Suppose that an astronaut travels to a distant star and returns to Earth. Except for brief intervals of time when he is accelerating or decelerating, his spaceship travels at the incredible speed of v = 0.995c relative to the Earth. The star is 40 light-years away. (A light-year is the distance light travels in 1 year.)
a. Show that the factor γ for this velocity is approximately equal to 10.
b. How long does the trip to the star and back take as seen by an observer on Earth?
c. How long does the trip take as measured by the astronaut?
d. What is the distance traveled as measured by the astronaut?
e. If the astronaut left a twin brother at home on Earth while he made this trip, how much younger is the astronaut than his twin when he returns?