# Positional Astronomy: Coordinate systems: the horizontal or "alt-az" system

The location of an object on the sky is fixed by celestial coordinates
analogous to the terrestrial latitude/longitude system.
There are various systems, suitable for different purposes;
each system needs a fundamental circle and a fixed point on it.

The simplest is the horizontal system, which uses the horizon as its fundamental circle.
The poles of this circle are the zenith overhead and the nadir underfoot;
these are defined by the local vertical (using a plumb-line or similar).

Draw a vertical circle from the zenith to the nadir through object X.

The altitude (a) of object X is the angular distance along the vertical circle from the horizon to X,
measured from -90° at nadir to +90° at zenith.
Alternatively, the zenith distance of X is 90° - a.
(Some authors use h instead of a .)
Any two objects with the same altitude
lie on a small circle called a parallel of altitude.

To fix a point of origin on horizon,
we look at where the spin axis of the Earth intersects the celestial sphere,
at the North and South Celestial Poles.
The vertical circle through these is called the principal vertical.
Where this intersects the horizon, it gives the north and south cardinal points
(the north point is the one nearest the North Celestial Pole).
Midway between these are the east and west cardinal points;
the vertical circle through these is called the prime vertical
(not shown on the diagram), at 90° to the principal vertical.

The azimuth (A) of object X is the angular distance around the horizon
from the north cardinal point to the vertical circle through X,
measured 0°-360° westwards (clockwise).

Note that the altitude of the North Celestial Pole is equal to the latitude of the observer.

Comparison with the terrestrial system:

 terrestrial alt-az equator horizon North Pole zenith South Pole nadir latitude altitude co-latitude zenith distance parallel of latitude parallel of altitude meridian of longitude vertical circle Greenwich Meridian Principal Vertical longitude azimuth

Exercise:

From St.Andrews, at 6 pm on 1998 February 2nd,
the Moon appeared at altitude +39°, azimuth 196°,
while Saturn was at altitude +34°, azimuth 210°.

How far apart did the two objects appear?

Which was further east?