Effect of Sun and Planet-Bound Dark Matter on Planet and Satellite Dynamics in the Solar System

We apply our recent results on orbital dynamics around a mass-varying central body to the phenomenon of accretion of Dark Matter-assumed not self-annihilating-on the Sun and the major bodies of the solar system due to its motion throughout the Milky Way halo. We inspect its consequences on the orbits of the planets and their satellites over timescales of the order of the age of the solar system. It turns out that a solar Dark Matter accretion rate of \approx 10^-12 yr^-1, inferred from the upper limit \Delta M/M= 0.02-0.05 on the Sun’s Dark Matter content, assumed somehow accumulated during last 4.5 Gyr, would have displaced the planets faraway by about 10^-2-10^1 au 4.5 Gyr ago. Another consequence is that the semimajor axis of the Earth’s orbit, approximately equal to the Astronomical Unit, would undergo a secular increase of 0.02-0.05 m yr^-1, in agreement with the latest observational determinations of the Astronomical Unit secular increase of 0.07 +/- 0.02 m yr^-1 and 0.05 m yr^-1. By assuming that the Sun will continue to accrete Dark Matter in the next billions year at the same rate as in the past, the orbits of its planets will shrink by about 10^-1-10^1 au (\approx 0.2-0.5 au for the Earth), with consequences for their fate, especially of the inner planets. On the other hand, lunar and planetary ephemerides set upper bounds on the secular variation of the Sun’s gravitational parameter GM which are one one order of magnitude smaller than 10^-12 yr^-1. Dark Matter accretion on planets has, instead, less relevant consequences for their satellites. Indeed, 4.5 Gyr ago their orbits would have been just 10^-2-10^1 km wider than now. (Abridged)

💡 Research Summary

The paper investigates how the gradual accretion of non‑self‑annihilating dark matter (DM) by the Sun and the major planets could affect orbital dynamics over the age of the Solar System. Building on a previously developed framework for motion around a mass‑varying central body, the authors assume that as the Solar System moves through the Milky Way halo, DM particles are captured and increase the mass of each body at a constant fractional rate. Using the upper limit on the Sun’s present‑day DM content (ΔM/M = 0.02–0.05) they infer an average solar DM accretion rate of roughly 10⁻¹² yr⁻¹ over the past 4.5 Gyr.

Applying the relation (\dot a/a = -\frac{1}{3}\dot M/M) that follows from Kepler’s third law for a slowly varying central mass, they calculate that the Earth’s semimajor axis (≈1 AU) should increase by 0.02–0.05 m per year. This prediction is remarkably close to recent observational determinations of the Astronomical Unit’s secular increase, which report values of 0.07 ± 0.02 m yr⁻¹ and 0.05 m yr⁻¹ from lunar laser ranging and planetary radar data.

However, independent constraints from lunar and planetary ephemerides limit the secular variation of the Sun’s gravitational parameter GM to less than about 10⁻¹³ yr⁻¹, an order of magnitude smaller than the DM‑induced rate required to explain the AU drift. This discrepancy suggests that either the DM accretion rate is overestimated, the DM is not captured as efficiently as assumed, or other mechanisms (e.g., solar mass loss, tidal effects) dominate the observed AU change.

Projecting the same accretion rate into the future, the authors find that planetary orbits would gradually shrink: over the next several billion years the Earth’s orbit could contract by roughly 0.2–0.5 AU, with inner planets experiencing even larger fractional changes. Such a contraction could have profound consequences for planetary climates and long‑term stability, potentially leading to the engulfment of Mercury and Venus as the Sun evolves.

In contrast, DM accretion onto the planets themselves is far less significant because planetary masses are orders of magnitude larger than the amount of DM they could capture. Consequently, the orbital radii of natural satellites would have been only 10⁻²–10¹ km larger 4.5 Gyr ago—well below the detection threshold of current ephemerides.

The study acknowledges several limitations. It assumes a constant DM density and relative velocity throughout the Solar System’s history, ignores possible temporal variations in the Galactic halo, and treats DM as perfectly non‑annihilating with a simple capture cross‑section. It also does not consider feedback on solar structure or nuclear fusion rates that could arise from a growing DM core.

In summary, the paper demonstrates that DM accretion at the level inferred from current upper limits could, in principle, produce a measurable secular increase of the Astronomical Unit and a long‑term inward drift of planetary orbits. Yet the tighter observational bounds on (\dot{GM}) and the many astrophysical uncertainties mean that the hypothesis remains speculative. Future improvements in high‑precision ranging, spacecraft tracking, and Galactic DM flow modeling will be essential to either confirm or rule out the proposed DM‑driven orbital evolution.