Did a discrete asteroid breakup event affect Gaspra's cratering record?

Mathematics – Probability

Scientific paper

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Scientific paper

Recent analysis of the cratering record on the asteroid (951) Gaspra has indicated an index (exponent of the power law describing the cumulative distribution of craters as a function of diameter) α = -3.3 +/- 0.3, definitely steeper than the theoretically derived value of -2.5 expected for a projectile population in collisional equilibrium. A single, very energetic breakup event which locally injected debris into the main-belt population with a size distribution unrelated to the equilibrium value has been proposed as a simple explanation for this finding. I have tested this hypothesis using the numerical algorithm described in Campo Bagatin et al. (Planet. Space Sci. 42, 1079-1092, 1099-1107, 1994) to model the outcome of impacts between asteroids of very large sizes and to assess their transient consequences on the main-belt size distribution as a function of time. The results show that the previous hypothesis is very unlikely in the case of Gaspra because it requires two ad hoc assumptions: (1) that the assumed impact should have involved two relatively large asteroids, hence its a priori probability of occurring during the whole history of the Solar System would have been low; (2) and that this event should have occurred as recently as <= 10 Myr ago.

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