If we assume the ISS would follow an orbit aligned to the ecliptic south / north (dark flow) axis, deviation from the time dilation predicted by special relativity (during one ISS orbit) can be calculated as follows;
Time dilation does not only happen on a vertical straight south / south axis, but also when moving in any horizontal direction.
This mean when the ISS is moving from ‘X’ to ‘E’, (see fig11) the expected time dilation due to SR influence will total only be 50% of the expected amount.
At ‘E’ time gain and loss of time will equalize.
When moving from ‘E’ and to ‘Z’ the clock on board ISS will gradually begin to thick faster, starting right after leaving ‘E’ and culminating at ‘Z’.
At ‘Z’ the SR-time-dilation “anomaly” will reach the culmination points that demonstrate the biggest discrepancy between expected time dilation according to the prevailing and modified theory of relativity.
At 'Z' the dark flow speed is reduced by 7660 m/s
1/sqrt(1-7660^2/299792458^2)- 1, = time will tick 3.26e-10s. faster according to modified theory of relativity, and not 3.26e-10 slower according to the prevailing theory.
The ISS orbital period = 5561 seconds. A quarter of that period (1390 seconds) .
During that period the effective average speed opposite dark flow is about 3830ms-1 /2 = 1900 ms-1
The average time dilation factor is therefore, - 1/sqrt(1-3830^2/299792458^2)- 1 = 8.16e-11
The total loss of time per orbit relative to a clock on Earth, - 1390s * 8.16e-11= 1.13e-7s.
The gain of time for the other quarter of the orbit relative to a clock on Earth, - 1390s * 8.16e-11= 1.13e-7s.
Which mean half of such orbit will have no SR time dilation effect.
But the inclination of the ISS is not aligned with the dark flow axis; it is however inclined relative to that axis somewhere between 20° to 25°, therefore we shall only expect an approximately time loss about 3.0e-8s
Off course the same principle applies for all kinds of orbits, and also the Galileo 5 & 6 satellites now dedicated for scientific tests.
Galileo 5 & 6 Kinematic Time Dilation (orbits aligned with the dark flow inclination)
If we assume that the Galileo 5 & 6 satellites will follow orbits aligned to the ecliptic south / north (dark flow) axis; - then the deviation from the time dilation during one Galileo (5 & 6) satellite orbit can be calculated as follows:
The orbital period = 46800 seconds.
A quarter of that period (11700 seconds) is where the Galileo will gain time due to gradually slower absolute dark flow speed. Speed is 3800 ms-1 .
The effective average speed is half of the orbit speed, - 3800 m/s /2 = 1900 ms-1
The average time dilation factor is therefor, - 1/sqrt(1-1900^2/299792458^2)- 1 = 2.0e-11
The total unexpected loss of time per orbit relative to a clock on Earth 11700 * 2.0e-11= 2.34e-7s
The gained time for the other quarter of the orbit relative to a clock on Earth, - 11700 * 2.0e-11= 2.34e-7s.
Which mean half of such orbit will see no SR time dilation effect.
Galileo 5 & 6 Kinematic Time Dilation (orbit 45° inclination relative to the dark flow axis)
If we assume that the Galileo 5 & 6 satellites will follow the orbits of 45° inclined relative to the ecliptic south / north axis, (relative to the dark flow axis) the time dilation during one Galileo 5 & 6 satellite orbit can be calculated as follows:
LOSS OF TIME (MODIFIED THEORY OF RELATIVITY)
Half of the satellite orbit, - the speed opposite Dark flow, = 33,3% of the orbit speed. 3800 ms-1 /3 = 267 m/s
The time dilation factor = 1/sqrt(1-1267^2/299792458^2) - 1 = 8.9e-12
The total unexpected loss of time per orbit relative to a clock on Earth = 23400s. * 8.9e-12 = 2.08e-7s
GAINED TIME (MODIFIED THEORY OF RELATIVITY)
Half of the satellite orbit, - absolute motion speed , = (66,6% of the orbit speed) 3800 ms-1 /3*2 = 2534 m/s
The time dilation factor = 1/sqrt(1-2534^2/299792458^2)- 1 = 3.57e-11
The total gain of time per orbit relative to a clock on Earth = 23400s. * 3.57e-11 = 8.35e-7s
GAINED TIME (ACCORDING TO PREVAILING THEORY OG RELATIVITY)
Half of the satellite orbit, - absolute motion speed , = (100% of the orbit speed) 3800 ms-1 = 3800 m/s
The time dilation factor = 1/sqrt(1-3800^2/299792458^2)- 1 = 8.03e-11
The total gain of time per orbit relative to a clock on Earth = 23400s. * 8.03e-11= 1,87e-6s