OP was referring to an orbit in the dynamical systems sense: https://en.wikipedia.org/wiki/Orbit_(dynamics) https://en.wikipedia.org/wiki/Orbit_(dynamics) which

OP was referring to an orbit in the dynamical systems sense: https://en.wikipedia.org/wiki/Orbit_(dynamics) https://en.wikipedia.org/wiki/Orbit_(dynamics) which is far more general. It simply refers to a dynamical system where the trajectory of a particle repeats. If you have a system of particles in 2D space, governed by central forces between the particles, you won't have any particles that behave periodically in general, regardless of what those forces actually are. (There's actually some caveats to that statement. I believe the theorem OP's quoting assumes that the system has rotational symmetry, but giving up that symmetry may or may not actually give you stable orbits). Having some underlying periodicity is pretty important for more complex structures to emerge, otherwise it's just random chaotic motion.