GPS and relativity

Stan Gosnell wrote:

(Everett M. Greene) wrote in
:

According to an article in the November 2004 edition of
Scientific American, the GPS satellites' clocks have a
7 microsec per day effect due to relativistic motion
and a 45 microsec per day effect due to the lower
gravity in orbit. The two effects partially cancel, so
the net adjustment is 38 microseconds.

It is left as an exercise for the student to determine
the effect of an uncompensated time value on position
values.

It's many miles. Nanosecond accuracy is required for the current ~10
meter accuracy. Linear extrapolation would lead to ~10 kilometers.


Is it as great as that? The relativistic effects would be the same for all
satellites, so, while a clock on Earth may disagree with a clock on the
satellite, all satellites would disagree by the same amount. Therefore,
while the uncompensated effect may well be several kilometres, wouldn't it
always be the _same_ kilometres?

--
Nick

Nick wrote in
:

Is it as great as that? The relativistic effects would be the same
for all satellites, so, while a clock on Earth may disagree with a
clock on the satellite, all satellites would disagree by the same
amount. Therefore, while the uncompensated effect may well be several
kilometres, wouldn't it always be the _same_ kilometres?

No. They originally tried it without any corrections, because many of
the design engineers didn't think it would matter. Turned out it did
matter. The theoretical error is large, although I can't remember the
exact numbers. BTW, it was September 2004, not November.

The GPS receiver doesn't really know the time, it just synchronizes with
the time reported by the satellites. If it thinks the time is different
than what it is, then it thinks it's in the wrong position, because it
calculates position based on the difference in time it takes the signals
to travel from different satellites. The SciAm article has a fuller
explanation, and you can also find several explanations on the net. You
can start at http://www.gpsinformation.net.

--
Regards,

Stan

"They that can give up essential liberty to obtain a little temporary
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