Planets move in slow motion compared to electrons...Nevertheless their orbits are far from being stable they only look like being so... But for our live Condensed matter physics is far more important thus please don't start a gravity discussion!
But a system of planets moving outside of a single plane (i.e., in three dimensions) would exhibit wildly chaotic behavior, whereas even in Gryzinski's classical model of electrons orbiting a nucleus in the manner of planets, the electrons exhibit stochastic behavior within well-defined grooves. I conclude from the analogy with the planetary system, which bears a lot of resemblance to Gryzinski's initial setup, that in order for the atomic system to show so much more order than the gravitational system there must also be standing waves which are not in evidence in the planetary system, and Jarek broadly agrees. Where we are still trying to find agreement is whether the standing waves are an intrinsic outcome of the operation Coulomb force (Jarek) or whether there is something else going on (my tentative conclusion). Drawing the analogy between the gravitational and Coulomb forces helps to highlight the key difference in the two systems.