Cumulative periastron-time shift from orbital decay ($\delta T\simeq \frac{1}{2}({\dot{P}}_b/P_{b0})t^2$)

A tiny orbital period change accumulates into a larger timing shift. Choose the original model $P_b(t)=P_{b0}+{\dot{P}}_{b}t$, with $P_{b0}=28,800\mathrm{s}$ and ${\dot{P}}_b=-2\times 10^{-12}s/s$. Expanding the accumulated cycle count givesNegative $\delta T$ means an event of fixed orbital cycle count arrives earlier than a constant-period prediction. After twenty Julian years, the chosen period has decreased by $1.262\mathrm{ms}$, while the accumulated event shift is about $-13.83\mathrm{s}$. This is a time shift of periapsis passage; it is different from a rotation of the direction of periapsis.