The nearest star to Earth is Proxima Centauri, 4.3 light-years away. At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 3.7 years, as measured by travelers on the spacecraft? How long does the trip take according to Earth observers?
Earth observer: Δt=x/(c*√(1-v2/c2))=Δto/√(1-v2/c2) where Δto=time observed by person on spacecraft
Δto=3.7 yr=1.164e8 s
x=4.3 ly=4.068e16 m
The Attempt at a Solution
I tried using the two versions of the equation above with the known quantities plugged in such that (1.164e8/√(1-v2/c2)=4.068e16/(c*√(v2/c2)), but this is a false statement, so there must be something wrong with my equations or the way I am using them because that method does not yield an answer. Any help is appreciated, thanks.