Solar System planetary orbital motions and dark matter

TL;DR

This study investigates how a uniform dark matter distribution would influence Solar System planetary orbits, using precise ephemerides data to set upper bounds on dark matter density.

Contribution

It provides the first explicit calculations of dark matter effects on planetary orbital elements and derives new upper limits based on observational data.

Findings

Upper bounds on dark matter density range from 10^-19 to 10^-20 g/cm^3.

Secular precessions of orbital elements are affected by dark matter.

Combined orbital element analysis yields tighter constraints.

Abstract

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.