# Homework Help: The average density of halo of non-baryonic dark matter?

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1. Mar 26, 2015

### LavaLynne

I've got a homework question that I'm particularly stuck on:

Suppose that the halo, assumed spherical, of non-baryonic dark matter surrounding our galaxy has mass ~ 5 x10^12 M solar and radius 0.1 Mpc. What it its average density in Kg m-3?

I think that I need to use the formula M= r v^2/ G

G being the gravitational constant.

What I'm really unsure of is how to rework the formula?

I'm assuming that the average density will be the volume?

I've come up with v= M(r)/G and then square the answer

Am I anywhere close?

2. Mar 26, 2015

### BiGyElLoWhAt

1st: I have no idea how you got from the first eq to the second.
2nd: Homework questions have a special place in the homework forum.
3rd: Average density $\neq$ volume

3. Mar 26, 2015

### LavaLynne

Sorry I'm very new to this site. I did look in the homework forum but I could not find a cosmology homework thread.
Also I'm a mature student and I haven't done this level of mathematics in years so I'm trying to re-learn as I go. The second equation was my best effort to re-work the first. :(

4. Mar 26, 2015

### BiGyElLoWhAt

Ok, so what is density? Let's start there.

5. Mar 26, 2015

### Staff: Mentor

I've moved this thread to Advanced Physics Homework, which is appropriate for cosmology questions.

LavaLynne, please fill out the homework template to help facilitate helper's responses:

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

6. Mar 26, 2015

### LavaLynne

Sorry I'm not sure what the density is as that's what I'm trying to find. I have previously found the average density of non-baryonic dark matter in the Universe by dividing it's percentage into the critical density. Should I be using that?

7. Mar 26, 2015

### LavaLynne

Sorry I'm not sure what the density is
1. The problem statement, all variables and given/known data

Suppose that the halo, assumed spherical, of non-baryonic dark matter surrounding our galaxy has mass ~ 5 x10^12 M solar and radius 0.1 Mpc. What it its average density in Kg m-3?

2. Relevant equations

M= r v^2/ G

3. The attempt at a solution

Try (unsuccessfully) to rework the above equation.

Last edited by a moderator: Mar 26, 2015
8. Mar 26, 2015

### Staff: Mentor

I think he's asking what the definition of density is.

9. Mar 26, 2015

### BiGyElLoWhAt

That is, in fact, what I'm asking.

10. Mar 26, 2015

### Chalnoth

[Mass] density is mass per unit volume.

11. Mar 26, 2015

### Staff: Mentor

That would give an average over the entire universe, yes, but the problem is not asking you for that. It's asking you for the average density in a particular region (the halo surrounding our galaxy). Averaging over the entire universe won't help with that; our galaxy is not an "average" region of the universe--it's much denser on average than the universe as a whole, since the universe as a whole includes all the empty space between galaxies.

(If this still isn't clear, consider a simpler example. Suppose someone asked you the average density of the Earth. You wouldn't use the figures for ordinary matter in the entire universe--what percentage that average density is of the critical density--to calculate that. You would use numbers for the Earth itself. Similarly, the problem is asking you to use numbers for our galaxy's halo to calculate the average density of dark matter there.)

12. Mar 26, 2015

### BiGyElLoWhAt

So its mass PER (divided by) volume? Whats the mass we're dealing with and what's the volume? You have a radius in megaparsecs. Google can convert that for you.