The trajectories of near-Earth objects (NEOs) under planetary encounters can be chaotic. Thus, the accurate propagation of NEO orbits over long timescales is limited due to their sensitive dependence on initial conditions. An implication of this fact is that long-term propagation of NEO trajectories must always be viewed in a statistical sense, and that it is most important that the dynamics capture the qualitative features of their dynamical evolution, as any single trajectory will tend to wander in the phase space. In this work we develop a semi-analytical propagation tool that qualitatively models the long-term dynamics of NEOs. The tool combines two main dynamical regimes in the long-term propagation: the slow secular perturbation of the planets in the solar system and the evaluation of planetary encounters.
The secular dynamics of NEOs are obtained from the averaged perturbing potential of the planets in the solar system. The secular cycles have timescales of hundreds of thousands of years. The configurations in which very close encounters are possible represent a small fraction of the secular cycles. This fact allows the prediction of the probability of very close encounters with the inner solar system planets. Modelling the frequency of these encounters we can compute the probability of collision or close approach, which can lead to disruption or significant spin state modification of single asteroids, and disruption of binary asteroids.
In this talk we show results of how the semi-analytical propagation of NEO orbits models the dynamics of NEOs over different timescales. Over a time scale of millions of years, the presence of encounters causes the orbits of NEOs to become uniformly distributed in the arguments of node and perihelion. By tracking close encounters, we can measure not only the events of collision but the characteristics of encounters over time. Over a time scale of millennia, many NEOs present a mainly secular orbit evolution. In this context, the semi-analytical propagation provides a powerful tool to characterize the hazardous nature of near-Earth objects. Understanding the dynamics of asteroids in these intermediate timescales allows us to better identify objects whose orbits are potentially hazardous in the future, or which may have had a period of close passages in the past.