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The horizontal coordinate system (az/el system, alt/az system, altazimuth system) is a spherical coordinate system used for directions into the celestial sphere, fixed to the horizon (i.e., the horizon from where you are) and north. It is stable in relation to you (if you remain in one place) rather than in relation to the sky, basically consisting of the compass direction and the angle up from the horizon to aim your telescope in order to point at a particular star at a given time. As such, it is directly related to observation from Earth, but the coordinates for a star are time-dependent: the rotation of Earth produces a constant minute-by-minute change in the whole sky, (termed the diurnal motion), so the star's horizontal coordinates are constantly changing as time passes, so you would have to pre-calculate the necessary coordinates for the exact moment in time when you are going to observe. In contrast, other celestial coordinate systems are tied to the position of the stars, their coordinates for a star remaining the same, despite the star's movement across the sky. Conceptually, you use other systems to know the position of the star, then convert to horizontal coordinates to observe it. (Some automated telescopes may do precisely this, but an individual is likely to locate a star based upon its position in relation to stars they see and recognize.) Elements of the horizontal coordinate system:
In addition to their use in setting up observations, they can be of use in recording observations (along with the time of the observation) for later conversion to other coordinate systems. Some terms based upon these, describing the position of astronomical objects in the sky: