  We consider the Kepler problem on surfaces of revolution that are
homeomorphic to $S^2$ and have constant Gaussian curvature. We show that the
system is maximally superintegrable, finding constants of motion that
generalize the Runge-Lentz 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.
