Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Find velocity given distance in one reference frame and time in another (relativity)

  1. Feb 9, 2012 #1
    1. The problem statement, all variables and given/known data

    The pilot of a rocket wants to reach a star in 1 year. The rocket is currently on Earth. The star is 4 light years away, measured from an observer on Earth. What velocity is needed for the pilot to reach the star in a year in the pilot's/rocket's time?

    2. Relevant equations

    See below. Relativistic Length = Proper Length / Lorentz factor is used below, to make the substitution from Line 2 to Line 3 of L to L'/(Lorentz factor). The gamma symbol indicates the Lorentz factor.

    3. The attempt at a solution

    I have been given a solution, I just don't understand it. Is someone able to explain the jump from lines 6 to 7 in this solution? http://i.imgur.com/F70Oy.jpg . T' and L' indicate the proper time (time is from pilot's perspective, hence 1 year, distance from Earth's perspective, hence 4 light years). Tp is used the in first line, it is the same as T', hence where the T' comes from in Line 4.

    I have been struggling with this for some time. Any help is appreciated, thank you!

    Edit: I believe there is a substitution of a formula from this section of Wikipedia but I am unsure which one. Also, Wikipedia uses different symbols (in each formula, variables without a dash indicate measurements made in the stationary reference frame, unlike mine). https://en.wikipedia.org/wiki/Special_relativity#Time_dilation_and_length_contraction
    Last edited: Feb 9, 2012
  2. jcsd
  3. Feb 9, 2012 #2
    Re: Find velocity given distance in one reference frame and time in another (relativi

    Why not just do it yourself? I'll get you started

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook