Haefele and Keating flew an atomic clock from the west coast to the east coast in 1971 and then they flew it back. The east going clock lost 59 +- 10 ns and the west going clock gained 273 +- 7 ns. What I do not understand is why they used the center of the earth as a reference frame, and not the surface-after all that's where the surface clock is located. They said: "The problem encountered with measuring the difference between a surface clock and one on an aircraft is that neither location is really an inertial frame. If we take the center of the earth as an approximation to an inertial frame, then we can compute the difference between a surface clock and the aircraft clock. " The need to establish a third frame of reference-the center of the earth-is confusing. Why is neither the surface clock's nor the airborne clock's frame of reference valid? Because the earth's surface is moving? But that's a major point of the einstein equivalence principle-that moving frames of reference have the same physics. I understand the equation for the time difference calculation: Ta-Ts=To[(2Rwv+v^2)/2c^2] where Ta is airborne time, Ts is surface time, To is center of the earth time R is earth radius, w is earth angular velocity, v is plane velocity, c is light speed And then they go on to use the following approximation: Ta-Ts=-Ts[(2Rwv+v^2)/2c^2] The difference being they use surface time instead of center of the earth time. They state: Note that the "earth center" time has been replaced by the surface time in this expression. This is a valid approximation in this case since the time difference is many orders of magnitude smaller than the time itself, and this allows us to model the difference between two measurable times. How can they conclude by using Ts when they started the whole analysis saying that surface time was not a proper inertial frame? And another confusing aspect of using the center of the earth as the reference frame is if you change the flight plan a little bit. Suppose the plane flies along a line of longitutude instead of latitude? Since v is orthogonal to earth angular velocity, is it measured as 0? A flight to south pole is the same as a flight to north pole in terms of time dilation? I wonder if that expt has been done?