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The Cavendish experiment first determined the mass of the Earth and (arguably) the gravitational constant. However, given the ubiquitous nature of dark matter, it seems reasonable that at least some of Earth's total mass comes from dark matter accumulated at the center of the Earth.

If this is the case, Earth's calculated mass would include the masses of both 'light' matter and dark matter. The Cavendish experiment would be offset less by this, because most of the dark matter in the Earth would be near to its gravitational center (which is far from the site of the experiment). So G would be more well-estimated than the light mass of the Earth.

This would all be academic, if it weren't for the fact that models of the interior of the Earth assume that all matter is light matter (I presume).

We know the mass of individual electrons and protons to high precision from particle physics, as well as the larger mass of atoms from the interactions of the strong force; this knowledge can used to estimate what materials Earth contains given its density (from mass and size). But the true light density of the Earth could be significantly less than Earth's combined masses would suggest. It seems to me that we could be greatly overestimating the amount of light matter inside the earth, leading to an overly-dense geologic model of the Earth's core.

Is this possible? Is it likely? If not, why not?

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Dark matter does not readily "accumulate". If(?) it exists then it interacts very weakly with normal matter and is primarily influenced by gravity. The Earth's gravity is far too small to make a local concentration of dark matter. The local dark matter would be moving in the Galactic potential at speeds similar to that of the Sun around the Galaxy ($\sim 250$ km/s); this is too fast to be gravitationally captured by the Earth and the cross-section to inelastic interaction by any other means is thought to be too small (this is why it is called dark matter - there are no electromagnetic interactions) to catch dark the matter. The same may not be true for the Sun, which offers a deeper gravitational potential and a "thicker" target (e.g. Vincent et al. 2015).

In fact there is little dark matter in the local disk plane of our Galaxy at all. It is estimated that the local dark matter density is around $\sim 0.01$ $M_{\odot}$/pc$^3$ (Garbari et al. 2012, Bovy & Tremaine 2012) corresponding to only a few $10^{-22}$ kg/m$^3$. For comparison, the density of the interplanetary medium is abut 100 times greater.

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  • $\begingroup$ Isn't there some DM distribution models with a local accumulation in the Sun ? (I'm mainly thinking about the models targeted by neutrino telescopes in directional detection) $\endgroup$ – Michaël Ughetto Mar 14 '15 at 11:34
  • $\begingroup$ @MichaëlUghetto I believe you are right. My answer (and the question) was about the Earth. But I'll edit to be clear. $\endgroup$ – Rob Jeffries Mar 14 '15 at 11:36

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