= Eccentricity-enhanced near-resonant transit-timing variation
{title2=$|A_t|/P_t\simeq3\mu_2\alpha|f|e/(2\pi|\Delta|)$}
A first-order <resonant orbital perturbation> changes the <semi-major axis> and therefore the <mean motion>. Integrating the sinusoidal mean-motion variation over the <near-resonant transit-timing superperiod> gives a mean-longitude amplitude proportional to $\mu_2e/\Delta^2$. Converting phase to transit time gives the displayed amplitude ratio. It assumes small perturbations, circulating <resonant argument>, effectively fixed free <orbital eccentricity>, and dominance of this enhanced term over direct phase and forced-eccentricity contributions. The formal divergence as $\Delta\to0$ signals failure of this expansion, not infinitely large transit times.
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