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No, I regret this isn't an entry on Warren Ellis's landmark sci-fi satire comic book series (I'm still figure out a way to make it apply to poi ;), the title is a great excuse to give it a plug. The planetary I'm talking about is the system by which planets rotate around a solar mass and create systems of compound elliptical orbits.
I've been trying to come up with natural phenomenon that match the properties of poi and other object manipulation spinning both as a way to double-check our ideas of poi motion and to see what applications there are for thinking of poi as a mathematical model for other types of motion.
The two models I've found that best fit are the orbits of planets and moons in a solar system and the orbits of electrons in atoms and simple molecules and compounds, though fascinatingly enough they yield very different systems of motion. Atoms yield very chaotic globes in which orbits may freely swing this way and that while planetary motion seems to stabilize more or less along a single axis. Given that the majority of poi spinning occurs with both poi spinning along the same plane (and that the extensions of this, flowers, also occur in the same plane), I think it's worth asking why it is that planetary motion seems to collapse to a single plane like this and the most simple poi movements to learn also seem to possess this property.
The best answer I've been able to come up with after some helpful suggestions from friends on Facebook is mutual attraction--that is planets are attracted to each other as well as to the sun. Likewise, poi heads are attracted both to the hand and the shoulder in the course of poi motion and both are attracted to the center of the Earth. Given the pull they all have on each other, it's little wonder that the most stable plane orientation for them all seems to be all along the same one, rather than the multiple planes one finds in subatomic interactions.
Here, the reason for the multiplicity of planes is that instead of being attracted to each other, electrons are repulsed by each other, making it so their planes are constantly being reformed and shifted over and over again. One could probably approximate this effect by putting magnets in the heads of one's poi that were powerful enough to push away from each other from a few inches in distance or by making it a rule in spinning that plane-bending should always occur when poi are within a few inches of each other. In fact, such a style might really be fascinating to watch.
Neither system is a perfect model for poi, but they both lend themselves to some fascinating spinning thought experiments. In fact, I'm willing to bet that going through planetary rotation models will yield some shapes both familiar and mindblowing to us.