By what formula is this graph predicted? Cumulative Periastron Time Shift

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SUMMARY

The discussion centers on the calculation of cumulative Periastron Time Shift using a specific formula derived from orbital measurements. The key finding indicates that over 10 years and 11,300 orbits, the cumulative shift amounts to approximately 4.3 seconds, aligning with the graph's predictions. The initial orbit measured 7.75 hours, with subsequent shifts calculated using an integrated approach, leading to a cumulative shift formula of 1/2 * 67 ns * 113002. This method clarifies the confusion regarding frequency changes versus cumulative time shifts.

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Meerio
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I'm confused about how the predictions of this graph were formed.
I have this formula:
Untitled.png

But the change in frequency per second is about : 2x 10^-12 which has a problem because when you multiply this by 10 years you don't even get a change of frequency of 1/1000 of a second and in the graph it says it's around 5 seconds.
Anyone know what I'm doing wrong?

Paper: https://arxiv.org/pdf/1011.0718v1.pdf
 
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This is the cumulative change in time, not in frequency. You need the integral or sum.

The first measured orbit was about 7.75 hours, the next was 2.4 * 10-12 * 7.75h = 67ns shorter (integrated shift: 67 ns), the following one was 2*67 ns shorter than the first one (cumulative shift: 67+2*67 = 201 ns) and so on.

In 10 years, there were 11300 orbits, for a cumulative shift of 1/2 * 67 ns * 113002 = 4.3 seconds, in agreement with the parabola shown there.
 
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Thx so much this was the answer I was looking for !
 

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