# Proper length

“proper” length

A spaceship travels past a planet at a speed of 0.80 c as measured from the planet’s frame of reference. An observer on the planet measures the length of a moving spaceship to be 40 m.
a) How long is the spaceship, according to the astronaut?
b) At what speed would the spaceship have to travel for its relativistic length to be half its “proper” length?

a) L=L0 sqr 1-v2/c2
b) the previous equation where c=3*10^8
is that right?

alphysicist
Homework Helper
Hi salsabel,

What did you get as the final answers?

i just want to know if these are the correct equations because i'm little confusing about the first one does he mean the time or the distance?

alphysicist
Homework Helper
I'm not sure what time or distance you are referring to; in the first question, they want to know if the astronaut (moving with the spaceship) measured the length of the spaceship, what length would he find? (The observer on the planet measured 40m for the length of the spaceship, but what does the astronaut measure?)

A spaceship travels past a planet at a speed of 0.80 c as measured from the planet’s frame of reference. An observer on the planet measures the length of a moving spaceship to be 40 m.
a) How long is the spaceship, according to the astronaut?
b) At what speed would the spaceship have to travel for its relativistic length to be half its “proper” length?

a) L=L0 sqr 1-v2/c2
b) the previous equation where c=3*10^8
is that right?

Question (a) is asking what is the proper length of the space ship and this is the variable L0 in your equation so the answer is

a) L0 = L/sqrt(1-v^2/c^2) = 40/0.6 = 66.66m

Question (b) is asking what the relative velocity has to be so that L/L0 = 0.5 so by simple rearrangement the answer is:

b) v/c = sqrt(1-(L/L0)^2) = sqrt(1-(0.5)^2) = 0.866c

Can someone please correct me if I'm wrong but I think that kev's answer is incorrect.

L is the relativistic distance measured by an observer in the moving space ship, which is something we want to find for question A)

L0 the proper distance, is measured by an observer at rest in the same reference frame as the two points, which is given as 40 meters.

So did kev mix L and L0 up, or is it me?

Doc Al
Mentor

Can someone please correct me if I'm wrong but I think that kev's answer is incorrect.

L is the relativistic distance measured by an observer in the moving space ship, which is something we want to find for question A)

L0 the proper distance, is measured by an observer at rest in the same reference frame as the two points, which is given as 40 meters.

So did kev mix L and L0 up, or is it me?
It's you. (kev is correct.)

Reread the problem statement: "An observer on the planet measures the length of a moving spaceship to be 40 m."

That means that the 40 m represents L, the contracted length of the moving ship as observed by the planet. The length of the ship according to the astronaut, which is what you are asked to find, is the proper length L0.

Ahh fudge. Keep getting proper and relativistic concepts mixed up in my head. Thanks for the correction Doc Al.