If astronauts could travel at v=0.89c, we on Earth would say it takes (4.20/0.890)=4.72 years to reach Alpha Centauri, 4.20 light years away. The astronaut would disagree. (a) How much time passes on the astronaut's clocks? (b) What is the distance to Alpha Centauri according to the astronauts?

Answer 1

β =0.89,
t = tₒ/sqrt(1-β²),
tₒ=t •sqrt(1-β²) = 4.4• sqrt(1-0.89²) = 2 years.
d = v•tₒ=0.89•3•10^8•2•365•24•3600 =1.68•10^16 m