Altazimutales

Altazimutales, or altazimuthal coordinates, are a local celestial coordinate system that specifies the position of an object in the sky using two angles: altitude and azimuth. Altitude is the angle above the local horizon, ranging from 0° at the horizon to 90° at the zenith. Azimuth is the compass direction along the horizon, usually measured clockwise from north, with values from 0° to 360°; some conventions use different zero points, such as from the south or from east.

These coordinates are defined for a specific observer and depend on the observer’s geographic location and the time of observation. The horizon plane attached to the observer rotates as the Earth turns, so the same celestial object moves in altitude and azimuth over the course of the night. Altazimutales are commonly used in practical astronomy for describing the apparent position of objects relative to an observer.

conversion from equatorial coordinates to horizontal coordinates

To convert from equatorial coordinates (right ascension α, declination δ) to horizontal coordinates (altitude a, azimuth A), one can use the hour angle H = local sidereal time − α. Then:

- altitude a = arcsin( sin φ sin δ + cos φ cos δ cos H ), where φ is the observer’s latitude.

- azimuth A = arctan2( sin H, cos H sin φ − tan δ cos φ ), with A measured from north toward the east.

These formulas require knowledge of the observer’s location and time, via the local sidereal time.

Applications and considerations

Altazimutales are favored by simple telescope mounts (azimuth and altitude), planetary simulators, and sky-tracking tools. They are intuitive for navigation and observing the sky, but the coordinates change continuously with time, causing field rotation in long exposures on fixed instruments; for such cases, equatorial mounts or computer-guided tracking are advantageous. The term altazimutales is used in some Spanish-language texts to refer to altazimuthal coordinates or systems.