# Where's the invisible matter?

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In a region of space are a bunch of stars in circular orbits at different radii and some unknown amount of non-visible matter. You observe the speeds of the stars and notice that the tangential velocity of each star is a constant $v_0$, independent of radius. If the non-visible matter is distributed spherically symmetrically around the center of the galaxy, what is the ratio of the density of the non-visible matter at some distance 10R to the density at some distance R?

### Details and assumptions

• You may assume the total mass of the stars is negligible compared to the mass of the non-visible matter.
3 tries left ·
* Use decimal answers like 3.001 or 6E-10 for 6×10-10. Enter answers to three significant figures – you will not be penalized for too many significant figures.