  We investigate the suggestion that the frequencies of the kilohertz and other
QPOs in the emission from neutron stars in low-mass X-ray binaries are
generated by geodesic motion of gas clumps around the star. First we assume,
following previous work, that the dominant frequencies produced by such motions
are the azimuthal frequency \nuk, the apsidal precession frequency \nuap, and
the first overtone of the nodal precession frequency \nunp. We investigate
whether geodesics can be found for which these frequencies agree with the
observed frequencies. Correcting calculational errors made when the geodesic
precession hypothesis was first proposed, we find that \nuk and \nuap disagree
qualitatively with the frequencies of the kilohertz QPOs for infinitesimally or
even moderately eccentric geodesics. These frequencies are similar to the
frequencies of the kilohertz QPOs only for highly eccentric geodesics, with
apastron to periastron ratios \sim3--4; for these geodesics, 2\nunp differs
qualitatively from the frequencies of the low-frequency QPOs. Next we
investigate whether these frequencies would be the dominant frequencies
produced by orbiting clumps. We find that they are not and that the dominant
frequencies are instead harmonics and sidebands of the radial epicyclic
frequency \nur. Finally, we show that gas dynamical constraints restrict the
radii of orbiting clumps to be \ll 10^{-3} of the stellar radius; the
fractional modulation that could be produced by clumps is therefore \ll
10^{-6}. We conclude that there are significant difficulties in interpreting
the kilohertz and low-frequency QPOs as consequences of geodesic motion of gas
clumps.
