Inclined comet collision time
= Inclined comet collision time
For a population with randomized vertical phases, <orbital inclination> $I$, and $R_p\ll a_p I$, the effective volume probability near the planetary plane is proportional to $\Sigma_c/(a_p I)$. The collision time then scales as $I Q^{3/2}M_p^{-2/3}a_p^2$, at fixed stellar mass and planetary <mass density>. An individual inclined <Kepler orbit> whose <orbital nodes> do not intersect the <planet>'s orbit need not collide at all.