Two atomic clocks are synchronized on Earth in a lab at an airport near the Equa

Question

Two atomic clocks are synchronized on Earth in a lab at an airport near the
Equator. One clock is then placed aboard a supersonic jet and own at a constant speed to the West around the world, so the jet remains stationary in the inertial frame of the center of the Earth (ignore other accelerations due to the motion of the Earth around the Sun and the Sun around the galaxy). The clock that remains in the lab rotates once around the Earth as the Earth rotates, traveling 40,000 kilometers. When the jet returns to the airport a day later, what is the difference in the clock readings? Give your answer in microseconds. Which clock detected less time than the other clock? Look up or estimate any necessary physical parameters, and make reasonable approximations. If you are confused, think of the clocks as light-clocks with two parallel mirrors and the light traveling vertically.

Explanation / Answer

the jet remain stationary, so in the frame of the center of the world. the clock in the jet show T0=24h=86400(s). speed of the other clock. 40000e3/86400=463(m/s). (tangential speed of the earth at the equator). so we have T'=T*phi=T/sqrt(1-v^2/c^2)=86400+1.03e-7(s). so difference is 0.1 microsec. the clock in the jet detected less time.

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