Measure of latitude with Polaris


Another method is to measure the height of Polaris above the horizon. A similar exercise as measuring the latitude with the Sun shows that:

Latitude phi = H measured


The precession of the equinoxes shifts the celestial system by around 50 seconds of arc per year (or 28° in 2000 years). This variation is due to a slow conical movement of the rotation axis of the Earth (one full turn in 25 800 years). This means that the Earth’s axis does not always point to the same location in the sky. In other words, todays “north star” has not always been on the Earth’s axis.

In fact, today’s north star, Polaris, is at less than 1° of the Earth’s axis, but ancient astronomers had no bright north star available.

Track of the Earth’s rotation axis on the northern celestial sphere: its present position (in +2000 AD) is close to Polaris located in the Lesser Bear and called “α Ursae Minoris” or “α UMi” (source: Wikipedia).

Ancient seafarers looked for “Cynosura” (Lesser Bear or Ursa Minor) to find the north at night (see Lucan, La Pharsale, Book 8) and looked for the Sun at zenith for the south in daytime. Cynosura, being close to the Earth’s axis, moves little during the night and is therefore quite convenient as a landmark in the night sky.

The northern night sky from the Ionian coast, 500 BC. Note the movements of Ursa Major and Ursa Minor (in blue dashes) due to the effects of precession over the past 2.5 millennia. (Danny Lee Davis, 2009).

However, this is not very accurate navigation: if you are sailing at 45° latitude (e.g. somewhere between the Danube estuary and Crimea) and heading north, Cynosura will be at 45° above the horizon. Seen from the position of the helmsman on board, near the stern, he will see Cynosura behind the mast of his ship, around halfway the mast height. When moving further north, increasing his latitude, Cynosura will appear higher above the horizon and higher behind the mast. If he is sailing eastbound, he will keep Cynosura to his left, on the “port side” of his ship, like Odysseus after leaving Calypso’s island:
“he sat and guided his raft skilfully with the steering-oar, nor did sleep fall upon his eyelids, as he watched the Pleiads, and late-setting Bootes, and the Bear, which men also call the Wain, which ever circles where it is and watches Orion, and alone has no part in the baths of Ocean. For this star Calypso, the beautiful goddess, had bidden him to keep on the left hand as he sailed over the sea.” (Homer, Odyssey, 5, 270).

Further reading:
Information accessible to non-specialists in astronomy is available in textbooks on sundials (e.g. by Denis Savoie (2003), ed. Belin, France) and, of course, on Wikipedia.
See also Journès & Georgelin (2000), “Pythéas, explorateur et astronome”, ed. Nerthes, Ollioules, France, for fascinating explanations on Pytheas’ astronomy.
Danny Lee Davis (2009), “Commercial Navigation in the Greek and Roman World”, PhD thesis, University of Texas, Austin, (359 pp).