Here we study the long-term evolution of Near-Earth asteroids. It is well known that the inner solar system is a chaotic orbital environment due to the repeated flybys of NEO by these planets. Even relatively distant flybys can cause similar trajectories to diverge, making these orbits highly sensitive to initial conditions. This means that the orbital evolution of NEO over timespans of longer than several hundred years must be treated as stochastic dynamical systems and described using methods from this field of study. One major result from this field is that, for strongly stochastic systems, the evolution of an object’s probability density function can be well modeled using dynamical solutions that are not highly precise, so long as they capture the important qualitative dynamics of these systems. We use this fact to develop a rapid semi-analytical tool to map NEO orbits over million year timespans and to determine the appropriate stochastic distribution of these object’s orbits. In this presentation we show preliminary results of long-term asteroid orbit simulations using a new semi-analytical tool.
To do this we leverage the fact that the dynamics of NEO in the inner solar system can be separated into two distinct regimes. One which has a characteristic times of days during flybys of a planet and the other with characteristic times of years during which the NEO orbits evolve secularly. The semi-analytical propagation consists in using a perturbed analytical solution of the asteroid elements until an encounter is found. Then, the outcome of the encounter is evaluated numerically. The perturbed analytical solution is derived from the averaged secular potential of the solar system planets, where Jupiter is the main source of secular perturbation.
Given the uncertainty in the orbit solution of various NEAs we generate long-term statistics of their origin and future, including tracking the frequency and depth of their flybys to the inner solar system planets. We show examples of many specific NEOs of interest, as well as presenting results for a diversity of trajectories from initially neighboring virtual particles.