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The architecture and evolution of planetary systems are shaped in part bystellar flybys. Within this context, we look at stellar encounters which aretoo weak to immediately destabilize a planetary system but are neverthelessstrong enough to measurably perturb the system's dynamical state. We estimatethe strength of such perturbations on secularly evolving systems using a simpleanalytic model and confirm those estimates with direct N-body simulations. Wethen run long-term integrations and show that even small perturbations fromstellar flybys can influence the stability of planetary systems over theirlifetime. We find that small perturbations to the outer planets' orbits aretransferred between planets, increasing the likelihood that the inner planetarysystem will destabilize. Specifically, our results for the Solar System showthat relative perturbations to Neptune's semi-major axis of order 0.1% arestrong enough to increase the probability of destabilizing the Solar Systemwithin 5 Gyrs by one order of magnitude.

On the long-term stability of the Solar System in the presence of weak perturbations from stellar flybys