The horizontal coordinate system, also known as topocentric coordinate system, is a celestial coordinate system that uses the observer's local horizon as the fundamental plane. Coordinates of an object in the sky are expressed in terms of altitude (or elevation) angle and azimuth.
This celestial coordinate system divides the sky into two hemispheres: the upper hemisphere, where objects above the horizon are visible, and the lower hemisphere, where objects below the horizon cannot be seen, since the Earth obstructs views of them. The great circle separating the hemispheres is called the celestial horizon, which is defined as the great circle on the celestial sphere whose plane is normal to the local gravity vector. In practice, the horizon can be defined as the plane tangent to a still liquid surface, such as a pool of mercury. The pole of the upper hemisphere is called the zenith. The pole of the lower hemisphere is called the nadir.
The following are two independent horizontal angular coordinates:
The horizontal coordinate system is sometimes called other names, such as the az/el system, the alt/az system, or the alt-azimuth system, from the name of the mount used for telescopes, whose two axes follow altitude and azimuth.
The horizontal coordinate system is fixed to a location on Earth, not the stars. Therefore, the altitude and azimuth of an object in the sky changes with time, as the object appears to drift across the sky with Earth's rotation. In addition, since the horizontal system is defined by the observer's local horizon, the same object viewed from different locations on Earth at the same time will have different values of altitude and azimuth.
Horizontal coordinates are very useful for determining the rise and set times of an object in the sky. When an object's altitude is 0°, it is on the horizon. If at that moment its altitude is increasing, it is rising, but if its altitude is decreasing, it is setting. However, all objects on the celestial sphere are subject to diurnal motion, which always appears to be westward.
A northern observer can determine whether altitude is increasing or decreasing by instead considering the azimuth of the celestial object:
There are the following special cases:
Note that the above considerations are strictly speaking true for the geometric horizon only. That is, the horizon as it would appear for an observer at sea level on a perfectly smooth Earth without an atmosphere. In practice, the apparent horizon has a slight negative altitude due to the curvature of Earth, the value of which gets more negative as the observer ascends higher above sea level. In addition, atmospheric refraction causes celestial objects very close to the horizon to appear about half a degree higher than they would if there were no atmosphere.