  We find that the momentum conjugate to the relative distance between two
gravitating particles in their center of mass frame is a hyperbolic angle. This
fact strongly suggests that momentum space should be taken to be a hyperboloid.
We investigate the effect of quantization on this curved momentum space. The
coordinates are represented by non commuting, Hermitian operators on this
hyperboloid. We also find that there is a smallest distance between the two
particles of one half times the Planck length.
