= Finite-age planetary scattering regimes
At fixed stellar <mass> $M_\star$, planetary <mass density> $\rho_p$, age $t_\star$ and initial ratio $\kappa=a_0/a_p$, the order-unity <Safronov number> comparison and <comet energy diffusion> give boundaries
$$
M_{\rm esc}=\sqrt{\frac{3}{32\pi}}M_\star^{3/2}\rho_p^{-1/2}a_p^{-3/2},
\qquad
M_{\rm age}=M_\star\sqrt{\frac{P_p}{100t_\star}}\kappa^{-1/4}.
$$
Their logarithmic slopes in planetary <mass> versus radius are $-3/2$ and $3/4$. Above both, strong kicks and a short estimated diffusion time favour ejection; below the escape boundary, repeated weak encounters favour collision statistically. Below the age boundary, the stated diffusion mechanism has not completed on its characteristic clock. Collision lifetimes require additional cross-section and encounter-rate information, so this map alone cannot establish retention or <accretion> within the age.
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