For example, the Moon sometimes moves slightly faster in the sky than at others because of the satellite's elliptic orbit.
To overcome this, the designer of the calculator used a "pin-and-slot" mechanism to connect two gear-wheels that introduced the necessary variations.
"When you see it your jaw just drops and you think: 'bloody hell, that's clever'. It's a brilliant technical design," said Professor Mike Edmunds.
The New York Times:
The mechanism, presumably used in preparing calendars for seasons of planting and harvesting and fixing religious festivals, had at least 30, possibly 37, hand-cut bronze gear-wheels, the researchers reported. An ingenious pin-and-slot device connecting two gear-wheels induced variations in the representation of lunar motions according to the Hipparchos model of the Moon’s elliptical orbit around Earth.
The functions of the mechanism were determined by the numbers of teeth in the gears. The 53-tooth count of certain gears, the researchers said, was “powerful confirmation of our proposed model of Hipparchos’ lunar theory.”
Jo Marchant writing in Nature:
The researchers realized that the ratios of the gear-wheels involved produce a motion that closely mimics the varying motion of the Moon around Earth, as described by Hipparchus. When the Moon is close to us it seems to move faster. And the closest part of the Moon's orbit itself makes a full rotation around the Earth about every nine years. Hipparchus was the first to describe this motion mathematically, working on the idea that the Moon's orbit, although circular, was centred on a point offset from the centre of Earth that described a nine-year circle. In the Antikythera Mechanism, this theory is beautifully translated into mechanical form. "It's an unbelievably sophisticated idea," says Tony Freeth, a mathematician who worked out most of the mechanics for Edmunds' team. "I don't know how they thought of it."
...
Charette also hopes the new Antikythera reconstruction will encourage scholars to take the device more seriously, and serve as a reminder of the messy nature of history. "It's still a popular notion among the public, and among scientists thinking about the history of their disciplines, that technological development is a simple progression," he says. "But history is full of surprises."
François Charette in Nature:
From the paper:
The Antikythera Mechanism shows great economy and ingenuity of design. It stands as a witness to the extraordinary technological potential of Ancient Greece, apparently lost within the Roman Empire.
Nature 444, 587-591 (30 November 2006)
T. Freeth et al.
The Antikythera Mechanism is a unique Greek geared device, constructed around the end of the second century bc. It is known1, 2, 3, 4, 5, 6, 7, 8, 9 that it calculated and displayed celestial information, particularly cycles such as the phases of the moon and a luni-solar calendar. Calendars were important to ancient societies10 for timing agricultural activity and fixing religious festivals. Eclipses and planetary motions were often interpreted as omens, while the calm regularity of the astronomical cycles must have been philosophically attractive in an uncertain and violent world. Named after its place of discovery in 1901 in a Roman shipwreck, the Antikythera Mechanism is technically more complex than any known device for at least a millennium afterwards. Its specific functions have remained controversial11, 12, 13, 14 because its gears and the inscriptions upon its faces are only fragmentary. Here we report surface imaging and high-resolution X-ray tomography of the surviving fragments, enabling us to reconstruct the gear function and double the number of deciphered inscriptions. The mechanism predicted lunar and solar eclipses on the basis of Babylonian arithmetic-progression cycles. The inscriptions support suggestions of mechanical display of planetary positions9, 14, 15, now lost. In the second century bc, Hipparchos developed a theory to explain the irregularities of the Moon's motion across the sky caused by its elliptic orbit. We find a mechanical realization of this theory in the gearing of the mechanism, revealing an unexpected degree of technical sophistication for the period.
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