Finding latitude from the sky

Before satellites, sailors found their latitude with an angle measured above the horizon. The idea is simple. Stand on the Equator at an equinox and the noon Sun is straight overhead, at 90°. Walk north and the noon Sun sinks lower in the southern sky. The angle drops by exactly one degree for every degree of latitude you move.

In the northern hemisphere, facing south at local noon, the Sun’s height is

h = 90° − φ + δ

where φ is your latitude and δ (delta) is the Sun’s declination: the latitude of the point on Earth directly beneath the Sun that day. It is 0° at the equinoxes and swings between about +23.44° and −23.44° during the year.

At an equinox δ = 0, so φ = 90° − h. A measured noon height of 49° means a latitude of 41° N. At the June solstice δ = +23.44°, so at 40° N the noon Sun reaches 90° − 40° + 23.44° = 73.44°. In practice you use a table of the Sun’s declination for the date, which is how navigators used the almanac.

At night there is a shortcut in the northern hemisphere. Polaris, the North Star, sits less than 1° from the north celestial pole, the point in the sky that the Earth’s axis points to. The height of that pole above your horizon equals your latitude, so Polaris’ altitude ≈ your latitude (to within about a degree). If Polaris is 52° above the horizon, you are near 52° N. At the North Pole it is overhead; at the Equator it is on the horizon.

From the southern hemisphere Polaris is below the horizon. No bright star marks the south celestial pole, so southern navigators relied on the Sun and on other methods.