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Lorentz transform problem

  1. Mar 18, 2008 #1
    1. The problem statement, all variables and given/known data
    Astronomers on the Earth (regarded as an inertial reference frame) see two novas flare up simultaneously. One of the novas is at a distance of 1.0x10^3 lightyears in the constelation Draco; the other nova is at an equal distance in the constellation Tucana in a direction (as seen from Earth) exactly opposite to that of the first nova. According to astronomers aboard an aircraft traveling at 750km/hr along the line from draco to tucana, the novas are not simulatneous. According to these astronomers, which nova happened first/ by how many hours?


    2. Relevant equations

    t' = [tex]\frac{t - \frac{Vx}{c^2}}{\sqrt{1 - \frac{V^2}{c^2}}}[/tex]


    3. The attempt at a solution
    So, i then have two equations:

    t'[tex]_{1}[/tex] = [tex]\frac{t_{1} - \frac{Vx_{1}}{c^2}}{\sqrt{1 - \frac{V^2}{c^2}}}[/tex]

    t'[tex]_{2}[/tex] = [tex]\frac{t_{2} - \frac{Vx_{2}}{c^2}}{\sqrt{1 - \frac{V^2}{c^2}}}[/tex]

    i know that:
    t1 = t2
    since the novas flare up at the same time on Earth, and i also set
    x1 = 0,
    x2 = 2*10^3 lightyears = 2(9.46*10^18m)
    V = 750*10^3m/hr

    my final equatin looks like so:

    [tex]\frac{t'_{2} - t'_{1} = \frac{Vx_{2}}{c^{2}}}{\sqrt{1-\frac{V^{2}}{c^{2}}}}[/tex]
    (The above fraction looks wrong. the fraction should only be on the right side.)

    So, plugging in all of my values i get a time of 12.16hrs, which is double the right answer. Can someone please tell me what I could have done wrong? any help at all would be greatly appreciated
     
  2. jcsd
  3. Mar 18, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    I agree with your answer. So unless we both made the same mistake, the book is wrong.
     
  4. Mar 18, 2008 #3
    Thank you Doc Al, i appreciate the response. I will ask my professor what he thinks of the problem
     
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