 Collision-ejection lifetime of a comet

The collision-ejection lifetime of a comet combines two ways to remove it from a specified orbital population: impact and gravitational ejection. If these can be approximated as constant competing Poisson process rates ${\lambda }_c$ and ${\lambda }_e$, the survival probability and mean lifetime areEquivalently, $1/\tau =1/{\tau }_c+1/{\tau }_e$. The probability that collision is the first removal is ${\lambda }_c/({\lambda }_c+{\lambda }_e)$.

Coplanar comet collision time and planetary ejection of a comet estimate the constituent processes under different encounter assumptions. Their reciprocal times should only be added when they refer to a consistent population and approximately stationary rates. Repeated planetary scattering can change the orbit and correlate encounters, invalidating a single exponential lifetime.