Example of determining latitude

You are sailing somewhere in the North Atlantic. It is evening twilight, so you can see both the horizon and stars through a telescope. You observe, among others, Alnilam rising toward its upper culmination point. This is the point where Alnilam is at its highest altitude above the horizon. Using a sextant, you can measure the angle between yourself, Alnilam, and the horizon. The angle increases, increases, increases, and then the next measurement shows it has slightly decreased. The largest angle you measured to Alnilam was 42° 13’ (42 degrees and 13 minutes). At that moment, Alnilam was at upper culmination and directly south of you. Now we need to determine your latitude.

We know that the declination of Alnilam is 1° 12’ S, so the situation is as follows:

Your latitude is equal to the angle between the plane of the equator, the Earth’s center, and your position.

The angle between the horizon you observe and your latitude is 90°.

Therefore, the angle you measure to Alnilam is 42° 13’ + Alnilam’s declination 1° 12’ S + latitude X = 90°.

In other words…

X = 90° - 42° 13’ - 1° 12’ = 46° 35’.

You are at latitude 46° 35’.

A simpler illustration of the situation:

Alnilam measured altitude above the horizon

Alnilam’s declination, i.e. how far it is above the plane of the celestial equator

your latitude
42° 13’ + 1° 12’ + X = 90°

C o n t e n t s

Hamburg VII 2026