Converting Redshift to Velocity: The Accurate Formula Explained

In summary, the formula used to convert the measured redshift into a velocity for cosmology is v=[((1+z)^2-1)/((1+z)^2+1)]c=Ho*D, where c is the speed of light, Ho is the Hubble constant, D is the distance, and v is the velocity.
  • #1
TrickyDicky
3,507
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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.
 
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  • #3
TrickyDicky said:
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?
 
  • #4
Passionflower said:
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.
 
  • #5
TrickyDicky said:
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
 
  • #6
TrickyDicky said:
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.
 
  • #7
TrickyDicky said:
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:

[tex]v=H_{0}D[/tex]

[tex]D=(c/H_{0})ln(1+z)[/tex]
 
  • #8
George Jones said:
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.

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

[tex]v=H_{0}D[/tex]

[tex]D=(c/H_{0})ln(1+z)[/tex]
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
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 want to 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
TrickyDicky said:
The one I wrote is exactly equation (2) from that paper.

Yes, but this is not the correct equation to use for cosmology.
Calimero said:
I don't think it is correct. For zero density universe it is:

[tex]v=H_{0}D[/tex]

[tex]D=(c/H_{0})ln(1+z)[/tex]

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
George Jones said:
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 [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:
  • #12
TrickyDicky said:
...and anyway this is a cosmology debate that I find artificial and tiresome and I don't really want to 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?

TrickyDicky said:
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.

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

1. How is redshift measured?

Redshift is measured by comparing the observed wavelength of an object's light to the expected or known wavelength. This can be done using a spectrometer or spectrograph.

2. What is the formula for converting redshift to velocity?

The formula for converting redshift to velocity is v = c * (z + 1), where v is the velocity, c is the speed of light, and z is the redshift. This is known as the Hubble-Lemaître law.

3. Why is it important to convert redshift to velocity?

Converting redshift to velocity allows scientists to determine the speed at which objects in the universe are moving away from us. This is a crucial component of understanding the expansion of the universe and the cosmic distance ladder.

4. How accurate is the redshift to velocity formula?

The redshift to velocity formula is considered accurate for small redshift values, typically less than 0.1. However, for larger redshift values, the formula may not accurately reflect the true velocity due to the effects of general relativity and the expansion of the universe.

5. Can redshift be used to determine the distance of an object?

Yes, redshift can be used in combination with the Hubble-Lemaître law to estimate the distance of an object from Earth. This is known as the cosmological redshift and is a key tool in measuring the distances of objects in the universe.

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