1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Coordinate distance

  1. Jan 23, 2007 #1
    1. The problem statement, all variables and given/known data
    For a universe with [tex]k=0[/tex] and in which [tex](a/a_0) = (t/t_0)^n[/tex] where [tex]n<1[/tex], show that the coordinate distance of an object seen at redshift z is


    2. The attempt at a solution
    I have used

    [tex]r=f(r)=\int_{t}^{t_0} \frac{cdt}{a(t)}=\frac{ct_0}{(1-n)a_0}\left(t_{0}^{1-n}-t^{1-n}\right)[/tex]

    but then what? I know that [tex]1+z=\frac{a_0}{a}[/tex] but I can't get it right.
    Last edited: Jan 23, 2007
  2. jcsd
  3. Jan 23, 2007 #2


    User Avatar
    Science Advisor

    You're missing a power of "n".
    [tex]f(r)=\int_{t}^{t_0} \frac{cdt}{a(t)}=\frac{1}{a_0}\int_{t}^{t_0}\fract_0^n t^{-n}dt= \frac{t_0^n}{a_0(1-n)}\left(t_0^{1-n}- t^{1-n}\right)[/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook