A recent article in Archaeoastronomy describes a study performed on an ancient lump of metal. It turns out that the Antikythera Mechanism is the equaivalent of an ancient Greek computer. Now, images of a P4 logo etched on face aside, this article leaves a few questions unanswered.
First, the device is supposed to be able to 'calculate' "the position of the sun, moon and planets against the celestial sphere". What the article does not specify is what version of the solar system it is employing. The ancient greeks had competing models of the universe: geo-centricism and helicentricism. Now, most people are familiar with the ancient geocentric model because most textbooks like to bash it to show how "stupid" everyone was until Copernicus.
So, which model does the device use? I am going to assume that it is the geo-centric model, but that is only because the Arab world and the medieval West both had similar devices that used it: the astrolabe and the armillary sphere.