Block regularization of the Kepler problem on surfaces of revolution with positive constant curvature

We consider the Kepler problem on surfaces of revolution that are homeomorphic to S2 and have constant Gaussian curvature. We show that the system is maximally superintegrable, finding constants of motion that generalize the Runge–Lenz vector. Then, using such first integrals, we determine the class of surfaces that lead to block-regularizable collision singularities. In particular we show that the singularities are always regularizable if the surfaces are spherical orbifolds of revolution with constant curvature.