Ancient astronomers, planetary conjunctions, and epicycles How did ancient astronomers predict planetary conjunctions?  I know they used a system of epicycles to represent the path of planets, but finding the point and time of alignment of two planets still seems like a rather difficult problem.
Supposing just a model system of two planets each with a single epicycle (that is, they have the larger circular orbit and a smaller epicycle sub orbit), how would an ancient astronomer predict conjunctions (where their apparent positions in the sky are identical)?  That is, what algorithm were they using?  Are there any modern methods that make the problem easier (it doesn't seem to be a problem where a heliocentric solar system makes things easier).
I'm guessing that ancient mathematicians just had a lot of spare time to crunch numbers, and the algorithm was basically something primitive and numeric.  But I wonder if there's any clever mathematics involved, since there was at least 1000 years of smart guys working on the problem.
 A: As explained in Wikipedia "Babylonian astronomers had developed arithmetical techniques for calculating astronomical phenomena and Greek astronomers such as Hipparchus had produced geometric models for calculating celestial motions". The oldest Astronomical Tables known were the Babylonian clay tablets which contained the future "Pythagorean theorem", the solar and lunar eclipses, the length of the year with an error of 0.001% only and so on. Hipparcus and the Greeks borrowed much from the Babylonians as well as Ptolemy after them. Ptolemy's very precise observations appeared in his famous Almagest (all the trigonometry required was in his books) and these precise tables were only superseded in 1551 by Kepler's Rudolphine Tables using Brahe's as well as his own observations and computations (reinterpreted with his three laws and introducing the recent logarithms). Of course exact Astrologic predictions required such tables! ;-) Titles of Ptolemy's book are revealing. 
Concerning the Greeks some centuries B.C. they could have used the very interesting (Angela and pedja's link) Antikythera and other mechanisms.
