I have no chops whatever in this field, but it's fun to think of experiments we might do: If I understand current theory, dark matter only interacts with itsel

I have no chops whatever in this field, but it's fun to think of experiments we might do: If I understand current theory, dark matter only interacts with itself and with ordinary matter through gravity. Hence the importance of Vera Rubin's observations [1] that some galaxies were rotating too darned fast to hold together based on the ordinary matter we could see. Gotta be something invisible generating more gravitational force. If so, couldn't we expect larger masses to attract more dark matter than lesser masses? And mightn't very high resolution measurements of those masses' gravitational forces disclose a discrepancy attributable to more dark matter clustering around a larger mass? I think of constructing two spheres, one of lithium (density = 0.534 g/cm^3), the other of platinum (density = 21.45 g/cm^3). Both have equal diameters, and very different masses. Park them out in space - maybe in an orbit inclined 90° to the ecliptic so there's some time when they're far away from the complicating effects of planetary masses. Then release test objects with accurately known masses (think the silicon spheres made for Gravity B Probe's gyroscopes [2]) near each of the two spheres. Minimum approach speeds would be given by the assumption of only ordinary matter in the spheres, no dark matter present. If there is dark matter, and if it accumulates according to gravitational interactions, the test mass approach speeds should be greater than calculated from ordinary matter gravitational force. Also, the larger mass should attract more dark matter and exhibit a greater deviation from ordinary matter force. Depending on the local density of dark matter, one might see the results change over time with differential accumulation of dark matter around the two spheres. Do we have the measurement capabilities to do something like this? I recall LIGO measures distances four orders of magnitude less than the width of a proton. [1] https://en.wikipedia.org/wiki/Vera_Rubin https://en.wikipedia.org/wiki/Vera_Rubin [2] https://einstein.stanford.edu/TECH/technology1.html https://einstein.stanford.edu/TECH/technology1.html