# How to determine the mass of a galaxy?

I am having a slight disagreement with my professor.

We can measure the mass of a distant star cluster from:

A.Its color

C.Its metallicity

D.Smearing of lines in its total spectrum

My thinking was:

Law of Conservation of Energy

Kinetic Energy = Gravitational force

1/2*m*v^2 =  G* m*M/r

v = sqrt(2GM/r)


So it is dependant on both velocity and 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?

• In the title you say "galaxy", but in the text you mention "cluster", which usually means either a stellar (globular) cluster, or a cluster of galaxies. If you mean "galaxy", then the problem with radius is that it's the virial radius, which is not readily measured, since it's dominated by dark matter. In that case, answer D is correct, since it gives you a good measure of the typical velocities, which can then be translated to M (since at a given redshift, there is a moderately tight relationship between M and r). – pela Apr 3 at 11:30

In stellar bounded system you should use virial theorem. By stating that $$-2=$$ and from there you get
$$M=v^2R/G$$