## 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?

E=mc^2

## The Attempt at a Solution

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

## Answers and Replies

tiny-tim
Homework Helper
Hi SAT2400!

(try using the X2 tag just above the Reply box )
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 )

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

what is his measurement of the distance?

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.

hmm, can you explain more easily/??:(

Thanks !!

tiny-tim
Homework Helper
Hi SAT2400!

Do you know the Lorentz transformation equations?

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

If not, look them up in your book.

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....:(

tiny-tim
Homework Helper
root of( 1-v^2/c^2) ...is this right??

Sort-of …

but how are you going to use it?

I still have no idea.......T_T

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

SO...

THank you very much!

tiny-tim
Homework Helper
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?

Matterwave
Gold Member

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: $$L=L_0\sqrt{1-\frac{v^2}{c^2}}$$ The time that they measure is then simply: $$t=L/v$$

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.