# Velocity and redshift

1. Oct 7, 2010

### TrickyDicky

What is the formula used to convert the measured redshift into a velocity?, not the approximated formula for low speeds v=cz , but the more general and accurate one.

Thanks.

2. Oct 8, 2010

3. Oct 8, 2010

### Passionflower

Do you want the answer for special relativity or cosmology or both?

4. Oct 8, 2010

### TrickyDicky

For cosmology, the one used to get a velocity from the redshift and plug it in the Hubble Law formula.

5. Oct 8, 2010

### TrickyDicky

I think , this is the one

v=[((1+z)^2-1)/((1+z)^2+1)]c=Ho*D

c=light speed constant
Ho=Hubble constant
D=distance
v=velocity

6. Oct 8, 2010

### George Jones

Staff Emeritus
No, this isn't correct. See section 3 from

http://arxiv.org/abs/astro-ph/0310808.

It is fairly easy to derive equation (1) from this paper.

7. Oct 8, 2010

### Calimero

I don't think it is correct. For zero density universe it is:

$$v=H_{0}D$$

$$D=(c/H_{0})ln(1+z)$$

8. Oct 8, 2010

### TrickyDicky

The one I wrote is exactly equation (2) from that paper.

This is not exactly what I wanted. I asked for the way to translate from z to velocity for high z or at least >1, this must be a very common formula for cosmologists, I'd say.
The formula I used maybe is not correct for the Hubble law but I'm interested in the first part, express v as a function of z, is that so difficult?

9. Oct 8, 2010

### TrickyDicky

Ok, I see what you mean, after looking at the paper and the formula again, I see what you mean, but according to some cosmologists the formula that doesn't give superluminal velocities is alright too, and anyway this is a cosmology debate that I find artificial and tiresome and I don't really wanna get into it , I think it's been discussed enough in these forums, just remember that people as prestigious as David Hogg supports the view of cosmological redshift as Doppler.

10. Oct 8, 2010

### George Jones

Staff Emeritus
Yes, but this is not the correct equation to use for cosmology.
This expression and the expression that TrickyDicky gave in post #5 are both true in special relativity, i.e., in an empty universe. The conventions used for distance, however, are different in posts #5 and #7, and this leads to differing expressions for speed.

11. Oct 8, 2010

### Calimero

Yes, for empty universe $$D=(c/H_{0})ln(1+z)$$ gives distance that goes into Hubble's law. Equation (1) you pointed at is general one, and $$\dot{R}$$ would depend on particular values of $\Omega_{\lambda}$ and $\Omega_{m}$ you choose.

Last edited: Oct 8, 2010
12. Oct 8, 2010

What debate?