Space Travel to the stars requires hundreds or thousands of years, even at the speed of light. Some people have suggested that we can get around this difficulty by accelerating the rocket (and its astronauts) to very high speeds so that they will age less due to time dilation. The fly in this ointment is that it takes a great deal of energy to do this. Suppose you want to go to the immense red giant Betelgeuse, which is about 500 light-years away. (A light-year is the distance that light travels in a year.) You plan to travel at constant speed in a 1000-kg rocket ship (a little over a ton), which, in reality, is far too small for this purpose. In each case that follows, calculate the time for the trip, as measured by people on earth and by astronauts in the rocket ship, the energy needed in joules, and the energy needed as a percentage of U.S. yearly use (which is 1.0 x 1019 J). For comparison, arrange your results in a table showing v rocket, t earth, t rocket E (in J), and E (as % of U.S. use). The rocket ship's speed is
(a) 0.50c;
(b) 0.99c;
(c) 0.9999c. On the basis of your results, does it seem likely that any government will invest in such high-speed space travel any time soon?