The Antikythera Mechanism: The World's First Analog Computer, ca.140 BC

Here we stray into Erich von Daniken territory: a shipwreck near Crete over 2000 years old yields technology so advanced it would not be rivaled for over a thousand years. The Antikythera Mechanism is so advanced it leaves all who study it in wonderment, unable to explain its existence. I must admit, I love this stuff.

The mechanism explores the relationship between lunar months -- the time it takes for the moon to cycle through its phases, say, full moon to full moon -- and calendar years. The gears had to be cut precisely to reflect this complex relationship; 19 calendar years equal 235 lunar months.

By turning the gear mechanism, which included what [Prof.] Edmunds called a beautiful system of epicyclic gears that factored in the elliptical orbit of the moon, a person could check what the sky would have looked like on a date in the past, or how it would appear in the future.

The mechanism was encased in a box with doors in front and back covered with inscriptions -- a sort of instruction manual. Inside the front door were pointers indicating the date and the position of the sun, moon and zodiac, while opening the back door revealed the relationship between calendar years and lunar months, and a mechanism to predict eclipses.

To state the obvious, how on earth did the ancient Greeks, lacking astronomical instruments, even know of the moon's elliptical orbit? How did they even know of planetary orbits at all?

And how did they manage to measure that orbit with such precision that they could build an Ancient Cartier Mystery Clock that would reliably predict lunar cycles and eclipses in perpetuity?