Distributions and moments of asteroid and comet impact speeds upon the Earth and Mars

Probability distributions of impact speeds (ν) upon the Earth and Mars are presented for (i). Observed planet-crossing asteroid orbit distributions; and (ii). The expected distribution of near-parabolic cometary orbits arriving from the Oort-Öpik cloud. For any particular phenomenon the effect produced may vary as νx, and one requires the mean value 〈νx〉 for the analysis (of crater sizes, for example) rather than 〈ν〉x as has often been employed. With this in mind the characteristic values of ν derived from calculations of 〈νx〉 for exponents x = 0.1 to 4.0 are presented. In the bioastronomical context the two opposite ends of the impact speed distributions are the regions of interest: the highest speeds to eject rocks which might carry microbial life to other planets, the lowest speeds to make more likely the survival of organic chemicals from the impactor. The speed distributions indicate that cometary impacts are much more likely to cause ejections from planetary surfaces into heliocentric orbits but, paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are apparently depleted in such constituents.