  We present distributions of the orbital parameters of dark matter
substructures at the time of merging into their host halo. Accurate knowledge
of the orbits of dark matter substructures is a crucial input to studies which
aim to assess the effects of the cluster environment on galaxies, the heating
of galaxy disks and many other topics. Orbits are measured for satellites in a
large number of N-body simulations. We focus on the distribution of radial and
tangential velocities, but consider also distributions of orbital eccentricity
and semi-major axis. We show that the distribution of radial and tangential
velocities has a simple form and provide a fitting formula for this
distribution. We also search for possible correlations between the infall
directions of pairs of satellites, finding evidence for positive correlation at
small angular separations as expected if some infall occurs along filaments. We
also find (weak) evidence for correlations between the direction of the infall
and infall velocity and the spin of the host halo.
