# GPS and relativity

by Suxxor
Tags: relativity
 P: 6 What they're saying is: If satellite and ground based clocks are initially synched, separated, and put into operation without correcting for relativistic effects the accuracy of the system would fail by 1 foot/ns. That's a fact. Read Ashby's paper or better yet do this project on the GPS. Student project on the Global Postioning System [Taylor and Wheeler Exploring Black Holes] http://www.eftaylor.com/download.htm...ral_relativity
 P: 601 Here's a video by the Perimeter Institute regarding GPS & GR/SR Source- http://www.perimeterinstitute.ca/Per..._Inspirations/
P: 19
 Quote by Brucep What they're saying is: If satellite and ground based clocks are initially synched, separated, and put into operation without correcting for relativistic effects the accuracy of the system would fail by 1 foot/ns. That's a fact.
Who is saying that? No-one is saying the system would fail 1 foot/ns. Some sources and Brian Cox is claiming the system would fail 38 000 feet per day which is not the same as 1 foot per ns.

1 foot/ns is the speed of light and means that 1 ns desync between GPS signals means approximately 1 foot of position error calculated in GPS receiver. This applies to all kind on GPS signal desynchronizations, not only those caused by not correcting relativistic effects.

This thread argues that since relativistic effects do not cause desynchronization build-up between satellite signals, there would not be GPS position error build-up and GPS would still work.

So far there is not a single argument in this thread to rebute that claim.

 Quote by Brucep Read Ashby's paper
The paper has been recommended before in this thread, but does not contain information how position error would behave if correction would not be used.

 Quote by Brucep or better yet do this project on the GPS. Student project on the Global Postioning System [Taylor and Wheeler Exploring Black Holes] http://www.eftaylor.com/download.htm...ral_relativity
The project has a statement
"Of course there is a wrinkle: The clock in your hand-held
receiver is not nearly so accurate as the atomic clocks carried
in the satellites. For this reason, the signal from a fourth
overhead satellite is employed to check the accuracy of the
the hand-held receiver to process GPS signals as though it
contained an atomic clock.
"

So, the paper admits that ground clock is in sync with one of the satellites.

But then suddenly on page A-4, it starts calculating the timing differences on satellite and ground and translating this to position error. How can it do that, when just before it concluded that ground time does not matter for position error, because it is synced by the satellite? This is a contradiction.

"To one signiﬁcant ﬁgure, the satellite clocks and Earth clock go
out of synchronism by about 50 000 nanoseconds per day due to their difference in altitude alone.
"

"In 1 nanosecond a light signal (or a radio wave)
propagates approximately 30 centimeters, or about one foot. So a difference of, say, hundreds of nanoseconds will create difﬁculties.
"

***

IMO, the argument is now even stronger than before, because we know from multiple sources, that only satellite signals are used on position calculation and ground time is not at all used.
 P: 6 Suxxor: "Who is saying that? No-one is saying the system would fail 1 foot/ns. Some sources and Brian Cox is claiming the system would fail 38 000 feet per day which is not the same as 1 foot per ns." Relativistic physics is saying the GPS system would fail at 1 foot for every ns the GPS satellite and ground based clocks fell out of synch. That would be 38,403 ns/day. Everything else about your argument is obfuscating nonsense. You argue that the correction isn't needed for the GPS to work. Complete nonsense.
PF Patron
P: 4,984
 Quote by Suxxor Did you use smaller font for all the reasoning to back up your argument? Because I cannot see any. To prove your point, you'd have to give at least some - in particular show that the two simple calculations in post #13 are wrong, incomplete or based on the wrong assumptions. Even Einstein had to back his theories up with reason for others to accept them. (And I believe in you. You are just like Einstein.)
I don't think Einstein would have felt compelled to waste his time refuting nonsense. I certainly don't.
P: 245
It is puzzling when someone drops by to say how the whole discussion is too ridiculous for him and how he couldn't care less to answer, yet still finds the time to say just that. Then please don't waste your time anymore and don't say anything anymroe.

 Quote by Brucep Relativistic physics is saying the GPS system would fail at 1 foot for every ns the GPS satellite and ground based clocks fell out of synch. That would be 38,403 ns/day. Everything else about your argument is obfuscating nonsense. You argue that the correction isn't needed for the GPS to work. Complete nonsense.
Perhaps you mean that the speed of light says that when the clock is wrong by 1 ns the inaccuracy would be 1 foot, not relativistic physics? Maybe you meant to say that according to relativity the time on the satellites advances 38 microseconds faster each day?

