Measure of latitude with the Sun

The ancients have of course much observed the Sun, its cycles and remarkable points in the sky, mostly at noon when the Sun is, by definition, at its daily highest point.

What is of interest to us here is to find the latitude of a given location (see also the chapter on Ptolemy hereafter).

Let’s consider the Earth’s yearly track around the Sun on an ellipse. The Earth also rotates on itself. The axis of the Earth is inclined on the plane of its orbit around the Sun with an angle of around 23° 26’ and this orientation is constant during one revolution around the Sun. Consequently, during one half of the year the northern hemisphere is more inclined to the Sun than the southern hemisphere, with a maximum on June 21st. During the other half of the year the southern hemisphere is more inclined to the Sun than the northern hemisphere, with a maximum on December 22nd. These maxima are called solstices. On these dates, the Sun at noon is at its highest above the horizon on June 21st and at its lowest on December 22nd (in the northern hemisphere).

http://freveille.perso.sfr.fr/ecliptique.png

At these two solstices, the Sun at noon is, by definition, vertical above the Tropic of Cancer (around June 21st) and vertical above the Tropic of Capricorn (around December 22nd). The ancients said that “there is no shade at noon”; today we say that the Sun is at its Zenith. Between these two dates, the Sun at noon is vertical above the equator on two days called equinoxes (around March 21st and September 23rd); we say that the declination of the Sun is nil on these two dates. The Sun at noon is in fact every day vertical of a point located between both tropics, and this happens twice a year for every location. E.g. the Sun is vertical of a point located at 17° of latitude 45 days before and 45 days after the solstice and this fits Plini’s description of Ptolemais Theron (now called Agig located at 18.18° of latitude North, Plini the Elder, Natural History, 6, 34).

If one measures the angle H of the Sun on the horizon at an equinox (when the Sun at noon is above the equator), one in fact measures the complement of the latitude, thus:

Latitude phi = 90° – H measured

References
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.