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; below the name of a pole and the names of the coordinates are also shown:

• Horizontal coordinate system - horizon - zenith/nadir - Altitude - azimuth
• 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

Converting coordinates

Equatorial to Horizontal coordinates

Let $\backslash delta$ be the declination and $H$ the hour angle.

Let $\backslash phi$ be the observer's latitude.

Let $Alt$ be the altitude and $Az$ the azimuth.

Then the equations of the transformation are:

$\backslash sin\; Alt\; =\; \backslash sin\; \backslash phi\; \backslash cdot\; \backslash sin\; \backslash delta\; +\; \backslash cos\; \backslash phi\; \backslash cdot\; \backslash cos\; \backslash delta\; \backslash cdot\; \backslash cos\; H$

$\backslash cos\; Az\; =\; \backslash frac\{\backslash cos\; \backslash phi\; \backslash cdot\; \backslash sin\; \backslash delta\; -\; \backslash sin\; \backslash phi\; \backslash cdot\; \backslash cos\; \backslash delta\; \backslash cdot\; \backslash cos\; H\}\{\backslash cos\; Alt\}.$

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

Celestial coordinate system

מערכת קואורדינטות שמימית | Nebeski koordinatni sistem | Astronomische Koordinatensysteme | Système de coordonnées célestes | Coordinate celesti | Nebeski koordinatni sustavi | Csillagászati koordinátarendszer | Hemelcoördinaat | Układ współrzędnych astronomicznych | Coordonate astronomice | Системы небесных координат | Hệ tọa độ thiên văn | 天球坐标系统