Horizontal coordinate system

Builds on Celestial coordinate system Celestial sphere

Definition

Fix an observer on the Earth at geographic latitude $\varphi$ . The horizontal coordinate system is the celestial coordinate system on the observer's celestial sphere with these data:

the fundamental plane is the local horizontal plane, and its great circle is the horizon;
the pole is the zenith, the direction opposite to local gravity;
the primary direction is the north point of the horizon.

The latitude is the altitude $a \in [-90^\circ, 90^\circ]$ . The longitude is the azimuth $A \in [0^\circ, 360^\circ)$ , measured from north through east.

Remarks

With azimuth from north through east, the frame (north, east, zenith) is left-handed, unlike the equatorial frame. Some older texts measure azimuth from the south instead. The zenith distance is $z = 90^\circ - a$ . For a star of declination $\delta$ and hour angle $H$ , the altitude satisfies $\sin a = \sin\varphi\sin\delta + \cos\varphi\cos\delta\cos H.$ Example: at the North Pole, $\varphi = 90^\circ$ , this gives $a = \delta$ , so each star circles at constant altitude. Non-example: the equatorial coordinates of a star are not horizontal coordinates. They do not depend on the observer, while the altitude of a star changes during the night.

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Tag	`V6M7XMFER7`
URI	`m2://V6M7XMFER7`
Kind	definition
Writing	W0 stub
MSC	85A04
Defines	Horizontal coordinate system
Uses	Celestial coordinate system, Celestial sphere
Changed	3 November 2026

Horizontal coordinate system

Definition

Remarks

Reading path

Further reading

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