In Example 2.5, we noted that Anna could go wherever she wished in as little time as desir...

In Example 2.5, we noted that Anna could go wherever she wished in as little time as desired by going fast enough to length-contract the distance to an arbitrarily small value. This overlooks a physiological limitation. Accelerations greater than about 30g are fatal, and there are serious concerns about the effects of prolonged accelerations greater than 1g. Here we see how far a person could go under a constant acceleration of 1g, producing a comfortable artificial gravity.

(a) Though traveler Anna accelerates, Bob, being on near-inertia I Earth, is a reliable observer and will see less time go by on Anna's clock (dt') than on his own (dt'). Thus, dt' = (l/γu)dt, where w is Anna's instantaneous speed relative to Bob. Using the result of Exercise 117(c), with g replacing F/m, substitute for u, then integrate to show that

(b) How much time goes by for observers on Earth as they "see" Anna age 20 years?

(c) Using the result of Exercise 119, show that when Anna has aged a time t', she is a distance from Earth (according to Earth observers) of

(d) If Anna accelerates away from Earth while aging 20 years and then slows to a stop while aging another 20, how far away from Earth will she end up, and how much time will have passed on Earth?