  The initial orbits of infalling subhalos largely determine the subsequent
evolution of the subhalos and satellite galaxies therein and shed light on the
assembly of their hosts. Using a large set of cosmological simulations of
various resolutions, we quantify the orbital distribution of subhalos at infall
time and its mass and redshift dependence in a large dynamic range. We further
provide a unified and accurate model validated across cosmic time, which can
serve as the initial condition for semi-analytic models. We find that the
infall velocity $v$ follows a nearly universal distribution peaked near the
host virial velocity $V_{\mathrm{h}}$ for any subhalo mass or redshift, while
the infall orbit is most radially biased when $v\sim V_{\mathrm{h}}$. Moreover,
subhalos that have a higher host mass or a higher sub-to-host ratio tend to
move along a more radial direction with a relatively smaller angular momentum
than their low host mass or low sub-to-host ratio counterparts, though they
share the same normalized orbital energy. These relations are nearly
independent of the redshift when using the density peak height as the proxy for
host halo mass. The above trends are consistent with the scenario where the
dynamical environment is relatively colder for more massive structures because
their own gravity is more likely to dominate the local potentials. Based on
this understanding, the more massive or isolated halos are expected to have
higher velocity anisotropy.
