<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!
www.physicsmyths.org.uk
www.plasmaphysics.org.uk
