Relativity(Light years)? PLEASE HELP!

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Relativity(Light years)??? PLEASE HELP!

Homework Statement


Imagine an astronaut on a trip to Siris, which is 8 light years from Earth. On arrival at Siris,
the astronaut finds that the trip lasted 6 years. If the trip was made at a constant speed of .8c, how can the 8 light year distance be reconciled with the 6 year duration?


Homework Equations


E=mc^2


The Attempt at a Solution


I don't know how to solve this question....8 light years-> 6 years. 3/.8c??
Please help!
 

Answers and Replies

  • #2
tiny-tim
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Hi SAT2400! :smile:

(try using the X2 tag just above the Reply box :wink:)
Imagine an astronaut on a trip to Siris, which is 8 light years from Earth. On arrival at Siris,
the astronaut finds that the trip lasted 6 years. If the trip was made at a constant speed of .8c, how can the 8 light year distance be reconciled with the 6 year duration?

(e = mc2 has nothing to do with it … and i think it's Sirius :wink:)

the astronaut's measurement of the time (on his own clock) is 6 years

what is his measurement of the distance?
 
  • #3


The relevant equations are:

γ=1/root(1-v2/c2)
t'=γt
x=γx'

The 6 years is measured from his frame of reference, you need to measure the distance in the same frame as well.
 
  • #4
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hmm, can you explain more easily/??:(

Thanks !!
 
  • #5
tiny-tim
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Hi SAT2400! :wink:

Do you know the Lorentz transformation equations?

(you didn't mention them in your "Relevant equations")

If not, look them up in your book. :smile:
 
  • #6
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root of( 1-v^2/c^2) ...is this right??

hmm...could you please explain more in detail??

Sorry,,but I still don't know how to solve this question....:(
 
  • #7
tiny-tim
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root of( 1-v^2/c^2) ...is this right??

Sort-of …

but how are you going to use it? :smile:
 
  • #8
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I still have no idea.......T_T

If I knew how to do this,,I would have not come to this website.......

SO...

Please help!!!!

THank you very much!
 
  • #9
tiny-tim
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Use x and t for the coordinates in the Earth's frame (so Sirius is at x = 8, for all t).

Use x' and t' for the coordinates in the astronaut's frame.

Start the trip at (0,0) in both frames.

What do you get? :smile:
 
  • #10
Matterwave
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For one such as yourself, who seems to have a very rudimentary understanding of SR, I wouldn't bother with Lorentz transforms. For the question all you need to utilize is Length-contraction.

To the people traveling on the rocket, the length between Earth and Sirius is contracted to: [tex]L=L_0\sqrt{1-\frac{v^2}{c^2}}[/tex] The time that they measure is then simply: [tex]t=L/v[/tex]

Now you will notice that since L is contracted, it is no longer 8 light years but something shorter, and hence t can be shorter than 8 years without the rocket traveling faster than c.
 

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