# Gravitational redshift units

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## Summary:

gravitational redshift units seem to be given as a velocity and not as a ratio
I noticed in physics papers that gravitational redshift is expressed in m/s or km/s.
I assume that this must be the equivalent velocity to produce that same redshift.

So for example, if the gravitational redshift was measured as 3x10 -4 then;

z= v/c

3x10^-4= v/c

v = 9x10^4 m/s

v=90km/s

Is this what they are doing? Why do they prefer velocity over the ratio z?

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## Answers and Replies

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Staff Emeritus
2019 Award
I noticed in physics papers
Can you give an example?

Hi,

This is from Wikipedia which refers to papers and gravitational redshift in km/s;
https://en.wikipedia.org/wiki/Gravitational_redshift

Initial observations of gravitational redshift of white dwarf stars
A number of experimenters initially claimed to have identified the effect using astronomical measurements, and the effect was considered to have been finally identified in the spectral lines of the star Sirius B by W.S. Adams in 1925.[1] However, measurements by Adams have been criticized as being too low[1][2] and these observations are now considered to be measurements of spectra that are unusable because of scattered light from the primary, Sirius A.[2] The first accurate measurement of the gravitational redshift of a white dwarf was done by Popper in 1954, measuring a 21 km/s gravitational redshift of 40 Eridani B.[2]

The redshift of Sirius B was finally measured by Greenstein et al. in 1971, obtaining the value for the gravitational redshift of 89±19 km/s, with more accurate measurements by the Hubble Space Telescope, showing 80.4±4.8 km/s.

Staff Emeritus
2019 Award
It looks like they are converting it to the equivalent Doppler shift.

PeterDonis
Mentor
2019 Award
Moderator's note: Thread moved to relativity forum.

PeterDonis
Mentor
2019 Award
I assume that this must be the equivalent velocity to produce that same redshift.
Yes, as @Vanadium 50 says, they are giving the recession velocity that would produce a Doppler redshift the same as the observed gravitational redshift.

I don't think there's any deep reason for this; it was simply that cosmologists, who were the target audience of the papers mentioned in the Wikipedia article, were used to giving redshifts in velocity units because that is how they are typically thought of in cosmology--not so much because of the ordinary Doppler shift in flat spacetime, but because cosmologists are used to thinking of redshifts due to the expansion of the universe and interpreting them as recession velocities.

vanhees71