Calculate the radii of trajectories that Denver and Washington will follow:
As we see from the figure:
RW=R cos47∘45′=4283649 m,RD=R cos39∘44′=4899476 m. But Denver is 1600 m higher, that is why make it more precise:
RD=4899476+1600=4901076 m. How much faster does a clock in Denver run than a clock in Washington?
Use equation (7.16):
ΔτWΔτD=exp(∫RWRDc2g(r)dr)= =exp(c2GM∫RWRDr2dr)= =exp(c2GM(RW1−RD1))= =exp((3⋅108)26.673⋅10−11⋅6⋅1024(42836491−49010761))=1. As we see, that difference is insignificant. The clocks can be considered as running at the same rate.
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