The virialized regions of galaxies and clusters contain significant amounts of substructure ; clusters have hundreds to thousands of galaxies , and satellite systems and globular clusters orbit the halos of individual galaxies .
These orbits can decay owing to dynamical friction .
Depending on their orbits and their masses , the substructures either merge , are disrupted or survive to the present day .

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 .
The eccentricity distributions in the case of an isotropic distribution function are strongly skewed towards high eccentricities , with a median value of typically \sim 0.6 , corresponding to an apo- to pericenter ratio of 4.0 .

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 due to the dominating deceleration at the orbit ’ s pericenter .
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 .

We briefly discuss several applications for our derived distributions of orbital eccentricities and the resulting decay rates from dynamical friction .
We compare the theoretical eccentricity distributions to those of globular clusters and galactic satellites for which all six phase-space coordinates ( and therewith their orbits ) have been determined .
We find that the globular clusters are consistent with a close to isotropic velocity distribution , and they show large orbital eccentricities because of this ( not in spite of this , as has been previously asserted ) .
In addition , we find that the limited data on the galactic system of satellites appears to be different and warrants further investigation as a clue to the formation and evolution of our Milky Way and its halo substructure .