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Velocity and redshift

  1. Oct 7, 2010 #1
    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.

  2. jcsd
  3. Oct 8, 2010 #2


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  4. Oct 8, 2010 #3
    Do you want the answer for special relativity or cosmology or both?
  5. Oct 8, 2010 #4
    For cosmology, the one used to get a velocity from the redshift and plug it in the Hubble Law formula.
  6. Oct 8, 2010 #5
    I think , this is the one


    c=light speed constant
    Ho=Hubble constant
  7. Oct 8, 2010 #6

    George Jones

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


    It is fairly easy to derive equation (1) from this paper.
  8. Oct 8, 2010 #7
    I don't think it is correct. For zero density universe it is:


  9. Oct 8, 2010 #8
    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?
  10. Oct 8, 2010 #9
    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.
  11. Oct 8, 2010 #10

    George Jones

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    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.
  12. Oct 8, 2010 #11
    Yes, for empty universe [tex]D=(c/H_{0})ln(1+z)[/tex] gives distance that goes into Hubble's law. Equation (1) you pointed at is general one, and [tex]\dot{R}[/tex] would depend on particular values of [itex]\Omega_{\lambda}[/itex] and [itex]\Omega_{m}[/itex] you choose.
    Last edited: Oct 8, 2010
  13. Oct 8, 2010 #12

    What debate?

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