September 12, 1997

Letters to the Editor
Sky & Telescope

Hipparchus' Polar Square

Dear Mr. Editor

People of the northern hemisphere are very fortunate in having a bright star, Polaris, very close to their celestial pole. However, this has not been the situation for most of recorded history. In classical times the pole was moving slowly between the Bears. We are told that Greek sailors used the Great Bear to steer their course, while the Phoenicians, better navigators, preferred the Little Bear. The Bears' approximate polar distances were 20° and 10°, respectively. With the expansion of traveling and trade brought by Alexander's conquests, a more precise location of the pole was needed.

In Hipparchus' commentary of Aratus' Phenomena (Greek Astronomy, Dover, 1991), I find this curious statement: 'About the north pole Eudoxus is in error, for he says: "There is a certain star which remains always in the same spot; this star is the pole of the universe," the fact being that at the pole there is no star at all, but there is an empty space, with, however, three stars close to it, with which the point at the pole forms a square, as Pytheas of Massalia also states.'

Which are the three stars mentioned by Hipparchus? The book's editor suggests alpha and kappa Draconis and beta Ursae Minoris. But these three stars form almost an equilateral triangle in the sky, which means that they would be corners of a pretty distorted square, and the closest they are to the 2nd century BC pole is 7°. They seem quite useless for pinpointing the position of the pole with the precision implied by Hipparchus' words.

The problem is that there is no other square available using bright stars. Yet we must believe Hipparchus, the greatest astronomer of antiquity, and Pytheas of Marseilles, the first navigator to explore the coasts of Britain and northern Europe.

As a possible solution to the puzzle, I suggest the three dim stars shown in the accompanying chart, labeled with their numbers in the Yale Bright Star Catalogue (magnitudes in brackets). The chart also shows the pole's position around the times of Pytheas (ca. 320 BC) and Hipparchus (150 BC). The square is quite regular (for 200 BC) and small (2.5° per side) to fit Hipparchus description. The only remaining issue is: could they see a 6th magnitude star in those unpolluted days?

Hipparchus' square

I need your help to validate my theory. Can anyone see those stars with his naked eyes? I cannot. My eyesight is poor, my skies are polluted and my hemisphere is the wrong one!

Eduardo Vila-Echagüe
Santiago de Chile  1