On 02/18/2011 10:17 PM, Rich Murray wrote: > does classical mechanics always fail to predict or retrodict for 3 or > more Newtonian gravity bodies? Rich Murray 2011.02.18 > [ ... ] > > In fall, 1982, I wrote a 200-line program in Basic for the > Timex-Sinclair $100 computer with 20KB RAM that would do up to 4 > bodies in 3D space... > [ ... ] > so I doubted that there is any mathematical > basis for the claim that classical mechanics predicts the past or > future evolution of any system with over 2 bodies, leading to a > conjecture that no successful algorithm exists, even without any close > encounters. > > Has this been noticed by others?
See, for example, http://en.wikipedia.org/wiki/Stability_of_the_Solar_System#Digital_Orrery There are also far better algorithms than what you were using, which, I'm sure, was a simple integrator of the nonlinear system of equations. Simply cutting the time step doesn't do much for you if the basic algorithm isn't very accurate. See, for example, http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TJ5-46DFTHW-8W&_user=10&_coverDate=12%2F31%2F1987&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=59646ea61335b206d3a7cea0bed0ce8d&searchtype=a <http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TJ5-46DFTHW-8W&_user=10&_coverDate=12%2F31%2F1987&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=59646ea61335b206d3a7cea0bed0ce8d&searchtype=a> (sorry, I don't have the full text, but the abstract sounds interesting.)
