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: Astronomy - Distance with different scale factors

  1. Jul 8, 2011 #1
    The problem statement, all variables and given/known data
    Expansion of the universe is described by the scale factor R(t), where t is the time after the Big Bang. For a flat universe the scale factor is today
    [itex]R(t)=C_{1}\cdot t^{\frac{2}{3}}[/itex]

    When the Universe was radiation dominated, for t <200,000 years, the scale factor was
    [itex]R(t)=C_{2}\cdot \sqrt{t}[/itex]

    Today, about 12 billion years after the Big Bang, we measure the distance to another superhop to 1 billion light years. How big would the distance between these sites one year after the Big Bang, if we assume that we live in a flat universe.

    The attempt at a solution
    I express the distance in meters
    [itex]R(t)=9.461\cdot 10^{24}\, m[/itex]

    Then I express the time in seconds
    [itex]t=3.787\cdot 10^{17}\, s[/itex]

    I found that the constant is
    [itex]C_{1}=1.8075\cdot 10^{13}[/itex]

    I need to know the constant [itex]C_{2}[/itex], but I'm not sure how I'll be able to calculate it.

    I have tested just to put [itex]C_{1}=C_{2}[/itex], but the result for the distance was wrong. I then realized that the two constants have different units.

    Does anyone have a suggestion how I may proceed?
  2. jcsd
  3. Jul 10, 2011 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    For t = 200,000 years, both expressions for R(t) should give the same result.

    To make your life easier, consider using units of years and light-years rather than seconds and meters.
  4. Jul 10, 2011 #3
    Thanks for your reply, now I was able to solve the problem.

    Thanks for your advice, I'll keep it in mind.
  5. Jul 10, 2011 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Glad it worked out.

    I know we get SI units drilled into our heads in intro physics classes, but they are not always the most convenient. If the problem statement uses alternate units, that's a hint for you to consider it too. :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook