Semi-analytical long-term propagation of asteroids

The long-term dynamics of asteroids in the inner Solar System can be computed using the secular interaction of the solar system planets and a massless particle. This secular model is interrupted by repeated planetary encounters that scatter asteroids into chaotic orbital evolutions. Combining numerical techniques for the computation of planetary encounters and analytical secular propagations we build a propagation tool for the rapid computation of asteroid orbits over millions of years. In limited situations planetary encounters can be evaluated analytically using the Opik theory, although this approach fails for relatively distant flybys. We correct for this limitation by integrating the Lagrange Planetary Equations with the planet as third body perturbing potential for these distant and frequent flybys. The secular model used to map between encounters takes into account the planets of the Solar System from Mercury to Neptune. The secular solution is obtained through the expansion of the gravitational perturbing potential to first order in masses and orbit elements of the bodies. In this talk we will introduce our propagation methodology and show multiple results. First, we generate a swarm of artificial planetary encounters to validate our flyby evaluation method. Then, we run simulations of fictitious populations of Near-Earth asteroids and compare the statistical distributions to numerical integrations. We use the propagations in Near-Earth space to identify different dynamical regimes where the secular model describes the planetary system. Additionally, given the uncertainty in the orbit of known NEA examples we compare the statistics of large number of trajectories obtained through numerical simulations and our propagation methodology. This research was supported by a grant from the Jet Propulsion Laboratory.