Azimuth Elevation(Az/El) System Help

Introduction to the Az/El System—Compass Bearing

Practice problems of this concept can be found at: Coordinating the Heavens Quiz

Compass Bearing

The azimuth of a celestial object is the compass bearing, in degrees, of the point on the horizon directly below that object in the sky. Imagine drawing a line in the sky downward from some object until it intersects the horizon at a right angle. The point at which this intersection occurs is the azimuth of the object. If an object is straight overhead, its azimuth is undefined.

Azimuth bearings are measured clockwise with respect to geographic north. The range of possible values is from 0 degrees (north) through 90 degrees (east), 180 degrees (south), 270 degrees (west), and up to, but not including, 360 degrees (north again). This is shown in Fig. 1-6 A . The azimuth bearing of 360 degrees is left out to avoid ambiguity, so the range of possible values is what mathematicians call a half-open interval . Azimuth bearings of less than 0 degrees or of 360 degrees or more are reduced to some value in the half-open interval (0°, 360°) by adding or subtracting the appropriate multiple of 360 degrees.

Figure 1-6 A . Azimuth is the compass bearing. The observer is shown as a black dot.

Angle Relative To The Horizon

The elevation of an object in the sky is the angle, in degrees, subtended by an imaginary arc running downward from the object until it intersects the horizon at a right angle. This angle can be as small as 0 degrees when the object is on the horizon, or as large as 90 degrees when the object is directly overhead. If the terrain is not flat, then the horizon is defined as that apparent circle halfway between the zenith and the nadir (the point directly below you, which would be the zenith if you were on the exact opposite side of the planet).

Elevation bearings for objects in the sky are measured upward from the horizon (Fig. 1-6 B ). Such coordinates are, by convention, not allowed to exceed 90 degrees because that would produce an ambiguous system. Although you might not immediately think of them, elevation bearings of less than 0 degrees are possible, all the way down to –90 degrees. These bearings represent objects below the horizon. While we can’t see such objects, they are there nevertheless. At night, for example, the Sun has a negative elevation. Technically, elevation bearings always have values within the closed interval [–90°, 90°].

Figure 1-6 B . Elevation is the angle above the horizon. The observer is shown as a black dot.

Sky Maps On The Web

Various Internet sites provide up-to-the-minute maps of the sky for stargazers. One excellent site can be found by pointing your browser to Weather Underground at the following URL

http://www.wunderground.com

and then clicking on the link that says “Astronomy.” From there, it’s a simple matter of following the online instructions.

Some star maps are drawn so that the sky appears as it would if you lie on your back with your head facing north and your feet facing south. Thus west appears on your right, and east appears on your left (Fig. 1-7 a ). Others are drawn so that the sky appears as it would if your head were facing south and your feet were facing north, so west appears on your left and east appears on your right (Fig. 1-7 b ). Points having equal elevation form concentric circles, with the zenith (90 degrees) being a point at the center of the map and the horizon (0 degrees) being a large circle representing the periphery of the map. Simplified sets of grid lines for such az/el maps are shown in both illustrations of Fig. 1-7.

Figure 1-7. Az/el sky maps for viewer lying flat, face-up. At A , top of head facing north; at B , top of head facing south.

These maps show the Sun and the pole star Polaris as they might appear at midafternoon from a location near Lake Tahoe (or anyplace else on Earth at the same latitude as Lake Tahoe). The gray line represents the path of the Sun across the sky that day. From this you might get some idea of the time of year this map represents. Go ahead and take an educated guess! Here are two hints:

• The Sun rises exactly in the east and sets exactly in the west.
• The situation shown can represent either of two approximate dates.

Practice problems of this concept can be found at: Coordinating the Heavens Practice Problems