Altitude, Azimuth and Your Latitude

On the celestial sphere we need a way to say where a star is in your sky right now. Two angles do it. Altitude is the angle above the horizon, from $0^\circ$ on the horizon to $90^\circ$ at the zenith. Azimuth is the compass direction, measured from north toward the east: north $0^\circ$, east $90^\circ$, south $180^\circ$, west $270^\circ$.

These angles change as the sky turns and from place to place. One of them is special: the altitude of the celestial pole never changes for you, and it tells you exactly where on Earth you are.

Why it works

Stand at the North Pole: the celestial pole is straight overhead, altitude $90^\circ$, and your latitude is $90^\circ$. Stand on the equator: the pole sits on the northern horizon, altitude $0^\circ$, latitude $0^\circ$. In between, every degree you walk north tilts your horizon by one degree on the curved Earth, so the pole climbs one degree. The two always match: the altitude of the north celestial pole equals your latitude. Polaris is within $1^\circ$ of the pole, so its altitude gives your latitude, which is how sailors once found theirs.

Key idea

Altitude of the celestial pole = your latitude. Stars closer to the pole than that angle never set (they are circumpolar); stars that close to the opposite pole never rise.

The north celestial pole stands at an altitude equal to the latitude. The white circles near it are the daily paths of circumpolar stars.

Worked examples

Worked example: Find your latitude

In Denver you measure Polaris $40^\circ$ above the northern horizon. What is your latitude?

The pole's altitude equals the latitude, and Polaris is almost at the pole.
So the latitude is about $40^\circ$ N.

Answer: $40^\circ$ N.

Worked example: Which stars never set?

At latitude $40^\circ$ N, does a star $30^\circ$ from the north celestial pole ever set? What about one $50^\circ$ from the pole?

The pole is $40^\circ$ above the northern horizon, so a circle around the pole of radius up to $40^\circ$ stays above the horizon all day.
The star $30^\circ$ from the pole circles it at a radius of $30^\circ$, dipping no lower than $40^\circ - 30^\circ = 10^\circ$ above the horizon. It never sets.
The star $50^\circ$ from the pole would dip to $40^\circ - 50^\circ = -10^\circ$: below the horizon. It rises and sets.
Astronomers give a star's angle north of the celestial equator as its declination $\delta$, so its distance from the pole is $90^\circ - \delta$. Circumpolar at $40^\circ$ N means $\delta \ge 90^\circ - 40^\circ = 50^\circ$.

Answer: The first never sets (circumpolar); the second rises and sets.

The same picture gives a star's highest altitude, when it crosses the meridian: $h_{\max} = 90^\circ - |\text{latitude} - \delta|$. A star whose declination equals your latitude passes straight overhead.

Common mistake

Two common mix-ups. First, Polaris is not the brightest star; it is only about the 50th brightest, and Sirius outshines it many times over. It matters because of where it is. Second, Polaris is not overhead everywhere in the Northern Hemisphere. It is overhead only at the North Pole; from Miami (latitude $26^\circ$) it hangs just $26^\circ$ up, and south of the equator it is below the horizon. Check yourself: at the equator, what is Polaris's altitude? (Zero: right on the horizon.)

In the Sky and Solar System lab you can choose your latitude and see how the stars around the pole shift.

Altitude, Azimuth and Your Latitude

Worked examples

Practice

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Sources and further reading