I'm working through "Exploring Black Holes" by Taylor and Wheeler. Their first project is on the GPS system and how GR must be accounted for. At the end you arrive at the conclusion that the satellite atomic clock will advance approximately 38,700 nanoseconds a day with respect to an atomic clock on earth. This part I understand, what I don't understand is why this matters. And I think my problem is that I don't understand how the GPS really works.(adsbygoogle = window.adsbygoogle || []).push({});

I understand that three satellites send out their signals and I take the intersection of those three spheres as my location. I also understand that to figure out what the radius of the sphere is, I would calculate the radius as c*(t_receive - t_send) where t_send was encoded into the signal.

Now, let's assume I had an atomic clock in my receiver (which I realize I don't have), that was synchronized with the satellite clock before it went into space. Furthermore, lets assume I ignore GR. Here I agree that every day that the satellite atomic clock advanced, my answer will get further and further skewed (since t_receive - t_send would get smaller and smaller and eventually turn negative). But, Ihave an atomic clock in my receiver, and the cheap clock I do have is not accurate enough for this calculation. The clock in my receiver probably skews more then 38,700 ns all on its own. Is this not why we add a fourth satellite to send us a time that we use to "correct" our own time? I'm guessing the algorithm for this correction will answer my question, but let me continue. Since I am somehow setting my receive time off this satellite clock which experiences the same effects as the other three satellite clocks, I would think that this daily advance of the satellite clocks would be canceled out since my reference (the 4th satellite) is also advancing. Now there would still be an error of the time dilation difference during the propagation of the signal, but I would think it would only be the difference experienced during that time, which would be on the order of .06 seconds. The time error effect do to GR then we only be on order tens of picoseconds (nothing at all to fuss about).don't

So I guess my question is, how does the 4th satellite "correct" my clock in my hand? Do I really care about the daily advance of the satellite clocks, doesn't the 4th satellite cancel this out since it is also advanced?

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# GPS and relativity.

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