  In this paper we explicitly work out the effects that a spherically symmetric
distribution of dark matter with constant density would induce on the Keplerian
orbital elements of the Solar System planets and compare them with the latest
results in planetary orbit determination from the EPM2004 ephemerides. It turns
out that the longitudes of perihelia and the mean longitudes are affected by
secular precessions. The resulting upper bounds on dark matter density,
obtained from the EPM2004 formal errors in the determined mean longitude shifts
over 90 years, lie in the range 10^-19-10^-20 g cm^-3 with a peak of 10^-22 g
cm^-3 for Mars. Suitable combinations of the planetary mean longitudes and
perihelia, which cancel out the aliasing impact of some of the unmodelled or
mismodelled forces of the dynamical models of EPM2004, yield a global upper
bound of 7 10^-20 g cm^-3 and 4 10^-19 g cm^-3, respectively.
