I can see how orbital mechanics would lead to these sorts of small-integer ratios being true for arbitrary periods and then disappearing, yet this fact still se

I can see how orbital mechanics would lead to these sorts of small-integer ratios being true for arbitrary periods and then disappearing, yet this fact still seems unintuitive/unsatisfying somehow. I think it's because we're so all familiar with quantum electrodynamics now, that it actually seems somewhat counterintuitive that the (stable) orbits of planets aren't quantized valence shells!