Problem dealing with a chapter on relativity

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The discussion centers on a problem involving relativistic travel to determine the speed required to perceive a distance of 35 light years to a star that is 82 light years away in an Earth reference frame. Participants clarify that light years measure distance, not time, and emphasize the use of Lorentz length contraction to solve the problem. The correct formula involves the Lorentz factor (gamma), which relates proper length and contracted length. A participant highlights a miscalculation regarding the use of 85 light years instead of 82 light years, leading to a correction in the application of the length contraction formula. The conversation concludes with an affirmation of the correct approach to solving for velocity using the appropriate values.
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I think I know how to do this problem, but need to make sure... so...

1) In an Earth reference frame, a star is 82 light years away. How fast would you have to travel so that to you the distance would only be 35 light years?

First I have two simple questions:

1. Light years is in a unit of time or length?

2. How to convert light years?

So I would use either:

a) L = Lo x sqroot(1-v^2/c^2) ~~~> 82 light years = 35 light years x sqr(1-v^2/(3.0 x 10^8)^2)

or

b) to = t x sqroot(1-v^2/c^2) ~~~> 35 light years = 85 light years x sqr(1-v^2/(3.0 x 10^8)^2)
 
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Light years is a unit of length, therefore, you would use Lorentz length contraction. A light year is the distance light can travel in the period of one year.

~H
 
A light year is a unit of length/distance.

If the distance between the Earth and the star (as seen from Earth) is 82 ly, how much of a contraction would be needed to make the distance only seem like 35 ly in the frame of someone traveling at relativistic velocities?

Lenth = Proper Length / gamma

where gamme is the lorentz factor,
gamma = 1/ sqrt(1 - v^2/c^2)

If we call "proper length" the length in the Earth's frame of reference, then we solve for gamma to be 82 ly / 35 ly = 2.3429

Now how fast must an object be flying fast Earth in order to have a lorentz factor this hight?

2.3429 = 1/ sqrt(1 - v^2/c^2)
solve for v.
 
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(also so you cannot use L = Lo x sqroot(1-v^2/c^2)?) Look below.

could you also have said --> 85 = 35 x sqroot(1-v^2/c^2) and then solve for V?
 
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jrd007 said:
(also so you cannot use L = Lo x sqroot(1-v^2/c^2)?) Look below.

could you also have said --> 85 = 35 x sqroot(1-v^2/c^2) and then solve for V?

You have applied L = Lo x sqroot(1-v^2/c^2) here, which is the correct thing to do. However, I am confused as to why you have used 85 lightyears.

~H
 
I mis typed it the first time.
 
Then you are correct, apply lorentz's length contraction and solve for v.

~H
 
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