= 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 are
$$
S(t)=e^{-(\lambda_c+\lambda_e)t},\qquad
\tau=\frac1{\lambda_c+\lambda_e}.
$$
Equivalently, $1/\tau=1/\tau_c+1/\tau_e$. 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.
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