  The central force problem is considered in a three dimensional space in which
the Poisson bracket among the spatial coordinates is the one by the SU(2) Lie
algebra. It is shown that among attractive power-law potentials it is only the
Kepler one that all of its bound-states make closed orbits. The analytic
solution of the path equation under the Kepler potential is presented. It is
shown that except the Kepler potential, in contrast to ordinary space, all of
the potentials for which all of the almost circular orbits are closed are
non-power-law ones. For the non-power-law potentials examples of the numerical
solutions of the path equations are presented.
