Is complexity an argument against design?

Good question I've never much thought about Lagrange points so now's a good time![edit - removed while checking a possible significant mistake!][edit - restored having checked]Ok, a quick look at the maths and some sketches... Yes!On an elliptical orbit of the primary masses, the third body will have a different orbit constructed from the first, using the construction of the equilateral triangle. It appears that the semi-major axes of the Lagrange orbits are 60 degrees either side of the primary orbit, but the same size. Very cool It should be pointed out that this is all an approximation, with the third mass negligible and the second mass significantly smaller than the first (probe <<<< Earth << Sun). Three body problems are in general unsolvable and highly chaotic...[ABE]I should have remembered this... we are in a special case of Lagrange's Solution to the three body problem. If the three bodies form an equilateral triangle , each equation of motion decouples and you get three elliptical orbits of the same period and same common focus. In our case, one body is so large that it's orbit is actually just a wiggle, and it essentially sits on the common focus while the other two bodies orbit elliptically, with an angle of 60 degrees as mentioned.Very very cool This message has been edited by cavediver, 04-18-2006 05:36 AM