How exactly is the correction needed for GPS to work?

Searching online, I found that good and accurate quartz clocks are wrong every day by +/- 0,02 seconds. That is 20 milliseconds or 20 000 microseconds each day. A 38 microsecond deviation would get lost somewhere in there. GPS relies on only the relative times and uses them to calculate an intersecting point.
PF Patron
P: 10,123
 Quote by chingel It is puzzling when someone drops by to say how the whole discussion is too ridiculous for him and how he couldn't care less to answer, yet still finds the time to say just that. Then please don't waste your time anymore and don't say anything anymore.
I think he has a point though.
I haven't determined exactly what you are arguing about. Is it the fact that clocks on satellites are not in sync with the ground? Is it that the difference in sync would produce laughably wrong results, if not corrected for? Or is it that, by compensating for this, it is easy (i.e. very cheap) to produce a receiver that gives very good answers? You just seem to be getting ratty with each other by not understanding where you're each coming from. In your own terms you could both / all not be too wrong at all.

Feedback is a wonderful thing and it is one of the secrets of the high accuracy of the system. The transmitter clocks are constantly being corrected from the ground by looking at the positioning errors at reference sites on the ground. The clocks in receivers just don't need anything special in the way of absolute timing. They just need to be able to look at differences. Not trivial, of course, but very doable using quartz oscillators.

It might be more fruitful to be discussing how such incredibly weak signals, received from the satellite network, can be processed by a handheld receiver with an antenna that is built into the case of an affordable mobile phone. The effective noise bandwidth must be way below 1Hz to get the system to work. Thats why it can take so long for a receiver to lock on, if it's been out of touch for any length of time (that's where the receiver clock accuracy comes in.

btw, I took exception to the statement about "triangulation" early on in that Utube movie. There is no directional information used in GPS - as we all know - and there was no real description about how GPS works at all. The SR and GR bits were useful, though.
P: 19
 Quote by Brucep Relativistic physics is saying the GPS system would fail at 1 foot for every ns the GPS satellite and ground based clocks fell out of synch. That would be 38,403 ns/day.
But ground based clock is not used at all! How can it cause an error then? You have missed the point.

 Quote by Brucep Everything else about your argument is obfuscating nonsense. You argue that the correction isn't needed for the GPS to work. Complete nonsense.
It is not. Several posters in this thread have understood the issue: #8, #9, #15, #16 .

The problem is, you have not understood the argument, but rant at me claiming I talk nonsense. If several other people understand the issue and you don't, don't you think the problem could be your own limitations.

I feel dissapointed, because I took time to respond to your post and explain the same thing again. None of it reached the target.
P: 19
 Quote by sophiecentaur I think he has a point though. I haven't determined exactly what you are arguing about.
We are arguing whether GPS positioning would work if relativistic time drift in satellites wasn't compensated.

One camp is saying that the position error build-up would be 38 000 feet per day (without compensation). The argument is based on the fact that ground clock would go out of sync with satellite clocks.

The other camp (me and few other people) are saying that there would be no error build-up, since position calculation involves only satellite signals and ground clock is not at all used.

***

The problem is that the 38000-feet camp does not understand the basis of our argument.
P: 245
 Quote by sophiecentaur I think he has a point though. I haven't determined exactly what you are arguing about. Is it the fact that clocks on satellites are not in sync with the ground? Is it that the difference in sync would produce laughably wrong results, if not corrected for? Or is it that, by compensating for this, it is easy (i.e. very cheap) to produce a receiver that gives very good answers? You just seem to be getting ratty with each other by not understanding where you're each coming from. In your own terms you could both / all not be too wrong at all.
It was very clear to me from the first post what the question was. He saw a video, where someone said that if relativity were not taken into account, the GPS would accumulate an 38000 feet error per day. The OP said that he thinks absolute time isn't important and such an accumulation wouldn't happen, then he asked what we think of it.

I said I think the error wouldn't accumulate either. Then someone said that it would and we would be driving in corn fields if we don't take relativity into account, which I am arguing against, but unfortunately the guy who said it doesn't want to discuss it because it is nonsense to him.

