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Homework Help: Rearranging equation - Relativistic doppler

  1. Sep 16, 2009 #1
    1. The problem statement, all variables and given/known data
    The hydra cluster is 900 Mpc (3x10^9 light years) away. Calcium atoms emit a spectral line of wavelength 396.8 nm. This line is observed at 487.5 nm. The velocity of the cluster, v, is given by ([tex]\lambda[/tex] =c/f)

    487.5 = 396.8 SQRT((1+v/c)/(1-v/c))

    How do i find v please?

    2. Relevant equations

    3. The attempt at a solution I need to rearrange and this example says take v/c to one side and solve but i dont know how. Well i have taken the numbers to one side, squared them and left with (1+v/c)/(1-v/c) on the other side, how do i find v? Thanks
  2. jcsd
  3. Sep 16, 2009 #2


    Staff: Mentor

    1. Divide both sides by 396.8.
    2. Square both sides.
    3. Multiply both sides by (1 - v/c).
    4. Carry out the multiplication on the left side.
    5. Get all terms involving v on one side.
    6. Factor v out.
    7. Divide both sides by the coefficient of v.
    That should pretty much do it
  4. Sep 23, 2009 #3
    Thanks :)
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