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Red-shift question from another thread.

  1. Sep 8, 2013 #1
    1. The problem statement, all variables and given/known data
    This is not a HW questions but from another thread.

    The statement I made was that if z increases for a source, then it is accelerating away. Or, it could that if z is constant then the sources moves with constant velocity away from an observer.

    I just need to know where my logic is breaking down and what direction I can try to find the right answer.

    2. Relevant equations

    I took the equation:
    1+z = [itex]\sqrt{\frac{1+v/c}{1-v/c}}[/itex]

    3. The attempt at a solution

    So taking d/dt on both sides I end up with:

    dz/dt = 1/2 [itex]\frac{1+v/c}{1-v/c}-1/2[/itex]*[itex]\frac{(1/c dv/dt)*(1-v/c)-(1/c dv/dt)*(1+v/c)}{(1-v/c)2}[/itex]

    Re-writting this:

    dz/dt= [itex]\frac{-v* dv/dt}{c2*(z+1)*(1-v/c)2}[/itex]

    Since the first term is negative (from the minus sign) and v is positive, then a positive dz/dt would require that dv/dt is negative or that the sources acceleration is radially inward when I had suspected outward.

    This may be a result of me using the flat-spacetime (Minkowski metric) but I am not sure. Can anyone point me in the right direction.

    Please and thank you.
  2. jcsd
  3. Sep 8, 2013 #2


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    You dropped a sign when you applied the quotient rule. The numerator should end up as a sum, not a difference.
  4. Sep 8, 2013 #3
    Ah, I used the wrong derivative in the second half of my quotient rule. Thanks for that.
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