Planetary orbits avoid exact integer ratios because resonance causes instability

Evidence

Exact harmonious ratios involving small integers are specifically weeded out, because they lead to orbital instability. Like Galileo’s bells, the meager but repetitious tugs of one planet on another can begin to add up if they are applied resonantly, resulting in a significant alteration of orbits. In the present configuration of planetary orbits, however, the frequency ratios would have to be very precise to cause trouble. For example, 8 earth orbits is within 0.032% of 13 Venus orbits, but the tug is weak enough that the little 0.032% “error” saves us from having to worry about this resonance. Like a sleepy bell ringer slowly drifting out of sync with the bell, the pulls remove energy as often as they add it, with no net result. The planets are high-Q oscillators; their resonances require precise frequency matching for significant perturbations to occur— lucky for us. — Eric J. Heller, Why You Hear What You Hear- An…, 921

Categorization

• XREF: Connect the ‘sleepy bell ringer’ drifting-out-of-sync analogy to the general resonance/mode-locking concept, and the planet-as-high-Q-oscillator idea to coupled oscillator physics familiar from other mechanics texts.
• SHARE: The 8-Earth/13-Venus orbits being within 0.032% of resonance, saved only by that tiny error, is a great tidbit for a physicist or astronomer friend.
• CANDY: Planetary orbits are fiddled so they avoid pure harmonic ratios because exact resonance would destabilize them — a nice dinner-party fact.