SR Homework problem. Help?
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06-12-2013, 08:52 PM
SR Homework problem. Help?
I need help from a physicist. My prof won't answer his email. He's out of the office till Wednesday. Here's the question:

Two stars are 70 light years apart. How fast does a spaceship need to travel for the astronauts inside to have aged 75 years?

Problem is I don't know how long this takes in the inertial reference frame, or how far it seems to the travelers. If I knew I could easily find the velocity.

Any hints? I just need the setup, I've tried the formula for time dilation and it isn't working out right.
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06-12-2013, 10:55 PM
RE: SR Homework problem. Help?
I'm not a physicist and I am rank amateur at the maths, and haven't actually studied maths for about 18 years. Nevertheless, I'm interested in this topic so I'll give it a go based on [1]. Let the stars be in the rest frame and the space ship be in the "moving" frame. I'll use years and light years to avoid the c terms.
t' = gamma (t - vx)
x' = gamma (x - vt)
where gamma = 1/sqrt(1-v^2).
The same is true in reverse (with the velocity switched to negative to reflect our changed perspective), so:
t = gamma (t' + vx')
x = gamma (x' + vt')
gamma has the same value in this frame because the squared v term loses the sign of v.

We have x=70ly and t' = 75y.
Therefore we have the following simultaneous equations:
(1) 75 = gamma(t - 70v) = (t - 70v) / sqrt(1-v^2)
(2) x' = gamma(70 - vt) = (70 - vt) / sqrt(1-v^2)
(3) t = gamma(75 + vx') = (75 + vx') / sqrt(1-v^2)
(4) 70 = gamma(x' + 75t) = (x' + 75t) / sqrt(1-v^2)
Solve for v. Easy, right?
Wink

Hrrm. Maybe the way to look at it is in terms of a space-time diagram with a t'=75 line that intercepts the x=70 line and solve for v that way?

[1] http://en.wikipedia.org/wiki/Lorentz_tra...figuration

Give me your argument in the form of a published paper, and then we can start to talk.
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08-12-2013, 01:41 PM
RE: SR Homework problem. Help?
Physics teachers may now beat me. It was a units issue I was having. I was entering my distance in light years and my time in years, but was entering my c value in meters per second.

I am ready to accept the dunce hat.
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08-12-2013, 05:40 PM
RE: SR Homework problem. Help?
Do you feel like presenting your answer on the forum?

Give me your argument in the form of a published paper, and then we can start to talk.
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08-12-2013, 06:56 PM
RE: SR Homework problem. Help?
(08-12-2013 01:41 PM)natachan Wrote:  Physics teachers may now beat me. It was a units issue I was having. I was entering my distance in light years and my time in years, but was entering my c value in meters per second.

I am ready to accept the dunce hat.

I can totally picture a bunch of physics students huddled around a watercooler telling jokes in this fashion.
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09-12-2013, 06:16 AM
RE: SR Homework problem. Help?
.683c

I know that t'=t/gamma and x'=x/gamma. velocity is equal to x/t, or x'/t'. It will be the same either way. t=t'*gamma. v=x/t'*gamma. Gamma is 1 divided by the square root of 1 minus v squared. solve for V.
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