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In astronomy, a celestial coordinate system is a coordinate system for mapping positions in the sky. There are different celestial coordinate systems each using a coordinate grid projected on the celestial sphere, in analogy to the geographic coordinate system used on the surface of the Earth. The coordinate systems differ only in their choice of the fundamental plane, which divides the sky into two equal hemispheres along a great circle. (The fundamental plane of the geographic system is the Earth's equator). Each coordinate system is named for its choice of fundamental plane.

• Horizontal coordinate system - horizon - zenith/nadir - Altitude - azimuth - meridian
• Equatorial coordinate system - celestial equator - celestial pole - declination - right ascension or hour angle. Popular choices of pole and equator are the older B1950 and the modern J2000 systems, but a pole and equator "of date" can also be used, meaning one appropriate to the date under consideration, such as that at which a measurement of the position of a planet or spacecraft is made. There are also subdivisions into "mean of date" coordinates, which average out or ignore nutation, and "true of date," which include nutation.
• Ecliptic coordinate system - ecliptic - ecliptic pole - ecliptic latitude - ecliptic longitude
• Galactic coordinate system
• Supergalactic coordinate system

Altitude, also referred to as elevation, refers to the vertical angle measured from the geometric horizon (0°) towards the zenith (+90°). It can also take negative values for objects below the horizon, down to the nadir (-90°). Although some will use the term height instead of altitude, this is not recommended as height is usually understood to be a linear distance unit, to be expressed in meters (or any other length unit), and not an angular distance.

The term zenith distance is more often used in astronomy and is the complement of the altitude. That is: 0° in the zenith, 90° on the horizon, up to 180° at the nadir.

Let δ be the declination and H the hour angle.

Let φ be the observer's latitude.

Let Alt be the altitude and Az the azimuth.

Let θ be the zenith angle (or zenith distance, i.e. the 90° complement of Alt).

Then the equations of the transformation are:

Use the inverse trigonometric functions to get the values of the coordinates.

This article is based on Jason Harris' Astroinfo which comes along with KStars, a Desktop Planetarium for Linux/KDE. See http://edu.kde.org/kstars/index.phtml