# Special Relativity - Proper Length

1. Jan 25, 2010

1. The problem statement, all variables and given/known data
An astronomer on Earth observes a meteoroid in the
southern sky approaching the Earth at a speed of 0.800c.
At the time of its discovery the meteoroid is 20.0ly from
the Earth. Calculate (a) the time interval required for the
meteoroid to reach the Earth as measured by the Earth-
bound astronomer, (b) this time interval as measured by a
tourist on the meteoroid, and (c) the distance to the Earth
as measured by the tourist.

2. Relevant equations

3. The attempt at a solution

I just need help with how to figure out what is the proper length. I don't know if the 20 ly measured from astronomer on earth is the proper length because it seems I could be on the meteoroid and calculate the same 20 ly and then that could be the proper length. But it seems that someone has to see some length contraction.

I know proper length is the length of something measured when at rest relative to that something. And here, the length we're measuring is the distance to the meteoroid, but that is changing constantly if the meteor is moving towards the Earth (or from the meteors perspective, if the earth is moving towards the meteor). So how do we know what the proper length is?

Thanks ahead of time for the help.

2. Jan 25, 2010

### dacruick

my guess would be that you're thinking a little bit too much. just find the percentage of length that something moving at .8c is, and then multiply that percentage by 20 light years.

3. Jan 25, 2010

### dacruick

and who is the tourist?

4. Jan 25, 2010

sorry about that. the tourist would be someone on the meteoroid.

5. Jan 25, 2010

### dacruick

so someone on the meteoroid sees earth coming to them at .8c and we on earth see the meteoroid coming to us at .8c. But for the tourist the distance to earth I believe is 60% of what it would be if he was not moving at all.