Relativistic effects and dark matter in the Solar system from observations of planets and spacecraft

Abstract

The high precision of the latest version of the planetary ephemeris EPM2011 enables one to explore more accurately a variety of small effects in the solar system. The processing of about 678 thousand of position observations of planets and spacecrafts for 1913--2011 with the predominance of modern radar measurements resulted in improving the PPN parameters, dynamic oblateness of the Sun, secular variation of the heliocentric gravitational constant $GM_{\odot}$, and variation range of the gravitational constant $G$. This processing made it possible to estimate the potential additional gravitational influence of dark matter on the motion of the solar system bodies. The density of dark matter ${\rho}_{dm}$, if any, turned out to be substantially below the accuracy achieved by the present determination of such parameters. At the distance of the orbit of Saturn the density ${\rho}_{dm}$ is estimated to be under $1.1\cdot10^{-20}$ g/cm$^3$, and the mass of dark matter in the area inside the orbit of Saturn is less than $7.9\cdot10^{-11}$ M$_{\odot}$ even taking into account its possible tendency to concentrate in the center.