Thanks, Warren! Simple CF approximations: Mercury/Earth = 6/25, 7/29 Venus/Earth = 8/13, 235/382 Mars/Earth = 15/8, 32/17, 47/25 Jupiter/Earth = 83/7, 261/22 Saturn/Earth = 265/9, 1119/38 Just choosing the denominators of a few of these, I get lcm(9,7,8,13,25) = 163,800 or lcm(29,382,25,22,38) = 57,882,550 So just doing the planets alone would give us a period of at least 163,800 years, and possibly as much as 57 million years. Could we say that the Greeks had already approximated the k-T event at 65 million years ago? :-) At 08:57 AM 12/6/2012, Warren Smith wrote:

Here's some data I got from some random web page http://www.princeton.edu/~willman/planetary_systems/Sol/ giving alleged orbital periods in "years."

Mercury := 0.2408467; Venus := 0.61519726; Earth := 1.0000174; Mars := 1.8808158; Jupiter := 11.862615; Saturn := 29.447498; #Greeks knew the above planets only Uranus := 84.016846; Neptune := 164.79132; Pluto := 248.0208;

eccentricities are known to only 3-5 figures, relative masses to only 4-5.

Using continued fractions, you may enjoy spotting near-rational ratios Venus/Earth=0.61518656 vs 8/13=0.61538461 Mars/Earth=1.88078307 vs 1057/562=1.88078292