  The architecture and evolution of planetary systems are shaped in part by
stellar flybys. Within this context, we look at stellar encounters which are
too weak to immediately destabilize a planetary system but are nevertheless
strong enough to measurably perturb the system's dynamical state. We estimate
the strength of such perturbations on secularly evolving systems using a simple
analytic model and confirm those estimates with direct N-body simulations. We
then run long-term integrations and show that even small perturbations from
stellar flybys can influence the stability of planetary systems over their
lifetime. We find that small perturbations to the outer planets' orbits are
transferred between planets, increasing the likelihood that the inner planetary
system will destabilize. Specifically, our results for the Solar System show
that relative perturbations to Neptune's semi-major axis of order 0.1% are
strong enough to increase the probability of destabilizing the Solar System
within 5 Gyrs by one order of magnitude.
