I am taking the answers 1 a) and 1 b) to be data.
Time in ship =100 y
time on earth =1 y
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time = 50 years
speed = 0.9994c
distance =speed *time = 50*365*24*60*60*0.9994*3*10^8 = 4.727*10^17 m
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Lorentz contraction effect:
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masses get more massive by the formula:
The rest mass m_0 is not given, but the above formula is to be applied.
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The Doppler effect for light:
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Assuming that they felt the initial acceleration and the acceleration during the instantaneous turn, they must know they were the ones who were traveling.
Thus, they will just take the total distance as twice the Lorentz contracted length.
d_tot= 2*d =2*4.727*10^15 m = 9.454*10^15 m
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