"Adam P. Goucher" <apgoucher@gmx.com> writes:

I wonder what happens if we have a solar system in the real projective plane, where all conics are indistinguishable? Then there is no definition of 'escaping from orbit'. Designing a set of physical laws invariant under projective transform would be difficult, though.

I'm pretty sure there's no physics in projective spaces. Certainly there's no native notion of distance since there are no parallel lines. So you can't gin up an inverse square law in any obvious way, nor even notions of velocity and acceleration. -- Tom Duff. Crop it, flop it or drop it.