Light travels to a certain star in 159 y. An astronaut makes thetrip in 18 y in

Question

Light travels to a certain star in 159 y. An astronaut makes thetrip in 18 y in his frame of reference. (a)How fast do we see him going (as a multiple of c)? Answerin units of c. (b)If he just signs the guest book and comes right back, in how manyyears will he return as seen in the earth frame of reference?Answer in units of y.
(a)How fast do we see him going (as a multiple of c)? Answerin units of c. (b)If he just signs the guest book and comes right back, in how manyyears will he return as seen in the earth frame of reference?Answer in units of y.

Explanation / Answer

t = 159 y, t' = 18 y, v = speed of the astronaut the distance measured in the earth frame = L = ct the distance measured in the astronaut's frame = L' = vt' use L' = L[1 - (v/c)2] vt' = ct[1 - (v/c)2] (v/c)2 = (t/t')2[1 - (v/c)2] a) v/c = (t/t')2/[1 + (t/t')2] =0.98735 b) 2*18/[1 - (v/c)2] = 227 years

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