The star alpha a- centuri is 4 light years from earth. a) To an observer on eart

Question

The star alpha a- centuri is 4 light years from earth.

a) To an observer on earth, how much time does it take for a light beam to reach alpha a-centuri?
b) The rocket travels at v=0.98c relative to earth. To an observer on the rocket, what does she measure for the earth, alpha a-centuri distance?
c) How much time does she claim it takes to go from earth to a-centuri? (be a bit careful here)
d) If an observer could travel at the speed of light, how much time would she claim it took to reach alpha a-centuri?

Explanation / Answer

t = 4/sqrt(1-c2/c2) = 4  years
y=1/sqrt(1-.98^2)=5
b. l=l0/5 = 4/5 light years
c. t = 4y =20  years
d. 4 years

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