Calculating Redshift to Using Hubble Constant and Distance

[elliottmarter]

A redshift survey has identified a galaxy cluster for which it infers a di stance of 520 Mpc. At what redshift is this cluster observed to be? You may use H0 = 72 km s−1 Mpc−1

Now call me old fashioned but don't i need some kind of relativistic speed to calculate the redshift, i mean i have a distance of 520Mpc (=16.12x10^21m) and the Hubble constant...but I am sure i need a value for how fast its traveling away from me...

Thanks

EDIT i think i just realized that i times its distance by Ho to get its speed as its Kms-1 Mpc-1

 

[nickjer]

Your edit is correct.

 

[mgb_phys]

Then as long as this speed is much less than 'c' you can just use classical redshift.
When you get redshifts approaching (or larger than) 1 you need to take into account the expansion of the universe.

 

[elliottmarter]

yeah the Lorentz factor was 1.00... so i just used z=v/c

 

[paranormal]

so its 520x72 = 37440 and that's its speed which is then divided by the speed of light to get its redshift...i think...

Yes, you are correct. In order to calculate the redshift, you need to know the distance and the velocity of the galaxy cluster. The Hubble constant, which is a measure of the expansion rate of the universe, can be used to calculate the velocity of the cluster. By multiplying the distance of 520 Mpc by the Hubble constant of 72 km s−1 Mpc−1, you can calculate the velocity of the cluster, which is 37440 km s−1. This velocity can then be divided by the speed of light (299,792 km/s) to get the redshift, which in this case is approximately 0.125. Therefore, the galaxy cluster is observed to be at a redshift of 0.125.