If astronauts could travel at 0.671 to Alpha Centauri, 6.11light years away, we

Question

If astronauts could travel at 0.671 to Alpha Centauri, 6.11light years away, we on Earth would say it takes t = 6.11 lightyears/0.671 = 9.10581 years to reach Alpha Centauri. The astronautsdisagree. a) How much time passes on the astronauts' clocks? Answer inunits of years. b) What distance to Alpha Centauri do the astronauts measure?Answer in units of light years. If astronauts could travel at 0.671 to Alpha Centauri, 6.11light years away, we on Earth would say it takes t = 6.11 lightyears/0.671 = 9.10581 years to reach Alpha Centauri. The astronautsdisagree. a) How much time passes on the astronauts' clocks? Answer inunits of years. b) What distance to Alpha Centauri do the astronauts measure?Answer in units of light years.

Explanation / Answer

i am assuming the speed is .671c. .671c corresponds to a gamma factor of = 1/(1-.6712) = 1.35 in earth frame, it takes 6.11 ly/.671c = 9.11 yrs in astronaut's frame, the interval is 9.11/ = 6.75 yrs in astronaut's frame, the distance to alpha centauri is contractedto 6.11/ = 4.53 ly

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