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Time Dilation relativity

  • #1
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Homework Statement


The Voyager 1 space probe, launched in 1977, is moving faster
relative to the earth than any other human-made object, at 17,000
meters per second.
(a) Calculate the probe's
. p
(b) Over the course of one year on earth, slightly less than one year
passes on the probe. How much less?


Homework Equations


[tex]\gamma[/tex]=1/[tex]\sqrt{}1-(v/c)^2[/tex]


The Attempt at a Solution


I calculated the [tex]\gamma[/tex] but i dont know how to get answer (b)
 

Answers and Replies

  • #2
Doc Al
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What's the time dilation formula?
 
  • #3
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What it says for the formula. On my first post.[tex]\gamma[/tex]=1/[tex]\sqrt{}1-(v/c)^2[/tex]
 
  • #4
Doc Al
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Last edited by a moderator:
  • #5
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[tex]\Delta t = \gamma(\Delta + v\Delta /c^2)[/tex]
By the way what does [tex]\Delta[/tex] mean?
 
Last edited:
  • #6
Doc Al
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[tex]\Delta t = \gamma(\Delta + v\Delta /c^2)[/tex]
That's not the one you want. (Look for "time dilation".)
By the way what does [tex]\Delta[/tex] mean?
Δ means "change"; Δt represents a time interval.
 
  • #7
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[tex]T[/tex]=[tex]\frac{}{}t/\sqrt{}1-(v/c)^{}2[/tex]
This is the one in my text book.
 
  • #8
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If thats the right formula I think I got the right answer, T= 31000000.05 seconds have passed for the 31000000 seconds on earth.
 
  • #9
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I think you have the values of T and t_0 mixed up. Remember time dilation would mean that slightly less time passes for the probe.
 
  • #10
Doc Al
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If thats the right formula I think I got the right answer, T= 31000000.05 seconds have passed for the 31000000 seconds on earth.
Yes, it looks like you mixed things up. The rule to remember is that moving clocks run slow by a factor of gamma. Viewed from earth, the earth clocks read a longer time than does the moving probe clock.

Since the speed is quite a bit less than c, I suggest using a binomial approximation for gamma.
 
  • #11
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So i just redid it and i got 30,999,999.95 seconds passed on the probe. Is that right?
 
  • #12
Doc Al
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Figure out how many fewer seconds passed on the probe, not the total number of seconds.
 
  • #14
Doc Al
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