Celestial coordinate system

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

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

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

Then the equations of the transformation are:

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

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

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

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