On the Orbital and Collisional History of (433) Eros

(433) Eros, a ~ 20 km S-type asteroid extensively explored by the NEAR spacecraft, has had a enigmatic collisional and dynamical history. Its orbital parameters (a = 1.46 AU, e = 0.22, and i = 10.8^o) place it in the Near-Earth object (NEO) population, defined as those asteroid and comets having perihelia q < 1.3~AU and aphelia Q > 0.983 AU. NEOs, however, tend to be short-lived; typical residents have dynamical lifetimes of 10 Myr before they strike the Sun, a terrestrial planet, or are ejected out of the inner solar system via a close encounter with Jupiter. For this reason, we hypothesize that Eros has only recently evolved out of the main belt and that it has followed a complicated dynamical path to reach its current orbit. A plausible evolutionary scenario for Eros is the following: (1) A catastrophic disruption event liberates Eros from its parent body. Given Eros's relatively large size, it is likely that this event also produced an observable asteroid family (e.g., Maria family; Zappalà et al., 1997, Icarus 129, 1.). (2) The Yarkovsky effect, a radiation drag force, causes Eros to migrate towards a resonant "escape hatch" (e.g., 3:1 mean motion resonance with Jupiter). Typical drift rates for Eros-sized bodies are slow enough (da/dt ~ 5 x 10^-6 AU Myr^-1) that Eros could have taken billions of years to escape the main belt (Farinella and Vokrouhlický, 1999, Science 283, 1507). (3) Eros reaches its escape resonance and has its eccentricity pumped up high enough to enter the NEO region. (4) A combination of close encounters with the terrestrial planets and inner solar system resonances move Eros to its current orbital position. If this evolutionary history is correct, the cratering record of Eros is linked to its dynamical history, such that numerical modeling can begin to fill in the qualitative gaps discussed above. Integration results of test bodies evolving from the main belt (Bottke et al., 2001, Icarus, in press) suggest that Eros has a ~ 20% chance of coming from the 3:1 mean motion resonance with Jupiter, a ~ 50% chance of coming from the ν ₆ secular resonance, and a ~ 30% chance of coming from the Mars-crossing asteroid population located adjacent to the main belt. The mean travel time for these test bodies to reach Eros's present orbit was ~ 16 Myr, with ~ 12 Myr spent collisionally decoupled from the main belt. If we assume that the intrinsic collision probability of NEOs striking other NEOs is 15 x 10^-18~km^{- 2}~yr^-1 (Bottke et al., 1994, Hazards, 337.) and that 2-10 m projectiles are needed to make 200 m craters on Eros, we estimate that the crater production rate of 200 m craters (and larger) on Eros over the last 12 Myr has been 2.2 Myr^-1 (Scheeres et al., 2002, Asteroids III). In other words, only ~ 26 such craters have formed on Eros since it became collisionally decoupled from the main belt. Since crater counts suggest that 200 m craters on Eros are near or at saturation levels (Veverka et al., 2000, Science 289, 2088), it seems unlikely that the NEO population has made a significant contribution to this population. Thus, we conclude that most of Eros's large craters must have formed while it was still inside the main belt, where the impactor flux and exposure time of Eros's surface may have both been > 100 times larger. This leads to the exciting possibility that we may be able to use the non-saturated component of Eros's cratering record to estimate its lifetime. Assuming we understand Eros's da/dt drift rates via the Yarkovsky effect, we may even be able to bracket the possible starting locations for Eros in the main belt.