Solar system planetary orbital motions and dark matter

Abstract

In this paper we explicitly work out the effects that a spherically symmetric distribution ofdark matter with constant density would induce on the Keplerian orbital elements of theSolar System planets and compare them with the latest results in planetary orbitdetermination from the EPM2004 ephemerides. It turns out that the longitudes of periheliaϖ and the meanlongitudes λ are affected by secular precessions. The resulting upper bounds on dark matter density, obtained fromthe EPM2004 formal errors in the determined mean longitude shifts over 90 years, lie in the range10−19–10−20 g cm−3 with apeak 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 mismodelledforces of the dynamical models of EPM2004, yield a global upper bound of7 × 10−20 and 4 × 10−19 g cm−3, respectively.