Who aobserves length contraction? I have a homework in our nuclear physics class. The question is "An astronaut whose height in the earth is exactly 6ft is lying parallel to the axis of a spacecraft moving at a 0.9C relative to the earth. what is his height as measured (a) by an observer on this earth? (b) by an observer on the same spacecraft?"
I used the formula $L=L_o \sqrt{1-(v/c)^2}$, and I got the answer $L=2.62\ ft$
Now I am confused if my answer was from observer from earth or from observer on the same spacecraft. 
Please teach me to solve (b) or (a).
Sorry if this is literally an assignment. Please don't vote down. I will delete or close this question once it is answered. 
 A: In your calculation you set $v=0.9c$, I assume. This holds for an observer on earth. For an observer in the spacecraft itself, it is $v=0$. You can make the same calculation again for b) with $v=0$, what do you get?
$L_0$ is what you observe when you're not moving relative to the measured object. Say, if I measure your height on earth, we're not moving relatively to each other (that we may be on a train moving relative to the earth and the earth moving relatively to the sun and so on is completely irrelevant). If you now board the spacecraft and fly with $v=0.9c$ and I measure your height again (given that you are parallel to $v$), I'd measure your height as only a fraction of it (this is your solution to question a). On the other hand, if I would board the spacecraft as well, I would not move relatively to you, the situation would be the same as on earth and obviously I should measure the same as on earth, i.e. $L=L_0$. I could also use the relativistic formula and put $v=0$, this would give me again $L=L_0$.
Now what do I mean when I talk about relative movements? For example, if you drive a car, it tells you how fast you are. This is meant as velocity relative to the ground. But you could also sit in your car on a train. The car would then tell you that it does not move, because it measures its speed relative to the train, the train itself has a velocity relative to the ground, in total your car will have a non-vanishing velocity relative to the ground as well. What's now important are always relative velocities, because absolute velocities do not exist.
