  The closedness of orbits of central forces is addressed in a three
dimensional space in which the Poisson bracket among the coordinates is that of
the SU(2) Lie algebra. In particular it is shown that among problems with
spherically symmetric potential energies, it is only the Kepler problem for
which all of the bounded orbits are closed. In analogy with the case of the
ordinary space, a conserved vector (apart from the angular momentum) is
explicitly constructed, which is responsible for the orbits being closed. This
is the analog of the Laplace-Runge-Lenz vector. The algebra of the constants of
the motion is also worked out.
