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by 21
2830 days ago
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> Is it really surprising that people who have extremely precise time needs and a whole team devoted to solving them would notice issues that other people wouldn't If GPS timing is bad, a lot of people will notice that their position on the map is incorrect, because that's the whole purpose of the GPS network. A 1 microsecond error is 300 meters. |
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While the speed-of-light propagation is about 300 meters in a microsecond, isn't the final position error possibly much greater? For calculating position on Earth, you can think about a sphere expanding at the speed of light from each satellite. The 1 microsecond error here corresponds to a radius 300m bigger or smaller, which only corresponds to 300m horizontal distance on the ground if the satellite is on the horizon (assuming that Earth is locally a flat plane for simplicity here). For a satellite directly overhead, the 300m error is a vertical distance. Calculating the difference in horizontal position from this error is then finding the length of a leg of a right triangle with other leg length D and hypotenuse length D+300m, where D is the orbital distance from the satellite (according to Wikipedia, 20180km). The final horizontal distance error is then sqrt((D+300)^2 - D^2), or about 110km.
Of course, this is just the effect of a 1us error in a single satellite, I'm sure there's ways to detect and compensate for these errors.