Two planes leave Washington DC with a clock each, one flying east and one west. Same flights, two points of view.
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| Clock | Time elapsed | Speed over the ground | Kinetic | Gravitational | Total vs DC clock |
|---|---|---|---|---|---|
| Washington DC (ground) | |||||
| Eastbound plane | |||||
| Westbound plane |
This is a simplified model: both planes circle DC's latitude at one constant speed and altitude, so it shows the idea rather than reproducing the measurements. The real flights used airline routes with stopovers, changing altitude and speed, took longer going west than going east, and averaged several clocks.
Published values from Hafele and Keating, in nanoseconds relative to the ground clock at the US Naval Observatory (please check these against the paper before using them on screen):
| Direction | Predicted | Measured |
|---|---|---|
| Eastbound | −40 ± 23 | −59 ± 10 |
| Westbound | +275 ± 21 | +273 ± 7 |
Coastlines: Natural Earth (public domain), simplified. Model: circle of latitude 38.9° N, earth radius 6371 km, one lap of the earth relative to the ground, kinetic dilation −(v² − vDC²)/2c² and gravitational gain (GM/c²)(1/R − 1/r), each multiplied by the elapsed time.