Your experiment has several fundamental flaws. Firstly, dark matter is weakly interacting (even with itself) which is why it doesn't "clump" the way atomic matt

Your experiment has several fundamental flaws. Firstly, dark matter is weakly interacting (even with itself) which is why it doesn't "clump" the way atomic matter does. The only "clumping" of dark matter happens on galactic scales, because the typical speeds of dark matter particles are in the range of orbital speeds around galaxies. Our measurements of the dark matter mass in galaxies don't have nearly enough precision to be able to determine the relationship you posit with much certainty. As to your own experimental design, using large spheres of matter, it's completely non-workable. As mentioned above, dark matter particles have velocities in the range of orbital speeds around the galaxy, which is 100s of km/s. So most of the dark matter particles in the vicinity of Earth are going to simply pass through your spheres without stopping, and certainly without increasing their mass. Additionally, you seem to be confused about the scales of densities here. Dark matter is distributed in a somewhat uniform density on interstellar scales (there are density gradients across the galaxy however). Near the Sun the density of dark matter is about 0.0025 solar masses per cubic light-year, or about 5e-20 kg per cubic meter. So, there really is not a lot of dark matter passing through objects around Earth, mass wise. There's only maybe 6 kg within the entire volume of the Earth at any given time, for example.