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- Can a horseshoe orbit be considered as two moons following hyperbolic orbits around each other?

Epimetheus and Janus switch places periodically, because they follow a horseshoe orbit around Saturn, which is considered a "pseudo-orbit" around each other. I'm thinking that if you look at the conic sections - taking an elliptical orbit of two moons to greater and greater extremes until they don't come back together again - you might end up at a horseshoe orbit, and that you might then view that as a hyperbolic orbit in which, due to the presence of the planet, the moons must inevitably meet up again. Maybe you could represent it as a hyperbolic orbit inside some manifold or curved space?? My intuition is sniffing around and I'm wondering if you can point it in the right direction. :)