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I Problem Hubble parameter

  1. May 13, 2017 #1
    This is the time derivative to calculate the speed which a galaxy moves away from another galaxy. I don't understand how they get from da/dt (xi − x1) to (∙a)/a a(t). (xi − x1). Could anyone explain this?


    vi(t) = d/dt (ri(t) − r1(t))
    = d/dt a(t)(xi − x1)
    = da/dt (xi − x1)
    = (∙a)/a a(t). (xi − x1) !
    =(∙a)/a (ri(t) − r1(t))
    = H(t) (ri(t) − r1(t))

    [ ∙a= da/dt ]
     
    Last edited: May 13, 2017
  2. jcsd
  3. May 13, 2017 #2

    sophiecentaur

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    It's a good idea to define the variables in an equation. Not everyone uses the same 'conventions'.
     
  4. May 13, 2017 #3

    Bandersnatch

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    Since ##\frac{da}{dt}=\dot a##
    and ##\frac{a}{a}=1##
    You have ##\frac{da}{dt} \Delta x## multiplied by 1 to net you ##\frac{\dot a}{a}a\Delta x##.

    If it still doesn't click, Leonard Susskind derives this here in a slightly different, but essentially the same manner:

    (starting at 21:22 mark)
     
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