# Are the planetary orbital effects of the Solar dark matter wake detectable?

## TL;DR

This study assesses the potential detectability of the Solar dark matter wake's effects on planetary orbits, concluding that current observational precision is insufficient to observe such effects unless dark matter density is vastly higher than accepted values.

## Contribution

The paper provides a detailed analysis of how a Solar dark matter wake could influence planetary orbits and range measurements, and evaluates the current observational limits for detecting these effects.

## Key findings

- Dark matter wake effects on planetary orbits are negligible at current measurement precision.
- The simulated Earth-Saturn range signature due to dark matter wake is much smaller than residuals in Cassini data.
- Detecting dark matter wake effects would require local dark matter density to be over 2.5 million times higher than current estimates.

## Abstract

Recently, a discussion about the effects of the anisotropy in the spatial density of Dark Matter in the Solar neighbourhood due to the motion of the Sun through the Galactic halo on the orbital motion of the solar system's planets and their ability to be effectively constrained by the radiotechnical observations collected by the Cassini spacecraft appeared in the literature. We show that the semilatus rectum $p$, the eccentricity $e$, the inclination $I$, the longitude of the ascending node $\Omega$, the longitude of perihelion $\varpi$, and the mean anomaly at epoch $\eta$ of a test particle of a restricted two-body system affected by the gravity of a Dark Matter wake undergo secular rates of change. In the case of Saturn, they are completely negligible, being at the $\simeq 0.1$ millimeter per century and $\simeq 0.05-2$ nanoarcseconds per century level; the current (formal) accuracy level in constraining any anomalous orbital precessions is of the order of $\simeq 0.002-2$ milliarcseconds per century for Saturn. We also numerically simulate the Earth-Saturn range signature $\Delta\rho(t)$ due to the Dark Matter wake over the same time span (2004-2017) covered by the Cassini data record. We find that it is as little as $\simeq 0.1-0.2\,\mathrm{m}$, while the existing range residuals, computed by the astronomers without modeling any Dark Matter wake effect, are at the $\simeq 30\,\mathrm{m}$ level. The local Dark Matter density $\varrho_\mathrm{DM}$ should be larger than the currently accepted value of $\varrho_\mathrm{DM}=0.018\,\mathrm{M}_\odot\,\mathrm{pc}^{-3}$ by a factor of $2.5\times 10^6$ in order to induce a geocentric Kronian range signature so large as to make it discernible in the present-day residuals.