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Spaceship travels at .83 c, relativity

  1. Jun 2, 2012 #1
    1. The problem statement, all variables and given/known data

    Suppose our sun is about to explode and we escape in a spaceship toward the star Tau Ceti. When we reach the midpoint of our journey, which takes place at v=.83 C we see our sun explode and, unfortunately, we see Tau Ceti explode as well (we observe the light arriving from each explosion. (there's a part a and b but i understand those parts, so i'll go straight to c and d)

    c)In the spaceship frame of reference, how long before we saw the Sun explode did it actually explode? (enter a positive value for times in the past.)

    d) In the spaceship frame of reference, how long before we saw Tau Ceta explode did it actually explode?

    2. Relevant equations

    Δt = [itex]\gamma[/itex](Δt' - v/c2Δx') } S'-->S


    3. The attempt at a solution

    c) I have worked out an answer using the equation I gave but I'm not sure if its correct.
    I said that S is my frame for the spaceship and S' is my frame for the sun.
    Δt = [itex]\gamma[/itex](Δt' - v/c2Δx')
    so Δt = 1/(sqrt(1-(.83c)2/c2))*((6 years)+(.83c*6c)/c2)
    Δt=19.686 years
    Δt' = 6 years
    So it actually exploded 13.686 years ago?

    for part d), i used the same equation but instead used -v
    so Δt = 1/(sqrt√(1-(-.83c)2/c2))*((6 years)+(-.83c*6c)/c2)
    = 1.823 years
    so it actually happened 1.823-6 = -4.171
    4 years into the future? This is the main reason why I'm not believing my answer.
     
  2. jcsd
  3. Jun 3, 2012 #2

    tiny-tim

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    welcome to pf!

    hi harts! welcome to pf! :smile:
    how can you subtract measurements in two different frames? :confused:

    (and what do you think "∆" means? :wink:)
     
  4. Jun 3, 2012 #3
    Thanks for the reply!
    OK, I thought I was finding the difference in time between the two frames, which is why I subtracted the change in time from one frame from the change in time in the other frame. Am I misinterpreting the question?

    "In the spaceship frame of reference, how long before we saw the Sun explode did it actually explode?"
     
  5. Jun 4, 2012 #4

    tiny-tim

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    hi harts! :smile:

    (just got up :zzz:)
    yup! …

    both measurements must be made in the spaceship frame …

    the time the sun exploded, and the time the light reached the spaceship :wink:
     
  6. Jun 4, 2012 #5
    OK I think I understand it now. I know that the sun actually exploded 6 years ago, but because of relativity I have to use a lorentz transformation to figure out how much time it took for us to see it.

    For part c, I use my equation

    t'= ((-6 years)-(.83c/c^2)(-6ly))/ sqrt(1-(.83c)^2/c^2)= -1.83

    For part d, I use the same equation but use 6 light years for my x value and I got -19.686 years.

    I guess it just took me a while to understand those lorentz transformation equations. Thanks tiny tim
     
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