The average density of halo of non-baryonic dark matter?

[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?

Thanks in advance!

 

[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

 

[LavaLynne]

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

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. :(

 

[BiGyElLoWhAt]

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

 

[PeterDonis]

I did look in the homework forum but I could not find a cosmology homework thread.

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:

Homework Statement

Homework Equations

The Attempt at a Solution

[/B]

 

[LavaLynne]

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

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?

 

[LavaLynne]

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

Sorry I'm not sure what the density is

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:

Homework Statement

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?

Homework Equations

M= r v^2/ G

The Attempt at a Solution

[/B]
Try (unsuccessfully) to rework the above equation.

 

[PeterDonis]

I'm not sure what the density is

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

 

[BiGyElLoWhAt]

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

 

[Chalnoth]

[Mass] density is mass per unit volume.

 

[PeterDonis]

I have previously found the average density of non-baryonic dark matter in the Universe by dividing it's percentage into the critical density

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.)

 

[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.