# Effect of the Solar dark matter wake on planets

## TL;DR

This paper investigates the gravitational effects of the solar dark matter wake on planetary motions, finding that over a century, the perturbations are negligible and consistent with current observations, challenging previous claims of detectable anomalies.

## Contribution

The study revises previous calculations of dark matter wake effects, demonstrating that the induced planetary perturbations are much smaller over realistic observation periods.

## Key findings

- Perturbations to Saturn's orbit are less than 1 cm over 100 years.
- No detectable anomalies in planetary motions due to the dark matter wake.
- Previous estimates overestimated the effect by assuming longer observation durations.

## Abstract

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.