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Relative to a clock at rest on the Earth's surface, the time recorded by an ideal clock after a circumnavigation of the Earth depends not only on the speed and altitude but also on the direction of the circumnavigation and on the rotational speed of the Earth. Such a clock may run either fast or slow, depending on the direction and ground speed for the circumnavigation. This directional dependence should be perceptible with commercial jet speeds and cesium beam clocks.
J. C. Hafele (Sat,) studied this question.