since we are using light-speed in our theory we must make an error at the order of S-radii since by definition S-radii is the distance over which the relevant-mass does not let even light escape (read the linked article above and here: All masses behave like black-holes to some extent). SO thats (S-radii) the minimum error or speed anomaly. That is where the singularity of Theory of Relativity exists. Sun’s S-radii is 3 kms hence 3 kms/sec order error on satellites is permitted by Theory of Relativity, at the surface or away from surface the anomaly gradually drops down, as we go far from the effect of gravity, asymptotically to zero. Which is what we are seeing, the speed-anomaly of pioneer is decreasing. Except we do not go close to Sun’s surface hence we do not see 3 kms/sec. We are far away from it and seeing 1.27 mm/sec. (That is our radar is not placed on Sun’s surface but earth’s surface)
400 kms/year is not small, this millimeter accuracy is inbuilt into theory of Relativity, or it would not explain cosmology.
Moving clocks run faster in the Doppler hemisphere of approach, run slower in the Doppler hemisphere of recession and run slower in the Doppler plane of intersection of hemisphere of approach and recession. The GPS satelites eg are in constant free fall towards earth and located in the Doppler plane of intersection, they never approach us as they never recede away, hence they induce a constant time dilation or a frequency redshift. That is the more time is spent the more the incorrectness grows.
As I had claimed a week ago, from binomial analysis I have proved that all inertial special relativistic effects (Doppler shift) are time dilation = red shift for transverse motion and time dilation = red shift for longitudinal recession and time contraction = violet/blue shift for longitudinal approach. In the transverse case which is exactly a time-dilation formula as taught (moving clocks run slower) is only a special case of time dilation/contraction. Moving clocks run faster if they are approaching us along our line of sight a thing not said enough times to our students. In other words for an observer inside a sphere of reference the general motion of a clock is one hemishphere (hemisphere of approach) Lorentz contracted and one hemi-sphere Lorentz dilated. (hemisphere of recession) The total sphere you can call a Doppler sphere. The satelites in free fall towards earth are neither in approach nor in recession hence they represent the transverse Doppler and always in red-shift or time dilation. This is a property of the binomial numbers.
I have the related diagrams and the calculations. I will update the calculations first and after some more additions the diagram.
For 2nd effect if the speed is negative that is source and observer are in relative approach the effect will always be anti-red shifted or as is known violet-shifted, again a distribution in angle which is extended towards translational vantage and line of sight vantage. (perpendicular to line of sight that is) The 3rd effect
2. relativistic time dilation: Dr Elburg calculated this to be 64 nanoseconds, but the correct value as it should be because of small GPS speed is 0.25 picoseconds, now he does not have to look towards OPERA team to falsify his hypothesis, accidentally I have done it )