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Ch. Froeschl\'e (OCA), P. Michel (Obs. Torino), P. Farinella (Univ. Pisa)
We have investigated the dynamical evolution of asteroid (433) Eros, soon to be explored by the NEAR probe, by performing 16 numerical integrations of ``dynamical clones'' of Eros' chaotic orbit over a time span of 5~Myr. By analyzing the results of these integrations we have found that: (i) In six cases a clone becomes an Earth--crosser, typically due to eccentricity increases caused by the \nu3 and \nu4 secular resonances; two clones become Venus--crossing and one eventually collides with the Sun. (ii) Some of the Earth--crossing clones go back to the Mars--crossing state after some time, and several have their inclination affected by the \nu13 and \nu14 nodal resonances. (iii) Nine clones have a slow evolution dominated by Mars encounters, and one of them is temporarily trapped into the 25/24 mean motion resonance with Mars, providing an effective protection from close encounters over more than 1~Myr. (iv) From the number of planetary encounters recorded during our integrations, Eros' lifetime vs. a collision with the Earth and Mars can be estimated to be about 1.84 and 2.9~Byr, respectively. (v) Due to the chaoticity of its orbit, it is impossible to estimate even as an order of magnitude the past or future mean impact rate onto Eros' surface. These findings have the following implications. Eros' dynamical lifetime is probably of the order of 50--100 Myr, and it has an \approx 5% probability of eventually hitting the Earth. Its shape may have been affected by tidal forces during past Earth encounters. Its birth location in the main belt cannot be traced back with certainty, but if Eros is a fragment from a family--forming catastrophic breakup, this must have been one of the last such events to occur in the main belt. Alternatively, Eros may have come through a ``weak'' resonance in the main belt, causing a slow orbital diffusion process and eventually leading to a strong resonance or to Mars crossing. Unfortunately, the forthcoming observations of Eros' cratering record by the {\it NEAR} probe will not be useful to discriminate between these possibilities, or to constrain its age or collisional lifetime, because the time span spent by Eros in the main belt depends on the chaotic history of its orbital elements.
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