A crucial experiment

We investigate a possible event in ancient science.

Last month there occurred a Great Conjunction: the planets Jupiter and Saturn appeared to lie in the same direction as seen from Earth. Or almost the same direction; they did not exactly line up, though they passed closer than they have in centuries, an impressive sight in telescopes.  The event prompted our astronomer to ask: could the ancient astronomers have used an actual line-up, where one planet covered the other, to determine the order of the planets?

Some background is in order.  The geocentric universe had all the planets (a term including the Sun and the Moon) moving on invisible spheres around the stationary Earth.  Clearly the Moon was in the closest sphere, since it was seen to pass in front of all the planets and the stars; the stars were in the highest sphere, since planets (much more rarely than the Moon) sometimes passed in front of them.  Most authorities placed the intermediate spheres in order of speed: the Sun passed around the sky (against the stars) in a year, Mars in almost two, Jupiter in twelve and Saturn in thirty; so Saturn was in the highest sphere below the stars, the others in their proper order below.  Mercury and Venus were puzzling, since their average periods were identical to the Sun’s: some authorities placed them below the Sun, some above.  Ptolemy’s refinement of this picture proved reasonably accurate in predicting the positions of the planets, but each one was calculated separately; his mathematics did not require any particular ordering.  Thus there was nothing in ancient physics or astronomy that required or determined the order of the planets.

So the observation of one planet passing in front of another could be a crucial experiment, something often emphasized in teaching the Scientific Method to students: if two theories predict different results, the experiment can be used to choose between them.  Could the ancients have seen one, and used it to order their universe?

Alas, an actual occultation of Saturn by Jupiter is an extremely rare thing.  One calculation we’ve seen places them hundreds to thousands of years apart, none occurring at the proper time for the ancients to use it.  Our astronomer then changed the question: could an ancient astronomer, meaning an expert naked-eye observer, have concluded anything if he had seen such an event? (Note that without a telescope all the planets look like points of light, and so the observation must be of the combination of two planets too close to separate with the eye.)

A bit of calculation shows that the combined light of the planets would dip by about 5% over almost 2 1/2 hours, which is too small and too slow for even a good observer to notice.  Add to this the fact that even the best ancient predictions weren’t accurate enough to be sure Jupiter did in fact pass in front of Saturn, rather than slightly to one side, and we conclude that the ancients could not have ordered the planets based on the closest possible Great Conjunction.

What about other planets?  Mars transiting Jupiter gives a drop of about 10% over half an hour, which is probably imperceptible without a comparison star, and there are none bright enough.  However, the combined color would certainly get redder, possibly enough to satisfy our ancient observer.  Our astronomer is still calculating other possibilities, though none of them look convincing so far.

So our astronomer’s idea of an ancient Crucial Experiment looks unworkable.  The actual order of the planets must wait for Copernicus and Kepler.