A 26 year-old biologist makes a trip to study life forms in a distant planet 18

Question

A 26 year-old biologist makes a trip to study life forms in a distant planet 18 light-years away. The round trip including a stay of 1 year in the distant planet takes 40 years according to the clock on earth. The biologist's son is 3.0 year-old when she left. Assume that the planet is not moving with respect to earth. How fast is the spaceship traveling? Give your answer in terms of the speed of light. You do not need to enter "c" as unit.
How old is she when she returns according to her clock? How old is her son according to the clock on earth?
What is the total distance traveled according to the biologist? Give your answer in light-years. You do not need to enter the units.

Explanation / Answer

a) Time taken for round trip, delta t0 = 2 (18 cy) / c = 36 y

Time dilation, delta t = delta t0 / sqrt [1 - v2/c2]

39 y = 36 y / sqrt [1 - v2/c2]

36 y / 39 y = sqrt [1 - v2/c2]

v = 0.385 c

b) Age of biologist = 26 + 36 + 1

= 63 y

c) Age of biologist son = 3.0 + 40 = 43 y

d) Total distance travelled = 2 (18.0 ly)

= 36 ly

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