Altitude and azimuth as sky coordinates

Choose a direction around the horizon, then an angle above it

To point towards an object, two choices are usually enough: which direction around the horizon, and how far above the horizontal reference. Azimuth makes the first choice numerical; altitude makes the second. Together they describe a sightline from a stated observing position.

In this chapter, azimuth A starts at geographic north and increases eastward: north is 0°, east 90°, south 180° and west 270°. Returning to north completes the turn at 360°, equivalent to 0°. Some sources use another zero or direction. Read their definitions before combining numbers; a different declared convention is not automatically an error.

Altitude h is the angular height above the local horizontal reference, measured along the vertical circle through the direction. It is 0° at that reference and +90° at the zenith. Negative altitude describes a direction below the reference horizon, down to −90° at the nadir, the direction opposite the zenith.

Altitude here is an angle, not elevation in metres

The word altitude also describes physical height in other contexts, such as a mountain’s height above sea level. In horizon coordinates it means an angle. A star at altitude 30° is not 30 metres above the observer, and the number does not specify how far the star is from Earth.

Zenith distance z measures from straight overhead down towards the direction. With the same reference and convention, z = 90° − h. For h = 30°, z = 60°. These are complementary angular descriptions of the same local sightline, not two different measurements of physical height.

At the zenith, every vertical circle meets. There is no unique direction around the horizon to attach to an exactly overhead sightline, so azimuth is undefined there. Near the zenith, a small change in direction can cause a large azimuth change. This is a coordinate limitation, not an object suddenly racing around a physical circle.

Read the pair before drawing a conclusion

An invented direction A = 135°, h = 30° points southeast, 30° above the horizontal reference. Its azimuth lies halfway from east at 90° to south at 180°. Its altitude is one-third of the 90° angle from the horizon to the zenith. State the pair’s order and units so another person does not swap the numbers.

A pair with h = −5° describes a direction below the reference plane. It is not an ordinary visible target above an unobstructed geometric horizon. Conversely, positive altitude does not guarantee visibility: terrain, a building, cloud or a bright background may prevent the observation.

Azimuth wraps at north. Going eastward from A = 350° to A = 10° crosses 0° and changes azimuth by 20°, rather than travelling 340° the long way around. That is a difference in azimuth. It is not necessarily the full angular separation of two sky positions, which also depends on altitude and spherical geometry.

The same object gets a changing local address

A distant star generally changes altitude and azimuth during a night as Earth rotates. Observers at different locations also assign different local coordinates at the same instant. A useful horizon-coordinate record therefore includes the observing location and time, with its date and time convention.

A numerical pair copied from a chart or app is only as meaningful as those settings. Check that the location, time and target are correct, and whether the display follows your current time automatically. A coordinate pair without context can be perfectly well formed yet point to the wrong part of your local sky.

The next lesson introduces a celestial coordinate grid that is more convenient for catalogues. Converting between that grid and your local horizon requires the observer geometry, time and a suitable astronomical model. The existence of conversion software does not make its inputs optional.

Read how apparent effects were treated

Atmospheric refraction changes the arriving ray’s direction, so an apparent altitude can differ from an unrefracted geometric one. The effect depends on the atmosphere and becomes especially important near the horizon. A fixed correction is not exact for every night or location.

USNO’s Sun/Moon altitude service explicitly states that its above-horizon values include standard refraction and refer to disc centres. That is an example of reading a service’s metadata, not a convention to assume for every table. A rise or set can additionally refer to an object’s edge under specified assumptions rather than its centre at h = 0°.

For introductory night-sky descriptions, preserve the convention supplied by your method and avoid false precision. For precise work, distinguish observed, apparent and geometric quantities and use the appropriate model. A coordinate is an organised description of a direction; it does not by itself establish that a target was detected.

Worked example

Try the reasoning

1. Moving eastward around the horizon from azimuth 355° to 5° changes azimuth by how much?

   Show the answer and reasoning

   10° across the north/zero boundary.

   Five degrees reaches360°/0°, then five more reaches5°. This is a coordinate difference around the horizon.

2. An illustrative direction has zenith distance 15°. What is its altitude?

   Show the answer and reasoning

   75°.

   h = 90° − z = 90° − 15°.

3. Someone sends “A = 90°, h = 20°” as a star’s permanent address. What is missing?

   Show the answer and reasoning

   At least the local convention, observing place, time/date and target context.

   Local horizon coordinates change with the observer and Earth’s rotation. They are not a permanent catalogue address.

What to carry forward

• Declare the azimuth origin and direction; here north 0°, east 90°.
• Altitude is an angle above a local reference, and azimuth is singular at the zenith.
• Preserve time, place and refraction conventions when exchanging coordinates.