Effect of the Solar dark matter wake on planets
  The Galaxy is conventionally thought to be surrounded by a massive dark
matter (DM) halo. As the Sun goes through this halo, it excites a DM wake
behind it. This local asymmetry in the DM distribution would gravitationally
affect the motions of Solar System planets, potentially allowing the DM wake to
be detected or ruled out. Hernandez (2019) recently calculated that the
DM-induced perturbation to Saturn's position is 252 metres net of the effect on
the Sun. No such anomaly is seen in Saturn's motion despite very accurate
tracking of the Cassini spacecraft, which orbited Saturn for >13 years. Here,
we revisit the calculation of how much Saturn would deviate from Keplerian
motion if we fix its position and velocity at some particular time. The DM wake
induces a nearly resonant perturbation whose amplitude grows almost linearly
with time. We show that the Hernandez (2019) result applies only for an
observing duration comparable to the ${\approx 250}$ million year period of the
Sun's orbit around the Galaxy. Over a 100 year period, the perturbation to
Saturn's orbit amounts to <1 cm, which is quite consistent with existing
observations. Even smaller perturbations are expected for the terrestrial
planets.
