An Ancient Greek Orrery
Suppose a traveller carried into Scythia or Britain the orrery recently constructed by our friend Poseidonius, which at each revolution reproduces the same motions of the sun, the moon, and the five planets that take place in the heavens every day and night, would any single native doubt that this orrery was the work of a rational being? Cicero
Kircher's reconstruction of the sphere of Archimedes, imitating the motion of the planets with the aid of magnets. From Magnes, sive de Arte Magnetica (1643 ed.) p. 305
The mechanical device of Antikythera could be considered as a planetarium, a mechanical model of the “universe” and not just a simple “clock”. Archimedes is considered to have build such devices. Although no writings with “technical details” of these constructions exist today. The use of mechanical devices could be used also for educational purposes.
The Planetariums or “Sphere” of Archimedes is mentioned by Cicero, Pappus and Claudius Claudian an Egyptian-Greek who mentions in a poem the planetarium of Archimedes in the year 395 AD, 600 years after the death of Archimedes.
Pappus says that Archimedes has written a book about the planetarium. Cicero 100 years after Archimedes death mentions also the sphere.
“Iuppiter in parvo cum cerneret aetherea vitro..” that lets us suppose that parts of the sphere were transparent using glass. The planetarium showed the motion of the five planets, the sun and the moon.
Reviel Netz discusses in his book “The shaping of deduction in Greek Mathematics” the use of diagrams, abaci, and planetaria as mathematical tools for education and scientific studies by the ancient Greeks:
The earliest and most extensive piece of evidence on planetaria in Greek astronomy is Epicurus - biased - description of astronomical practices, in On Nature XI. The description is of a school in Cyzicus, where astronomers are portrayed as using organa, "instruments", while sullogizesthai, dialegesthai (i.e. reasoning in various ways), having dianoia and epinoesis (thought process) and referring to a legomenon (something "said" or "asserted").
What is the exact relation between these two aspects of their practice, the instrument and the thought? One clue is the fact that Epicurus claims that the aspects are irreconcilable because, according to him, the assumption of a heavens/model analogy is indefensible. This assumes that some dependence of the verbal upon the mechanical is necessary. This dependence might be merely the thesis that "the heavens are a mechanism identical to the one in front of us", or it might be more like "setting the model going, we see (e.g.) that some stars are never visible, QED". Where in the spectrum between these options should we place the mathematicians of Cyzicus?
No doubt much of the difficulty would have been solved by the Greek acquaintance with the sky. But a model would certainly be helpful as well, at such a stage. After all, you cannot turn the sky in your hands and trace lines on its surface. An object which can be manipulated would contribute to concept-formation. This acquintance is more than the mere analogy claim - the model is used to understand the heavens – yet this is weaker than actually using the model for the sake of proof.
This is certainly not the only purpose of building planetaria. Planetaria could do what maps did: impress. Epicurus is setting out to persuade students away from Cyzicus. The planetarium seems to have been set up in order to persuade them to come.
Timaeus excuses himself from astronomy by claiming (Plato, Timaeus, 40d2-3)
“again, explaining this without watching models would be a pointless task”. It seems that models were almost indispensable for the pedagogic level of astronomy. The actual setting out in writing of mathematical astronomy, however, does not register planetaria.
The Antikythera Mechanism: Physical and Intellectual Salvage from the 1st Century BC
Eudoxus Hippopede Machine
Ptolemy's Equatorial Ring
Reviel Netz , The shaping of deduction in Greek Mathematics, A study in Cognitive History, 1999, Cambridge University Press
S V Zitomirskii, The "celestial globe" of Archimedes (Russian), Istor. Astronom. Issled. 14 (1978) 271-302