In 1971 four portable atomic clocks were flown around the world in jet aircraft, two eastbound and two westbound, to test the time dilation predictions of relativity.

(a) If the westbound plane flew at an average speed of 1500 km/h relative to the surface, how long would it have had to fly for the clock on board to lose 1 second relative to the reference clock on the ground at the U.S. Naval Observatory?

(b) In the actual experiment the planes circumflew Earth once and the observed discrepancy of the clocks was 273 ns. What was the average speed of each plane?