Those are the theory numbers, not the results of experimentation. The 10 km&#x2F;day number (with a bad reference) comes from removing the calculation of relativistic doppler and the sagnac effect. Without Einstein, classical doppler would be used and the difference would be tiny.<p>Part of the considerations sometimes labeled &quot;relativistic&quot; are also those which compensate for the sagnac effect, this effect however, behaves no differently than classical expectation and was originally an experiment created by Sagnac to falsify special relativity. From an ECI frame, some changes to clock rates would be considered under a classical regime just like under the relativistic one. The sagnac effect is perfectly classical. (though without Sagnac trying to show Einstein wrong would we have the Sagnac effect understood well?)<p>It&#x27;s a personal interest of mine so I&#x27;ve directly contacted numerous engineers at the FAA who manage the GPS satellite system and even gotten a little info from Raymond DiEsposti.<p>What it boils down to is that there is a negligible difference between relativity and classical in this context when you understand the system and all that would need to be considered under a classical treatment.<p>Here&#x27;s an entertaining quote (not perfectly explicative, but indicative of the larger issue):<p><a href="http:&#x2F;&#x2F;www.gps.gov&#x2F;technical&#x2F;icwg&#x2F;IS-GPS-200H.pdf" rel="nofollow">http:&#x2F;&#x2F;www.gps.gov&#x2F;technical&#x2F;icwg&#x2F;IS-GPS-200H.pdf</a>
20.3.3.5.2.3 page 123<p>Since the periodic relativistic effect is less than 
25 meters, it need not be included in the time scale used for almanac evaluation. Over the span 
of applicability, it is expected that the almanac time parameters will provide a statistical URE 
component of less than 135 meters, one sigma. This is partially due to the fact that the error 
caused by the truncation of af0 and af1 may be as large as 150 meters plus 50 meters&#x2F;day relative 
to the toa reference time. 
During extended operations (short-term and long-term) the almanac time parameter may not 
provide the specified time accuracy or URE component. Additionally, occasional CS actions to 
manage clock offsets may also inhibit the ability to provide specified almanac time parameter 
accuracies