P (t) is the hour angle of S; that at Z (A) is the azimuth of S. The sides are equal to the zenith distance (ζ), the complement of the terrestrial latitude (90°–⊂), and the complement of the declination (90°–δ). The parallactic angle, for example, is given by the sine rule:
sin q = (cos ⊂ sin t )/sin ζ = (cos ⊂ sin A )/cos δ

## astronomical triangle

[‚as·trə′näm·ə·kəl ′trī‚aŋ·gəl]
(astronomy)
A spherical triangle on the celestial sphere.

## astronomical triangle

The spherical triangle formed by joining the observer's elevated pole, his zenith, and the position of the body on the celestial sphere.
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