1. The problem statement, all variables and given/known data An observer at a station on the moon measures the time of a spacecraft passing with constant speed v. The front of the spacecraft passes him at 0 s and the rear at 0.2 μs. The observer measures the length of the spacecraft to be 1.5 m. Explain briefy the term proper length. What is the proper length and the speed v (in units of c) of the spacecraft? 2. Relevant equations L=Lo/γ T=To*γ 3. The attempt at a solution The definition for proper length we've been given is "The length Lo of an object measured in the rest frame of the object is the PROPER LENGTH". I've tried to think of it in terms of "events" and i'm getting the timings occur at the same place in space by the observer, but the measurements aren't as its at the back and front of the rocket (probably where i'm going wrong). So i'm saying L=1.5m and To=0.2μs, which from v=L/To gives 7.5E6 m/s or 2.5E-2 c. so to find Lo use L=Lo/γ→ Lγ=Lo then because its fairly slow speed use low speed approximation (because γ=1.0005 without it) of γ=1+(1/2)β^2 which give the proper length to be 1.5007m and yeah that seems wrong. any help appreciated, and more so how to think when tackling these problems?