Well, technically, it's not impossible just highly unlikely. As I said, the ancients "solved" the problem with ever more complex sets of epicycles upon epicycles. The problem comes in trying to explain how those epicycles work now that we know the planets aren't just lights on the dome of the sky, but are rather large bodies flying through space under the laws of physics.
I am sure SO will find a way - I'm interested to see what it is!
The problem is even worse if we take into account precession of orbits - particularly Mercury's. Ironically that's explained by general relativity. Or not if you're SO.
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