Reference
The words for where things are in the sky
Zenith, azimuth, altitude, and their neighbors are a coordinate system with you at the center. Move a star around it and each word becomes something you can see.
Navigators describe the sky with two sets of words. One set is tied to you: where is the star from where you stand, how high and in what direction? The other is tied to the sky: where is the star among the stars? Most of celestial navigation is moving between the two. This page shows both, starting from the only reference you carry with you, the direction of straight up.
Zenith, nadir, and horizon
Hang a weight on a string. The string points at two places in the sky. Above you it points at your zenith, and below you, through your feet and through Earth, it points at your nadir. Square to that line, level in every direction, lies your horizon.
All three belong to you alone. Drag the two observers below and notice that each has a different straight up.
That equality is why the sky can tell you where you are. Walk 60 NM along Earth and your zenith tilts 1° against the stars.[1] Latitude and longitude are, in effect, a record of which way your straight up points.
Altitude, azimuth, and zenith distance
Two numbers pin down any point in your sky. Altitude (h) is how far it stands above the horizon, and azimuth (Zn) is its direction around the horizon, measured from true north through east. Together they form the horizontal coordinate system, also called altazimuth or alt-az.
The figure shows the same star in two views. Pick a term to isolate it, then drag the star in either panel.
Three things to notice. First, altitude and zenith distance (z) measure the same arc from opposite ends, so they always add up to a right angle:
Second, the arc from the horizon through the star to the zenith is part of a vertical circle. Every point in the sky has one. The vertical circle running through north and south has its own name, your meridian, and any body stands at its highest as it crosses it.
Third, the right-hand panel answers a fair question: are these polar coordinates? In effect, yes. The zenith is the pole of the system. On the plot, zenith distance is the radius and azimuth is the angle, the same pair you would use on any polar graph. Because you are looking up at the plot from inside the dome, east falls on the left and azimuth runs counterclockwise on the page. From above, as on the dome, it runs clockwise.
Two words that trip people up. In navigation, altitude is an angle, not a height above sea level. Astronomers and engineers often call the same angle elevation. And azimuth is a direction to something in the sky or on a chart, which is different from your heading, the way your vessel is pointing.
Three words from one
Zenith, azimuth, and nadir all reach English from Arabic astronomy, and all contain the Arabic samt, “direction.” Zenith comes from samt ar-raʾs, “direction of the head,” by way of Medieval Latin cenit. The -ni- where Arabic has m may be a misreading of three pen strokes, or may be a phonetic approximation; the evidence does not settle it.[2] Azimuth comes from the plural as-sumūt, “the directions.”[3] Nadir comes from naẓīr as-samt, “counterpart of the zenith.”[4]
The sky’s own grid
Altitude and azimuth have one drawback for a navigator: they keep changing. As Earth turns, every star’s altitude and azimuth run through a daily cycle, and the numbers differ for every observer. An almanac can’t list them. It needs coordinates that belong to the sky.
Extend Earth’s axis outward and you get the two celestial poles. Extend Earth’s equator outward and you get the celestial equator. From these comes a second grid, which turns with the stars. Declination (δ) is a body’s angle north or south of the celestial equator, the sky’s version of latitude. Hour angle is the sky’s version of longitude, measured westward along the equator. Measured from your meridian it is the local hour angle (LHA); measured from Greenwich’s it is the Greenwich hour angle (GHA).
Press “Turn the sky” and watch which numbers change.
Your latitude ties the two grids together: the altitude of the celestial pole equals your latitude, so the whole grid tips over as you travel north or south. At the North Pole the celestial equator lies on your horizon. At the equator it passes through your zenith.
The navigational triangle
Three points connect the two systems: the elevated pole P, your zenith Z, and the body X. Join them with great-circle arcs and you have the navigational triangle.[1]
Each side is a term you have already met, read as an angle. Pole to zenith is 90° minus your latitude. Pole to body is 90° minus the declination when the body is on the same side of the equator as the pole. Zenith to body is the zenith distance. The angle at the pole comes from the local hour angle, and the angle at the zenith comes from the azimuth.
Know two sides and the angle between them, and spherical trigonometry gives you the rest. With your latitude, the body’s declination, and its local hour angle:
The figure opens at latitude 40° N, declination +20°, and LHA 320°, which gives an altitude of 50.5° at azimuth 108.4°. This is the calculation at the center of a sight reduction: predict the altitude from where you think you are, measure the real one, and let the difference say how far off you are.
The terms at a glance
| Term | What it is | Measured from | Range |
|---|---|---|---|
| zenith | Point straight overhead | Your plumb line | A point |
| nadir | Point straight below | Your plumb line | A point |
| horizon | Great circle level all around you | 90° from the zenith | A circle |
| meridian | Great circle through north, zenith, and south | Your position | A circle |
| altitude h | Height of a body, as an angle | Up from the horizon | 0° to 90° |
| azimuth Zn | Direction of a body | True north, through east | 0° to 360° |
| zenith distance z | Angle from overhead to a body | Down from the zenith | 0° to 90° |
| celestial pole | Earth’s axis extended to the sky | Its altitude is your latitude | Two points |
| celestial equator | Earth’s equator extended to the sky | 90° from the poles | A circle |
| declination δ | The sky’s latitude | North or south of the celestial equator | −90° to +90° |
| hour angle (LHA, GHA) | The sky’s longitude, turning daily | Westward from a meridian | 0° to 360° |
Altitude and zenith distance run past these ranges for a body below the horizon. For fuller definitions, see the Glossary.
Sources
- National Geospatial-Intelligence Agency. The American Practical Navigator (Bowditch), Pub. No. 9. NGA, 2019. Chapters on navigational astronomy and sight reduction; glossary. reference
- zenith: etymology. Wiktionary. reference
- azimuth: etymology. Wiktionary. reference
- nadir: etymology. Wiktionary. reference