Perhaps the most astonishing accomplishment of ancient astronomers was the discovery of the precession of the equinoxes.
The tale, as told by Ptolemy: Around 220 BCE, the Greek astronomer Timocharis mapped out the motions of the sun against the background of the celestial sphere, and determined where the sun’s orbit crossed the equator of the sphere from north to south – the point of the autumnal equinox. He described this as 8º behind Spica, a bright star in Virgo, which lies close to the equator of the sphere. (See Almagest VII.i through VII.iii.)
Roughly 90 years later, Hipparchus undertook the same observations and calculations, but got a different result, placing the equinox just 6º behind Spica. Now, Hipparchus might have simply said that he trusted his own determination, arguing that Timocharis had mis-measured or mis-calculated. But he felt strongly about his own measurements, as well as those of his predecessor. To account for the disparate results, Hipparchus proposed that the axis of rotation of the celestial sphere might be undergoing a gradual shift.
(Today, of course, we see this as a result of the slow precession of the earth’s axis of rotation.)
Hipparchus recognized that this was a profound change in natural philosophy, based on just two data points. Further observation by astronomers generations hence was necessary to confirm or disprove his conjecture. So he called upon later astronomers to re-determine the equinoctal point, to confirm the motion which he’d reported. This was an experiment intended to span a century or more.
It took two and a half centuries for somebody to continue this experiment, but Ptolemy did, and that was that – the celestial sphere precessed.
That’s the tale as typically told in a modern Intro to Astronomy textbook.
But there’s more to the story. For Hipparchus proposed an alternate explanation for the discrepancy between his measurements and those of Timocharis, and called on future observers to put this idea to the test as well.
Instead of the entire celestial sphere shifting, he wondered, might there be instead a gradual systemic distortion of the celestial sphere in the region of its equator? In modern terms, we’d say that Hipparchus proposes a slow, plastic deformation of the equatorial region of the celestial sphere, relative to the polar stars.
What’s more, he devised an experiment to test this hypothesis – an experiment meant to span a century or more. He set forth a series of stellar alignments, connecting stars in the region of the zodiac with stars to the north or south. If the celestial sphere were undergoing a systemic deformation, as proposed, then many or most of these starlines would drift out of alignment in a century or two.
(Pause a moment to reflect upon the hopeful audacity of Hipparchus.)
In Book VII of Almagest, Ptolemy describes the measurement of the equinoctal point in his own day, confirming the gradual drift reported by Hipparchus. In addition, Ptolemy addresses the other experiment of Hipparchus, meant to test if the stellar equator of the celestial sphere was drifting relative to the regions north and south.
In VII.i, Ptolemy lists each of the starlines of Hipparchus—e.g., ‘the star in the mouth of the southern fish [of Pisces], and the bright star in the shoulder of the Horse, and the bright star in the chest of the Horse lie on a straight line’. He reports that he has reviewed these alignments, and finds no change; the shift of the equinox cannot be explained by the proposed plastic drift of the equatorial region. He clearly argues that, if the celestial sphere was undergoing a slow, sytemic deformation, at least some of the starlines of Hipparchus should have fallen out of alignment; but as there is no sign of such drift, the change in the point of equinox is best explained by the precession of the whole of the sphere of the fixed stars.
Upon stating that conclusion, Ptolemy turns around and proposes that the starline experiment be continued by observers of later generations. What’s more, he adds a new set of star alignments – like Hipparchus’ initial set, Ptolemy circles the zodiac.
Curious, that.
Having disproven Hipparchus’ proposal, why would Ptolemy want to continue his experiment?
We suspect that Ptolemy had another question in mind.
Having reviewed the starlines of Hipparchus, and those of Ptolemy, we find that there’s a qualitative difference between the alignments each sets forth. Like the brushstrokes of different master painters, the starlines of Hipparchus and Ptolemy exhibit distinctive styles.
The style of Ptolemy’s lines, we argue, reveals the question(s) he was asking.
If you’d like to look at some of these lines for yourself, to get a feel for their distinct ‘style’, we invite you to investigate the starlines of VII.i.
We’ve worked our way through this text and mapped out these lines and the surrounding sky. Two turns round the Zodiac: A dozen flipbook presentations for the starlines of Hipparchus [LINK], and another dozen for those of Ptolemy [LINK]. (We hope to re-present these as narrated video animations in the near future.)
Along the way, we discovered many errors in the surviving text. We suspect that most who studied Ptolemy’s work had little interest in the experiment of Hipparchus [LINK].