Dynamical evolution of 1036 Ganymed, the largest near-Earth asteroid

We have studied numerically the dynamical evolution of 1036 Ganymed, the largest near-Earth asteroid, by integrating the orbits of tens of "clone" particles with similar initial conditions. Typically, the orbit initially undergoes large, coupled oscillations of the eccentricity and inclination; then, Mars encounters random-walk the semimajor axis until it reaches a strong Jovian resonance; and eventually, resonant effects pump up the eccentricity until the orbit becomes Sun-grazing or hyperbolic (after encountering Jupiter). The median dynamical lifetime is of about 10 Myr. Most orbits become Earth-crossing within 10 Myr of evolution. The origin of Ganymed and a few other sizable Mars-crossing asteroids with similar orbital elements is an open problem, since the main-belt asteroid population in the neighbouring lower-eccentricity portion of the phase space is quite sparse. Although Ganymed's reflectance spectrum has some similarity to those of the ordinary chondrites, the Earth delivery efficiency from bodies with this type of orbits is low, because they are short-lived after they become Earth-crossing.