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Archimedes constructed a planetarium where as described by Cicero "he had thought out a way to represent accurately by a single device for turning the globe those various and divergent movements with their different rates of speed. And when Gallus moved the globe, it was actually true that the moon was always as many revolutions behind the sun on the bronze contrivance as would agree with the number of days it was behind in the sky. Thus the same eclipse of the sun happened on the globe as would actually happen..." (see sources).

When the Antikythera mechanism was found some suggested that similar gear system was used by Archimedes. However, the Antikythera mechanism (dated to 150-100 BC) has an epicyclic gear for the lunar motion, so under the conventional timeline there are two problems with this idea.

The first problem is Apollonius. In Almagest XII,1 Ptolemy credits him with proving theorems about epicycles, and this seems to be the earliest association of epicycles with anybody's name. Some biographers say that "the theory of epicycles certainly predates Apollonius", but I am not sure where this "certainly" comes from.

The second problem is Hipparchus. Even Apollonius is only credited with theorems, Hipparchus (again according to Ptolemy) was the first one to apply epicycles to lunar motion, and he did it based on Babylonian data, which Archimedes presumably didn't have a century earlier. By the way, Hipparchus lived around the time the Antikythera was made. However, a gear similar to Antikythera's, but dated to before Hipparchus (200-150 BC), was found in a shipwreck that can be linked directly to Syracuse, and hence to Archimedes.

On the other hand, if Archimedes did not use epicycles the only model available to him would have been of Eudoxian homocentric spheres. According to modern reconstructions (p.226) reproducing the uneven motion of the Moon even crudely (and predicting eclipses mentioned by Cicero) would require at least three spheres rotating at different speeds under different inclinations, and with outer spheres transferring motion to inner spheres to combine it with their internal rotations. Even more spheres are required to reproduce retrogressions of the planets.

Ptolemy is not exactly a great authority on historical matters (he managed to mention no astronomer between himself and Hipparchus, a span of over 200 years), and his attributions to Apollonius and Hipparchus were specifically questioned by some scholars. Life dates of Archimedes (287-212 BC) and Apollonius (262-190 BC) overlap, and we know that both corresponded with Alexandrians, at least two of which, Eratothenes and Aristarchus, performed astronomical measurements (Archimedes wrote to Eratothenes and mentioned Aristarchus in Sand Reckoner). Finally, some arrangements of Eudoxian spheres are suggestive (p. 227) of the simpler epicyclic scheme.

Is it plausible in the light of recent developments that Archimedes/Alexandrians already developed epicyclic models of the Moon (and possibly planets) a century before Hipparchus? Alternatively, is there a mechanical arrangement of multiple nested spheres with motion transfer combined with internal rotations, that uses gears and can be powered from a single rotational driving source (within Archimedes's capabilities)? Modern reconstructions of the planetarium that I've seen do not seem to be up to the task.

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    $\begingroup$ As per (unofficial) policy, we're not going scientist tags. . . (Sigh) $\endgroup$
    – HDE 226868 ♦
    Commented Nov 18, 2014 at 1:47
  • $\begingroup$ Do you know where to find more details of this newly found mechanism from Olbia? Pictures, description etc.? Folowing your link I could not find any details. $\endgroup$
    – Alexandre Eremenko
    Commented Nov 18, 2014 at 2:37
  • $\begingroup$ Your post contains very interesting information, but I do not see how can one possibly give a definite answer to your question. Probably he used epicycles (modeled by toothwheels). What else ? On what other principle such a mechanical device can be made? $\endgroup$
    – Alexandre Eremenko
    Commented Nov 18, 2014 at 2:42
  • $\begingroup$ I think it's a single gear, and it took them from 2006 to 2011 to present findings publicly. Geymonat's book may have details, but I haven't seen it first hand. $\endgroup$
    – Conifold
    Commented Nov 18, 2014 at 3:02
  • $\begingroup$ If he did use epicycles it would be quite a revision of conventional history, but I am not convinced that it's "probable" if gears can be used in a homocentric contraption also. Planetarium was known long before Antikythera, so someone might have thought of one. I am also interested if these finds change the assessment of the reliability of Ptolemy's attributions by classical scholars, and if they would consider the alternative more likely than the conventional version now. Of course the latter answer depends on the former. $\endgroup$
    – Conifold
    Commented Nov 18, 2014 at 3:03

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Let me try to summarize this long discussion to an "answer".

All that we know about epicycle theory comes from Ptolemy. Ptolemy credits Apollonius (262-190 BC) with one mathematical theorem (which says that excentric motion is equivalent to epicycle), and Hipparchus (190-120) with using epicycles to describe the motions of Sun, Moon and possibly planets. (Ptolemy credits planets to himself, correct?). Archimedes (287-212) died when Apollonius was 50 years old, so it is very plausible that they knew each other and perhaps even corresponded. (It is known that Archimedes did correspond with other Alexandrian scholars).

There is no historical evidence relating Archimedes to epicycle theory.

The story of the recently found object in Olbia which is presumably a piece of a toothwheel from Archimedes "planetarium" is strange. All information about this object found on the Internet comes from a single person who is an engineer, and who wrote a book about it. No photo or description of this object could be found. No reference except on the writings of this single person.

Information about Archimedes planetarium which exists in the surviving literature does not permit to judge on what theory it was based.

I hope this is a fair summary. Please correct if necessary.

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  • $\begingroup$ We should add that there appears to be no plausible mechanical reconstruction of Archimedes's planetarium, with or without gears. Ironically, if the conventional story is true and Apollonius worked with epicycles Archimedes was most likely aware of them through his Alexandrian correspondents, but there is no evidence he used them in the planetarium, even if he did use gears. $\endgroup$
    – Conifold
    Commented Nov 24, 2014 at 21:31
  • $\begingroup$ However, the conventional story is very weakly suppported, it entirely hinges on a single passage from Almagest, which is directly contradicted by Theon of Smyrna, who wrote around the same time. According to Goldstein "the role of Apollonius in the history of astronomy has been exaggerated. Moreover, the evidence for Hipparchus’s knowledge of the equivalence of the eccentric and epicyclic models is very weak, and there is no evidence for his familiarity with the theorem on stationary points." On the other hand, familiarity of Hipparchus with epicycles is confirmed independently of Almagest. $\endgroup$
    – Conifold
    Commented Nov 24, 2014 at 21:31
  • $\begingroup$ I agree. Everything that we know about that time is very weakly supported. The principal source is Ptolemy, but he lived centuries later. And the authors Plutarch or Pliny or Cicero just did not understand what they were writing about (speaking of exact science). Like the modern authors who are not scientists:-) $\endgroup$
    – Alexandre Eremenko
    Commented Nov 24, 2014 at 21:37

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