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•• Consider a GPS satellite in circular orbit 20,200 km above the earth’s surface, moving with orbital speed υs. If the speed of light were not constant, but instead obeyed the classical velocity-addition formula, then an observer on earth receiving a radio signal from a satellite would observe that the signal moves with speed υ0 = c ± υr, where υr is the radial speed of the satellite relative to the observer. (a) Find the orbital speed υs of the satellite. (b) As a rough estimate, take υr ≈ υs. (Computing υr exactly is actually quite messy because of the complex relation of the velocities of the satellite and observer.) If the observer calculated the distance of the satellite using r = υ0 Δt instead of the correct r = υ0 Δt, estimate the maximum error in r that would result.
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