3 ms·
Yup. For more accuracy, you can also vary the timestep by small amounts and rerun the simulation. If they give the same results you assume that numerical errors
by quantumhobbit 10y ago
Yup. For more accuracy, you can also vary the timestep by small amounts and rerun the simulation. If they give the same results you assume that numerical errors aren't a problem.
Depending on the integration scheme used, the errors sometimes bias in the direction of adding energy, so normally numerical errors would look like all the planets gaining velocity and leaving orbit. "Blowing up" the simulation if you will. The wiggles in orbits of the video look like a legit chaotic system to me.
- antognini 10y agoOne thing to note, though, is that if the two calculations match, then that's great and you can trust the results. But even if they don't agree, you still might be able to trust the results. Often these sorts of long-term simulations are only done in a statistical way. You can't trust the results of any individual simulation due to numerical uncertainties, but you can trust the aggregate results of a large set of simulations all run with slightly different initializations. (So, you could run many long term simulations of the Solar System to conclude that there is a 3% chance that Mercury will be ejected.)