I am having a slight disagreement with my professor.
We can measure the mass of a distant star cluster from:
D.Smearing of lines in its total spectrum
My thinking was:
Law of Conservation of Energy Kinetic Energy = Gravitational potential energy 1/2*m*v^2 = G* m*M/r v = sqrt(2GM/r)
So it is dependant on both velocity and radius.
Answer choice D would give you the velocity but I responded with answer choice B, radius.
After talking it over with my professor, she responded with:
If we think about it conceptually, the dominant parameter is the velocity. In other words, you can get a meaningful estimate of the cluster mass from the velocity dispersion without knowing the radius (because all clusters are the "same" size), but not vice versa.
So I'd say it still seems pretty clear that the best answer is the velocities.
Is she right or is the question worded poorly?