# Hubble's Law of Redshifts using observed distances

Moved from a technical forum, so homework template missing
The problem statement, all variables, and given/known data:

Assume that the radial velocities vr of galaxies, at the present time, are given by Vr=H0*r, where H0 = 65 km/(s*Mpc). However, we do not observe the present distances of galaxies, but the distances they had when light left them.

Plot the relation between radial velocity and distance that would be obtained directly from observations (i.e. the relation corresponding to measured distances, not present distances). Consider several values of distance, up to 2x109 pc. Comment briefly on the shape of your curve.

relevant equations:

Vr=H0*r

attempt at a solution:

I'm familiar with the shape of the graph showing Hubble's Constant, how radial velocity is proportional to the distance of the galaxy. I also understand, I think, that radial velocity is equal to the redshift z times c. What I'm really lost on is applying that to this question. We have a redshift -> recessional velocity because the galaxies are moving away, and that velocity/redshift is proportional to how far away that galaxy currently is. But I don't understand how this would change the relationship between the values/ the shape of the graph if we consider the measured/observed distances instead of their actual distances.

I'm not looking for someone to draw the graph for me, just to maybe help explain the question a little better and help me understand the information behind the answer.

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