# NED velocity to redshift conversion?

I've done some search with the Nasa Extragalactic Database (NED) and I have a very basic question about the velocity/redshift conversion. For example, for the first object of this page, we have $v=19791km/s$ and $z=0.066016$.

If we use the simple formula $z=v/c$, we find the result of the database : $19791/299792=0.0660157709345$. But now if we use the formula : $z = \sqrt{\frac{c+v}{c-v}}-1$ we find $0.0683461749892$

Which is the correct one and why ?

Thank you very much.

-
I suspect that the velocity formula must incorporate the expansion of the Universe. I'm not sure though: I wouldn't expect it to be a ~3% effect at that redshift. – Warrick Jun 25 '12 at 11:29

The simple formula is just the first-order expansion of the more complicated one about $v = 0$, the latter being exact for the Doppler effect of motion purely along the line of sight. The $v$ here refers to the peculiar motion of the galaxy.
Edit: Since I have lately been using NED a lot, I came across this page in their documentation. Point 1 in particular notes that "no relativistic correction is applied" and so you may see "velocities in excess of the speed of light." (It also says $v = z/c$, but I hope that's just a typo.) There are two important points here. The first is that you can safely assume the values reported are redshift times the speed of light, possibly with a correction to a certain reference frame. The second is that even NASA is under the misconception that redshift of distant galaxies has something to do with Doppler shift, when this is just fundamentally false. The quantity $zc$ is really just a way of putting units to redshift, nothing more.