In Celestial Mechanics and Dynamical Astronomy for Dec (vol. 137 #6):
Knežević, Z. Failures and optimization in computation of asteroid synthetic proper elements 39 s10569-025-10272-0
We track asteroids… oh boy, do we track asteroids. As a matter of routine, we project asteroid trajectories forward >100 years, in case of any impact risk. The question remains, though- are some asteroid orbits unstable over some timeframe, which we may be approaching? Knežević is asking, and checking. It’s a cumbersome but straightforward task to include the planets in our asteroid calculations; they perturb lesser masses with their gravities, resulting in somewhat new orbits. But are the new calculations themselves still valid? If we take calculations far enough, we will start to see ‘chaotic’ states, which Knežević has identified: certain planet-asteroid interactions result in nontrivial perturbations, and we then need to redo the math.