Solving Redshift Confusion Homework Problem

[MoAli]

Homework Statement

I encountred a question that says : Assume that gravitational interactions between galaxies in groups lead to random galaxy velocities of 300 km/s At what distance would the redshift predicted by Hubble's law dominate over that produced by individual velocities? and what is the redshift at that distance?
I don't understand what's the difference between the 2 redshifts mentioned here, so I am confused on how to approach this

Homework Equations

V= h_0 * D
where D is the distance and the Hubble constant is 2.18*10^-18 s^-1
V /c = Δλ/λ

The Attempt at a Solution

I tried substituting in the numbers and got D= 1.36*10^20 km and v/c=0.001. [/B]

 

[phyzguy]

I think you did it right. There is a smoothly increasing velocity moving away from us faster and faster as the distance increases (the "Hubble flow"), and superimposed on this is a random set of what are called "peculiar velocities". You are asked to determine how far away you need to look before the smooth Hubble velocities begin to dominate. A couple of comments: (1) I would put the distance in units more used by astronomers, like parsecs or Megaparsecs in stead of km, and (2) you gave a velocity, but you were asked for the redshift z.