A 26-year-old biologist makes a trip to study alien life-forms in a distant planet 10 light years away. The round-trip including a stay of 1 year in the distant planet takes 21.5 years according to the clock on Earth. The biologist's son is 3 years old when he leaves. Assume that the planet is not moving with respect to Earth, and the speed is the same for both the outbound and inbound part of the journey. What is the total distance traveled according to the biologist? Give your answer in light years.
A) 1.69
B) 4.39
C) 6.78
D) 7.45
E) 9.45

Question

Quizplus · Accepted Answer

The total distance traveled is the distance from Earth to the planet and back, which is 20 light years (10 light years out and 10 light years back). The biologist's clock runs slower than the Earth's clock, so the biologist experiences less time than the people on Earth. The biologist's clock runs at a rate of 1/√(1 - v²/c²) = 1/√(1 - 0.8²/1²) = 0.6, where v is the speed of the spaceship and c is the speed of light. So, the biologist experiences 21.5 years * 0.6 = 12.9 years of time. The distance traveled according to the biologist is therefore 20 light years * 12.9 years / 21.5 years = 12 light years.

A 26-Year-Old Biologist Makes a Trip to Study Alien Life-Forms