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