  We use N-body simulations to explore the influence of orbital eccentricity on
the dynamical evolution of star clusters. Specifically we compare the mass loss
rate, velocity dispersion, relaxation time, and the mass function of star
clusters on circular and eccentric orbits. For a given perigalactic distance,
increasing orbital eccentricity slows the dynamical evolution of a cluster due
to a weaker mean tidal field. However, we find that perigalactic passes and
tidal heating due to an eccentric orbit can partially compensate for the
decreased mean tidal field by energizing stars to higher velocities and
stripping additional stars from the cluster, accelerating the relaxation
process. We find that the corresponding circular orbit which best describes the
evolution of a cluster on an eccentric orbit is much less than its semi-major
axis or time averaged galactocentric distance. Since clusters spend the
majority of their lifetimes near apogalacticon, the properties of clusters
which appear very dynamically evolved for a given galactocentric distance can
be explained by an eccentric orbit. Additionally we find that the evolution of
the slope of the mass function within the core radius is roughly
orbit-independent, so it could place additional constraints on the initial mass
and initial size of globular clusters with solved orbits. We use our results to
demonstrate how the orbit of Milky Way globular clusters can be constrained
given standard observable parameters like galactocentric distance and the slope
of the mass function. We then place constraints on the unsolved orbits of NGC
1261,NGC 6352, NGC 6496, and NGC 6304 based on their positions and mass
functions.
