The most intuitive way to describe a spot in the sky is also the simplest: how high above the horizon is it, and which direction do you face to see it? Those two numbers are the altitude-azimuth (alt-az) system. Altitude runs from 0° at the horizon to 90° at the zenith. Azimuth runs from 0° to 360°, measured clockwise around the horizon starting from due north — so north is 0°, east is 90°, south is 180°, and west is 270°.
Alt-az is great for pointing a telescope right now, but useless for a catalog — an entry that reads "45° up, facing southeast" is meaningless without also specifying exactly when and where on Earth it was measured. Astronomers solve this with the equatorial system, built the same way Earth's own latitude and longitude are built, but projected onto the sky.
Declination is the sky's latitude — the angular distance north or south of the celestial equator, from −90° (south celestial pole) to +90° (north celestial pole). Right ascension is the sky's longitude — measured eastward along the celestial equator, starting from a fixed reference point called the vernal equinox (the point where the Sun crosses the celestial equator every March). Right ascension is given in hours, minutes, and seconds rather than degrees, because Earth's 360° rotation happens to take 24 hours: 1 hour of right ascension always equals 15° of sky.
It seems redundant to track two full coordinate systems for the same sky — until you notice they're solving two different problems. One answers "where do I look right now?" The other answers "which object, exactly, are we talking about?"
| Alt-Az (Horizon) | Equatorial (RA/Dec) | |
|---|---|---|
| Depends on | Your location and the exact time | Nothing — fixed to the stars |
| Changes overnight? | Constantly, every minute | Essentially never |
| Best for | Pointing a telescope right now | Cataloging and looking up an object |
| Zero point | Due north, your horizon | The vernal equinox, the celestial equator |
The two systems aren't unrelated — they meet at one specific moment each night: when an object crosses your local meridian, the imaginary north-south line running through your zenith. That's the instant an object reaches its highest altitude for the night, and that altitude depends only on your latitude and the object's declination:
This is the same relationship you already used in Activity 1.1.1 to find the celestial pole's altitude — it's just the general-purpose version, which works for any declination, not only 90°.
Set your latitude and a star's declination. The star's altitude at the moment it crosses your local meridian — its highest point of the night — is 90° − |latitude − declination|.
An observer at 42°N is tracking a star with a declination of +10°. What altitude does the star reach when it crosses the meridian?