Chapter 39, Problem 39.22P

Review. In 1963, astronaut Gordon Cooper orbited the Earth 22 times. The press stated that for each orbit, he aged two-millionths of a second less than he would have had he remained on the Earth. (a) Assuming Cooper was 160 km above the Earth in a circular orbit, determine the difference in elapsed time between someone on the Earth and the orbiting astronaut for the 22 orbits. You may use the approximation

$\frac{1}{\sqrt{1-x}}=1+\frac{x}{2}$

for small x. (b) Did the press report accurate information? Explain.