Without friction, resonances can both expel particles and later restore them indefinitely.

Evidence

If friction does not take over to assure the “max power” (see section 10.5) alignment of velocity and force (there is very little friction in the vacuum of space), resonances can just as easily bleed energy out of a system as pump it in. If nothing else is around, particles expelled from their lanes by resonance can find their way back: once expelled, force and velocity drift by 180 degrees, and particles reverse their history, winding back into their former orbit. (A graphic example of this is a resonant double pendulum; see figure 10.6.) This can happen repeatedly and stably; essentially forever. Dione and Enceladus, two of Saturn’s moons, are caught in an exact 1:2 resonance with each other in just this way. So are Tethys and Mimas, caught in a 2:4 resonance. There is even a resonance involving three moons: the 1:2:4 Ganymede-Europa-Io caught in the so-called Laplace resonance. This is a fine example not only of celestial mechanics but also of what all high-Q resonant systems can do. — Eric J. Heller, Why You Hear What You Hear- An…, 926

Categorization

• XREF: Connects to the reader’s existing interest in resonance as a general physical principle — the same high-Q behavior that applies to sound resonators (his hearing question) applies to celestial mechanics.
• SEED: Angle: orbit reversal as a toy model for how resonators store and return energy — a bridge between planetary physics and audio resonator design.