Then there is also someone else who says it is nonsense that correction for relativity isn't needed to make GPS work, but it seems he doesn't understand the question either.

I don't understand why is such a hard time given to someone who just asks a simple question. I think the question was very clear.
P: 1,555
 Quote by chingel I don't understand why is such a hard time given to someone who just asks a simple question. I think the question was very clear.
I am not surprised, often on this forum when someone has a question about relativity the first reaction of many here is to be defensive and assume relativity as a theory is questioned. It is rather annoying and a hostile learning environment.

I do not think anybody here questions that clocks in GPS satellites run faster due to the gravitational field of the Earth even if we subtract the time delay of relative motion.

The question here is if we would not compensate for relativistic and gravitational effects would the error accumulate over time. That to me seems a legitimate question.
 P: 6 The argument is simple for me. GR & SR predict the GPS failure rate would be ~ 1 foot per nanosecond with no relativistic correction and perform, as designed, with the correction. Suxxor says that's not true. The GPS would function just fine without the relativistic correction. Fortunately the GPS operation proofs he's wrong while being considered a best test for GR in the weak field. I did provide a detailed explanation with the link to the GPS project in Edwin Taylor's and John Wheeler text Exploring Black Holes. In geometric units, used in the project, this is the weak field approximation derived from the Schwarzschild metric. dt_satellite/dt_earth = 1 - M_earth/r_sat - v^2_sat/2 + M_earth/r_earth + v^2_earth/2 The GPS correction dt_sat - 4.4453EE-10 = dt_earth 86,400 seconds/day * 4.4453EE-10 = 38,407 nanoseconds/day Suxxor is claiming that doesn't matter. The reason you have to account for this correction is that light travels 1 foot per nanosecond and GR says it's required. The GPS is unique as a weak field experiment where the miniscule effects of gravity can't be ignored. I called his comments nonsense because they are. He intimated that the GR correction is so small that it would hide inside 'other corrections'. Ignoring the fact that all the signals travel at 1 foot per nanosecond. So what you have is somebody who knows very little about the literature trying to challenge it.
 PF Patron Sci Advisor P: 10,123 I don't think anyone could question the straightforward predictions of SR & GR in this context. Any serious challenge would not be worth this length of thread. There must have been a misunderstanding coupled with a bit of testosterone, I think.
 Mentor P: 5,909 Please keep the discussion dispassionate and free from insult, either explicit or implicit.
P: 21
 Quote by Brucep I called his comments nonsense because they are. He intimated that the GR correction is so small that it would hide inside 'other corrections'. Ignoring the fact that all the signals travel at 1 foot per nanosecond. So what you have is somebody who knows very little about the literature trying to challenge it.
I don't think his argument is that an error exists due to SR/GR, I think he is implying that the error is static, not compounding. This appears to be more of an engineering/computing than a physics question.

Others correct me if I am mistaken, but the reason the error compounds is because in order to determine your location, the GPS receiver uses distances to the satellites. Since the satellites constantly change position relative to the receiver (they are orbiting the earth), you must determine distance through timing, which will necessarily involve your planetside clock and the relativity corrections that go with it.

I actually think everyone here is wrong - if uncorrected the error is neither static nor strictly compounding; it is semi-periodic (there is a maximum error for satellite position, even in a system of dozens of satellites).
P: 19
 Quote by Brucep I called his comments nonsense because they are. He intimated that the GR correction is so small that it would hide inside 'other corrections'. Ignoring the fact that all the signals travel at 1 foot per nanosecond. So what you have is somebody who knows very little about the literature trying to challenge it.
You are still not getting the point. I don't think it can be explained more clearly than chingel and Passionflower have done in posts #28 and #29.

I would not mind getting adequate counter-arguments, but this is getting frustrating.

Nevertheless, I'll try explaining one more time.

***
I accept that time on satellites would go 38 us per day faster on the satellites than on ground without the correction - no question about that.

If ground time was used in GPS position calculation, the position error would indeed build up 38 000 ns/day.

However, ground time is not used for position calculation. Even your own Taylor and Wheeler paper confirms that. That's why they use 4 satellites instead of 3.

Do you see now what I mean? Ground time is not used. So for position calculation, time difference between ground and satellite does not matter. Because ground time is not used. Get it?