# Velocity and redshift

by TrickyDicky
Tags: redshift, velocity
 P: 3,035 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.
P: 1,555
 Quote by 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.
Do you want the answer for special relativity or cosmology or both?

P: 3,035
Velocity and redshift

 Quote by Passionflower Do you want the answer for special relativity or cosmology or both?
For cosmology, the one used to get a velocity from the redshift and plug it in the Hubble Law formula.
P: 3,035
 Quote by TrickyDicky For cosmology, the one used to get a velocity from the redshift and plug it in the Hubble Law formula.
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
Mentor
P: 6,242
 Quote by 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
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.
P: 256
 Quote by 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
I don't think it is correct. For zero density universe it is:

$$v=H_{0}D$$

$$D=(c/H_{0})ln(1+z)$$
P: 3,035
 Quote by George Jones 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.
The one I wrote is exactly equation (2) from that paper.

 Quote by Calimero I don't think it is correct. For zero density universe it is: $$v=H_{0}D$$ $$D=(c/H_{0})ln(1+z)$$
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?
 P: 3,035 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.
Mentor
P: 6,242
 Quote by TrickyDicky The one I wrote is exactly equation (2) from that paper.
Yes, but this is not the correct equation to use for cosmology.
 Quote by Calimero I don't think it is correct. For zero density universe it is: $$v=H_{0}D$$ $$D=(c/H_{0})ln(1+z)$$
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.
P: 256
 Quote by George Jones 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.
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.
P: 256
 Quote by TrickyDicky ...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.

What debate?

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

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