A 27 year-old biologist makes a trip to study lifeforms in a distant planet 17 l

Question

A 27 year-old biologist makes a trip to study lifeforms in a distant planet 17 light-years away. The round tripincluding a stay of 1 year in the distant planet takes 38 yearsaccording to the clock on earth. The biologist's son is 4.0year-old when she left. Assume that the planet is not moving withrespect to earth. How fast is the spaceship traveling? Give youranswer in terms of the speed of light. You do not need to enter "c"as unit.

How old is she when she returns according toher clock?

How old is her son according to the clock onearth?

What is the total distance traveled accordingto the biologist? Give your answer in light-years.

Explanation / Answer

2 * 17 L-y = distance traveled as measured on earth 37 * v = 34 *c         time traveled atspeed v = time for light to travel same distance v / c = 34 / 37 Let = (1 - v2 / c2) =.394 = T      where is the proper time as measured by the clock at rest inthe spaceship = 37 * .394 = 14.6 years   the timespent in travelling as measured on the spaceship So the biologist ages 14.6 + 1 = 15.6 years The biologist is then 27 + 15.6 = 42.6 years old Her son ages 38 years according to a clock on earth and isthen 42 yrs old L = L0    where L0 = 34 L-y    the totalproper distance traveled (measured on earth) L = 34 * .394 = 13.4 L-y    the totaldistance traveled as measured on the moving spaceship

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