Newton's Off-center Circular Orbits and the Magnetic Monopole

Introducing a magnetic field into Newton's off-center circular orbits potential in such way as to preserve the E = 0 dynamical symmetry leads to a unique choice that can be identified as the inclusion of a magnetic monopole in the inverse stereographically projected problem. One finds also a phenomenological correspondence with that of the linearly damped Kepler model. The presence of the monopole field deforms the symmetry algebra by a central extension, and the quantum mechanical version of this algebra reveals a number of zero modes equal to that counted using the index theorem of elliptic operators.