A 26 yearold biologist makes a trip to study life forms in a

A 26 year-old biologist makes a trip to study life forms in a distant planet 19 light-years away. The round trip including a stay of 1 year in the distant planet takes 42 years according to the clock on earth. The biologist\'s son is 2.0 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.hintDon\'t forget to substract the 1-year stay from the total time.

How old is she when she returns according to her clock? Units required.

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.

Solution

I light traveled this distance, at its velocity \'c\', it would take 19 years. Since it takes 42 - 1 = 41 years for the biologist to make the trip, so the speed is
19 x 2 / 41 = 0.9268 c [multiplication by 2 is because of the round trip]

Time dialation that is occurred is expressed by
t\' = t * squareroot(1 - (v^2/c^2))
t\' = 41 * squareroot(1 - 0.9268^2) = 15.40 years
so the biologists age is 26 + 15.40 + 1 =42.40 years
Her son is 2 + 42 = 44 years

To the spacecraft observer, the distance to the planet is contracted

L\' = L* squareroot(1 - (v^2/c^2)) = 2 x 19 x squareroot(1 - 0.9268^2) = 14.27 ly