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Does it favor a Heliocentric, or Geocentric Universe?

Does it favor a Heliocentric, or Geocentric Universe?

In a word neither. The purpose of the mechanism is clearly to position 'heavenly bodies' with respect to the 'celestial sphere', with reference to the observer's position on the surface of the earth. In order to achieve this, the mechanism has to use a geocentric model. However this does not imply that the manufacturer favoured a geocentric model of the universe. In fact it was Aristarchos of Samos (310 - c.230 BC) who first proposed a heliocentric solar system in 297 BC. Unfortunately proponents of the heliocentric universe were increasingly persecuted for their beliefs in Ancient Greece and in later times. It is highly probable that the maker of the mechanism was aware of the heliocentric universe, but it does not imply he favoured it.

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The object of the mechanism is to make specific astronomical predictions. This requires a geocentric model, since actual observations require everything to turn around the observer, think of the coordinates you use to point your telescope. In fact, there is a slight discrepancy since the observer is not at the center of the Earth, which is the actual center of the geocentric model, but this was already taken into account in antiquity and was estimated by Archimedes in his paper "The Sand Reckoner."

The geocentric/heliocentric debate is more of a conceptual issue as geocentric will eventually be required for observations. Moreover, until the 17th century, astronomy was mathematical astronomy in which one constructs the best model fitting the data without giving physical reasons why the model occurs in nature. Since the geocentric and heliocentric models are mathematically equivalent, the distinction is once again moot.

Moreover, the heliocentric theory certainly didn't have any observational support at the time (experimental verification only came in 1838) and it loses conceptual significance without physical explanations such as gravitation and Newton's Laws. Therefore, there was no scientific reason to adopt a heliocentric model in antiquity. The only exception is Archimedes who did adopt it in his paper "The Sand Reckoner" because he wanted to use the largest theoretical model of the universe, which is the case for the heliocentric model in order to avoid parallax issues. He was never persecuted for this view and there is no evidence that anyone supporting the heliocentric model was ever persecuted in Ancient Greece.


To reinterate what has been said above, from possibly a little different angle:

Ιον Αστρουομερ (pardon my Greek) is standing in the night sky, and wants to locate Saturn in the sky. Like all ancient Greeks, he believes that these bodies travel in circles, but to explain why they back up occasionally in the sky, he needs epicycles (his drinking buddy Hipparchus told him about them, and how they work computationally). So, he starts the indicated computation which involves a circle that Saturn is travelling along the ecliptic and an epicycle, which proportions to the size of Earth's orbit, and arrives at the location. He knows where to look.

1500 years later, his English descendant, John Astronomer, needs the same information. His friend Kepler has not yet let him into his new secret about orbits, but John is none-the-less a modern fellow, so he uses the new-fangled celestial mechanics as Tycho Brahe taught him: he determines his location on Earth, translates and rotates that into a solar-centered coordinate system, and then applies the six orbital variables of Saturn and derives the location in his sky.

Both got an equally close answer, because both of their methods were the same. The two epicycles of Ptolomy and the two orbits of Copernicus equate to the same computations, perhaps ordered differently and certainly different in viewpoint and technique, but, in essence, the same.

The upshot is that the two theories which explain who moves around whom are not relevant to the Antikythera Mechanism; it uses a mechanical equivalent which could be explained by either Ιον or John in terms of epicycles or celestial mechanics. Until Kepler expands the universe of the mind to include all conics as orbits, the two are entirely equivalent to the problem that these two have, and which the Antikythera Mechanism addresses.