= Forced eccentricity circle
{title2=$z=Z_f(1-e^{iAt})$}
With a fixed planetary <pericentre>, the linear secular equation $\dot z=iA(z-Z_f)$ has solution $z=Z_f+(z(0)-Z_f)e^{iAt}$. An initially circular orbit follows $z=Z_f(1-e^{iAt})$, a counterclockwise circle in the complex plane centered at the <forced eccentricity> $Z_f$, with <free eccentricity> amplitude $Z_f$. Its maximum <orbital eccentricity> is $2Z_f$ and its phase-averaged mean <orbital eccentricity> is $4Z_f/\pi$.
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