# How long does an observer moving at 99% of the speed of light think he has traveled? [closed]

An observer is moving at 90% speed of light, and crosses a distance of 100.000 ly. In order to find how much he experienced that he has travelled, we use the formula $$\frac{100.000}{L_0}=\frac{269813212.2}{299792458}$$ but I get 110000 ly. This is certainly not correct. What is the correct formula?

• Although you cannot just use this factor haphazardly, as a general rule of thumb, the amount of contraction is related to the gamma factor, which is $\gamma=\left(1-\left(\frac{v}{c}\right)^2\right)^{-0.5}$. For a full answer, look up Lorentz Transformation Equations. Jun 13, 2022 at 13:10
• As already pointed out in the anwer, the question does not make too much sense. You have to think more about what do you want to find out. The distance in what reference frame?
– nasu
Jun 13, 2022 at 13:45

He thinks he has travelled $$0\rm\, ly$$. He believes he is stationary and that you are moving at $$0.9c$$ because motion is intrinsically relative.