Limits on dark matter and cosmological constant from solar system dynamics

Abstract

We discuss the influence of the cosmological constant $\Lambda$ on the solar system dynamics. Observational constraints are derived from measurements of the periastron advance of the planets. Moreover, we consider the change in the mean motion due to $\Lambda$. Up to now, Earth and Mars data give the best constraint, $\Lambda~\sim~10^~\mathrm{km}^$. If properly accounting for the gravito-magnetic effect, this upper limit on $\Lambda$ could greatly improve in the near future thanks to new data from planned or already operating space-missions. Dark matter or modifications of the Newtonian inverse-square law in the solar system are discussed as well. Variations in the 1/r2 behavior are considered in the form of either a possible Yukawa-like interaction or a modification of gravity of MOND type.