Prospects for a local detection of dark matter with future missions to
  Uranus and Neptune
  We investigate the possibility of detecting the gravitational influence of
dark matter (DM) on the trajectory of prospective Doppler ranging missions to
Uranus and Neptune. In addition, we estimate the constraints such a mission can
provide on modified and massive gravity theories via extra-precession
measurements using orbiters around the ice giants. We employ Monte Carlo-Markov
Chain methods to reconstruct fictitious spacecraft trajectories in a simplified
solar system model with varying amounts of DM. We characterise the noise on the
Doppler link by the Allan deviation $\sigma_{\rm A}$, scaled on the Cassini-era
value of $\sigma^{\rm{Cass}}_{\rm A}= 3 \times 10^{-15}$. Additionally, we
compare the precision of prospective extra-precession measurements of Uranus
and Neptune with the expected rates from simulations, in the context of
modifications to the inverse square law. We estimate that the prospective
mission will be sensitive to DM densities of the order of $\rho_{\rm{DM}} \sim
9 \times 10^{-20} \, (\sigma_{\rm A}/\sigma_{\rm A}^{\rm{Cass}}) $ kg/m$^3$,
while the $1\sigma$ bound on the expected galactic density of $\rho_{\rm{DM}}
\sim 5 \times 10^{-22}$ kg/m$^3$ decreases as $1.0 \times 10^{-20} \,
(\sigma_{\rm A}/\sigma^{\rm{Cass}}_{\rm A})^{0.8}$ kg/m$^3$. An improvement of
two to three orders of magnitude from the baseline Allan deviation would
guarantee a local detection of DM. Only a moderate reduction in ranging noise
is required to rule out Milgrom's interpolating function with solar system
based observations, and improve constraints the graviton mass beyond current
local- or gravitational wave-based measurements. Our analysis also highlights
the potential of future ranging missions to improve measurements of the
standard gravitational parameters in the solar system.
