As Danny and I had already discussed offline, John McCarthy et al have described how to implement Steve Gray's solution via a giant game of billiards with Kuiper object cue balls. Gene's tidal deceleration might be handled by noncircular gears feeding a differential. The solution Danny posted (which is only good to 1.5 lsd, sorry) models n bodies with 4 n + 2 gears and no gear fanout, only shaft fanout. A partial solution using two gear fanouts, but lacking Earth and Mars, is 149 293 157 --- --- --- = 29.5350888532671 +.3 lsd 12 83 233 149 293 103 143 (--- ---) --- --- = 87.969257189543 +1 lsd 12 83 41 179 149 152 293 (---) --- --- = 224.700799133144 -.7 lsd 12 107 23 (Don't see how to reuse 293.) <Inter Venerem et Jovem planetas quaeremus.> 149 259 259 174 (--- --) --- --- --- = 4332.82012915184 +.1 lsd 12 83 13 31 149 259 259 321 183 (--- --- --- ---) --- --- = 10755.6986497112 +1 lsd 12 83 13 31 136 The idea here is to spend five gears followed by three. One avenue I didn't explore is to handle one or more intermediate planets with shaft fanout. --rwg ULTONIAN LUNATION, PRICELESS ECLIPSERS, TIME-SHARINGS MISSING-EARTH ASTROMETRIC MERITOCRATS