Solar System planetary orbital motions and dark matter

In this brief note we explicitly work out the effects that a spherically symmetric distribution of dark matter 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. Even if realistic errors on mean longitudes may be one order of magnitude larger, such results are up to 2-3 orders of magnitude better than other Solar System-based constraints