martyb and aristarchus both made submissions about:
In modern terms, all the moving astronomical bodies have orbits close to the plane of Earth's motion around the sun—the so-called ecliptic—meaning that they all follow much the same path through the stars. Predicting the positions of the planets along the ecliptic was very difficult for early astronomers. This task, it turns out, was one of the primary functions of the Antikythera mechanism. Another function was to track the positions of the sun and moon, which also have variable motions against the stars.
[...] The second key figure in the history of Antikythera research was British physicist turned historian of science Derek J. de Solla Price. In 1974, after 20 years of research, he published an important paper, "Gears from the Greeks." It referred to remarkable quotations by Roman lawyer, orator and politician Cicero (106–43 B.C.E.). One of these described a machine made by mathematician and inventor Archimedes (circa 287–212 B.C.E.) "on which were delineated the motions of the sun and moon and of those five stars which are called wanderers ... (the five planets) ... Archimedes ... 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." This machine sounds just like the Antikythera mechanism. The passage suggests that Archimedes, although he lived before we believe the device was built, might have founded the tradition that led to the Antikythera mechanism. It may well be that the Antikythera mechanism was based on a design by Archimedes.
[...] It seems that the device could be used to predict the positions of the sun, moon and planets on any specific day in the past or future. The maker of the machine would have had to calibrate it with the known positions of these bodies. A user could then simply turn a crank to the desired time frame to see astronomical predictions. The mechanism displayed positions, for instance, on a "zodiac dial" on the front of the mechanism, where the ecliptic was divided into a dozen 30-degree sections representing the constellations of the zodiac. Based on the x-ray data, Price developed a complete model of all the gearing on the device.
[...] A third key figure in the history of Antikythera research is Michael Wright, a former curator of mechanical engineering at London's Science Museum. In collaboration with Australian professor of computer science Alan G. Bromley, Wright carried out a second x-ray study of the mechanism in 1990 using an early 3-D x-ray technique called linear tomography. Bromley died before this work bore fruit, but Wright was persistent, making important advances, for example, in identifying the crucial tooth counts of the gears and in understanding the upper dial on the back of the device.
[...] We proposed that any method the Antikythera creators used would have required three criteria: accuracy, factorizability and economy. The method must be accurate to match the known period relations for Venus and Saturn, and it must be factorizable so the planets could be calculated with gears small enough to fit into the mechanism. To make the system economical, different planets could share gears if their period relations shared prime factors, reducing the number of gears needed. Such economy is a key feature of the surviving gear trains. Based on these criteria, our team derived the periods 462 and 442 using the idea from Parmenides and employed the same methods to discover the missing periods for the other planets where the inscriptions were lost or damaged.
[...] We now understood how the front display matched the description in the back-cover user's manual, with the sun and planets shown by marker beads on concentric rings. The front cover also displayed the moon's phase, position and age (the number of days from a new moon), and the dragon hand that showed eclipse years and seasons.
With the concentric rings for the planets, we realized that we could now make sense of the front-cover inscription as well. This writing is a formulaic list of the synodic events of each planet (such as its conjunctions with the sun and its stationary points) and the intervals in days between them. On the back plate, the eclipse inscriptions are indexed to markings on the saros dial. On the front plate, inscriptions about the risings and settings of stars are indexed to the zodiac dial. Our insight was that the inscriptions on the front could refer to index letters on the planetary rings: if the sun pointer is at one of these letters, then the corresponding inscription entry describes the number of days to the next synodic event. Because the left-hand side of the inscription, where we would expect these index letters to be, is missing, we cannot prove the hypothesis—but it is a compelling explanation.