  The velocity distribution of dark matter near the Earth is important for an
accurate analysis of the signals in terrestrial detectors. This distribution is
typically extracted from numerical simulations. Here we address the possibility
of deriving the velocity distribution function analytically. We derive a
differential equation which is a function of radius and the radial component of
the velocity. Under various assumptions this can be solved, and we compare the
solution with the results from controlled numerical simulations. Our findings
complement the previously derived tangential velocity distribution. We hereby
demonstrate that the entire distribution function, below 0.7 v_esc, can be
derived analytically for spherical and equilibrated dark matter structures.
