  We examine the distributions of eccentricities of orbits within mass
distributions like those we see for galaxies and clusters. A comprehensive
understanding of these orbital properties is essential to calculate the rates
of physical processes relevant to the formation and evolution of galaxies and
clusters. We derive the orbital eccentricity distributions for a number of
spherical potentials. These distributions depend strongly on the velocity
anisotropy, but only slightly on the shape of the potential. We also present
high resolution N-body simulations of the orbital decay of satellite systems on
eccentric orbits in an isothermal halo. The dynamical friction timescales are
found to decrease with increasing orbital eccentricity, but the dependence is
weaker than previously suggested. The orbital eccentricity stays remarkably
constant throughout the decay; although the eccentricity decreases near
pericenter, it increases again near apocenter, such that there is no net
circularization. Finally, we discuss a number of applications. We find that the
distribution of orbital eccentricities of the globular clusters in the Milky
Way is consistent with a close to isotropic velocity distribution. The limited
data on the galactic system of satellites, however, appears to be different and
warrants further investigation as a clue to the formation and evolution of our
Milky Way and its halo substructure.
