The two atomic clocks are precisely synchronized. One of the clocks is placed on an airplane flying at an average speed of 260 m/s above the ground, and the other clock remains on the ground. When the airplane returns to the ground, the clock on the ground has recorded exactly 4.0 hours.
a) How much do the clock readings differ? Tip: Convert time dilation into a series using the binomial formula and view the result at the non-relativistic boundary with v << c.
b) Which clocks are left behind?
1) Earth clock
2) Airplane clock