Coplanar comet collision time
= Coplanar comet collision time
The <geometric collision cross-section> in a coplanar calculation is a length $2R_p$, rather than an area. For one <comet> with local surface probability $\Sigma_c$ and <relative velocity> $v_{\rm rel}$, the rare-event rate is $2R_p\Sigma_c v_{\rm rel}$. Without <gravitational focusing>, the resulting mean collision time scales as $Q^{3/2}M_p^{-1/3}a_p$ for deep planet-crossing orbits at fixed stellar mass and planetary <mass density>.