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Celestial coordinate system

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

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.

This article originates from Jason Harris' Astroinfo which comes along with KStars, a Desktop Planetarium for Linux/KDE. See

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