Global Positioning System and Relativity

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20 years 1 month ago #11902 by Jim
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What difference does it make how the correction is made? The issue is not how to fix the difference but what causes the difference. Or not? To me it seems the cause is the bone of this thread-right or wrong?

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20 years 1 month ago #11904 by Thomas
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<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Jim</i>
<br />What difference does it make how the correction is made? The issue is not how to fix the difference but what causes the difference. Or not? To me it seems the cause is the bone of this thread-right or wrong?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote"> The bone of this thread is the conceptual integrity of the GPS- technology. If this is not given, the questions to be asked may also extend to the science behind this technology.
One has to remember that GPS is essentially a technology invented and run by the military, so the details released to the public are always likely to be a mix of fact and fiction (or should I say propaganda). In this sense, the relevance of the GPS-technology as a practical example for the real-world importance of relativity should probably be met with some scepticism, especially if some of the technological details seem to be non-sensical.


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20 years 1 month ago #11839 by makis
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<i>Originally posted by Thomas</i>
...As I said, the addition to the already existing program code by incorporating the 38 microseconds per day offset would be completely insignificant. Anyway, why would a program malfunction if it has no bugs and is thouroughly tested? It is much more likely that a hardware component on the satellite malfunctions and changes the time signal in an unpredictable and uncorrectable way.



Think about it: a few sat clocks, millions of ground receivers. What does really make sense? Correcting a few clocks or millions of receivers?

Now there is another issue here you seem not to understand. In order to correct on a daily basis in the receiver you would need clocking the daily cycle and applying the correction. The quartz clocks in GPS receivers are by far not as accurate as GPS clocks. The accumulated error will be too high. You will need to add hardware to reset clocks using a signal from an atomic clock standard in regular intervals. Hardware starts getting complicated and expensive.

As a matter of fact, you may need to do the above in real time, since in the GPS clocks the correction is spread accros the 24 hour interval but then each time you get the uncorrected signal in a receiver you would have to figure out the proper amount of correction to apply.

Needless to say, I do not see the point of your argument against the intuitively obvious and correct approach taken. Except if you think all these people who have designed and build this exceptionally good system made a blunder you were so smart to realize and they did not.

Makis

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20 years 1 month ago #11626 by Jim
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Thomas, Well ya, the military is going to confuse everyone as a matter of defence-its part of the mission it has. The GPS it seems to me can work as well or better if the unneeded confusion is removed from the system. Knowing why the 38 millisecond/day is in the system seems a logical thing to explain by some other means than the slowing of clocks. And as for confusion why is the cesium atom used at a time keeper?

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20 years 1 month ago #11665 by Thomas
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<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by makis</i>
Think about it: a few sat clocks, millions of ground receivers. What does really make sense? Correcting a few clocks or millions of receivers?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Makis,

You still aren't getting my point: the GPS receivers are already programmed such as to apply all sorts of complicated corrections, so why not the additional simple correction due to the satellite clocks running at a different rate?


<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Now there is another issue here you seem not to understand. In order to correct on a daily basis in the receiver you would need clocking the daily cycle and applying the correction. The quartz clocks in GPS receivers are by far not as accurate as GPS clocks. The accumulated error will be too high. You will need to add hardware to reset clocks using a signal from an atomic clock standard in regular intervals. Hardware starts getting complicated and expensive.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">It seems it is you who misunderstands the way the clocks on the satellites are corrected: this is not achieved through resets but by an electronic circuit that changes the oscillation frequency of the atomic clock.


<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">The quartz clocks in GPS receivers are by far not as accurate as GPS clocks. The accumulated error will be too high<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">The 'accumulation' argument is frequently given when trying to underline the importance of the relativistic correction in the GPS, however in reality the positions are actually not obtained by comparing the time signal received from the satellite with the receiver time, but by observing the difference between the time signals obtained from a number of different satellites.

Consider for simplicity a one dimensional problem where your receiver is located somewhere on the line connecting the two transmitters. In this case the signal from transmitter 1 reaches the receiver at time
t1=t0+x1/c
and the signal from transmitter 2 reaches the receiver at time
t2=t0+x2/c ,
where t0 is the time the signal is being sent out (assuming both transmitter clocks are synchronized), x1 is the distance of the receiver from transmitter 1, x2 the distance of the receiver from transmitter2, and c the speed of light.
Now if you subtract the two equations you get
x1-x2=c*[t1-t2].
You know therefore the position of the receiver just by comparing the time signals from the two transmitters (the receiver clock is completely irrelevant).
If you assume now that the transmitter clocks are running fast or slow by a relative factor (1+e), you have instead:
x1-x2=c*[(1+e)*t1 -(1+e)*t2]=c*(1+e)*[t1-t2]
which means that your position will simply be wrong by a relative amount e, but there is obviously no accumulation as the transmitter clocks run at the same rate relatively to each other.
Now, the quoted value of 38 microseconds/day allegedly due to relativity corresponds to e=4.4*10^-10. As the satellites are at a distance of around 20000 km (=2*10^9 cm), the positional error due to relativity should actually be only be 4.4*10^-10 * 2*10^9 cm = 0.8cm! This is even much less than the presently claimed accuracy of the GPS of a few meters, so the Relativity effect should actually not be relevant at all!



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20 years 1 month ago #12055 by Thomas
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<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Jim</i>
<br />Knowing why the 38 millisecond/day is in the system seems a logical thing to explain by some other means than the slowing of clocks. And as for confusion why is the cesium atom used at a time keeper?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">It is actually 38 <b>micro</b>seconds/day (see also my reply to Makis just above).
Atomic microwave transitions of Cesium and Rubidium are apparently used because of their accuracy and stability.


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