(March 13, 2015 at 11:51 am)Smaug Wrote:(March 13, 2015 at 6:30 am)jesus_wept Wrote: And I don't think it takes much computational power to approximate the orbits of the planets so your c64 probably wasn't too far out. In astronomical terms at least.
In fact it does depending on how precise you want the result to be. If simple Kepler laws based model is enaugh any computer will do fine. If you want a highly precise model you'd have to have a very powerful machine. Since there's no general solution for the N-body problem and no way to obtain analytical solution for a corresponding Cauchy problem (i.e. analytically solve the system's differential equations with set initial conditions) the only way to obtain the solution is through numerical computatuon. Longer timespans lead to larger computational errors. In order to eliminate computational errors one has to increase computational power.
I'm aware of this. IIRC it was only about 10 years ago that the orbit of the earth was mapped properly with a supercomputer, but to just approximate the orbits, a c64 should be able to do it. Either way you can get much more accurate models and powerful computers these days and I'm not advising anyone to study cosmology with a c64.
