The Lunar Cratering Record

Because of the near absence of a terrestrial geological record of the period prior to 3.5 Gyr ago, we look to other worlds in the Solar System for insights. The Moon is by far the most useful for this purpose, for it alone has been sufficiently sampled to allow a tentative - though still controversial - history of its cratering record to be developed, based on radiometric dating of returned lunar samples.

Our goal is to make use of the observed lunar cratering record to estimate the mass incident upon the Moon as a function of time prior to around 3.5 Gyr ago. This mass flux may then be extrapolated to the Earth, using the ratio of the two worlds' gravitational cross sections to determine how much larger the impactor flux was on Earth compared with that of the Moon. At the high-mass end of this extrapolation (Chyba et al., 1994), this calculation must be modified to take into account the fact that nearly all of the largest objects impacting the Earth-Moon system should have impacted Earth (Zahnle and Sleep, this volume). This need not concern us here since, as described below, organic survivability in impacts is dominated by comets approximately 1 km in size, rather than by the largest, basin-forming impactors. Ultimately we will be interested in the fraction of mass accreted by Earth that consisted of intact organic molecules. These would have represented an exogenous contribution to the terrestrial prebiotic organic inventory.

Melosh (1989) comprehensively reviews the physics of impact cratering. Chyba and Sagan (1992, 1997) review the application of cratering physics to the lunar impact record, shown in Fig. 6.4, to derive estimates of mass flux accreted by the Earth through time. For their smooth monotonic "procrustean fit" to the lunar impact record (Fig. 6.4), they derive an expression for the mass flux on the Earth at time t, m(t), in terms of the contemporary mass flux, m(0):

Fig. 6.4. Analytical monotonic fit to cumulative lunar crater density as a function of surface age, with a decay time constant t=144 Myr (100 Myr half-life). From Chyba (1991). No attempt is made in this figure to model a possible terminal lunar cataclysm, but see the discussion in Sect. 6.4 of the text.

Fig. 6.4. Analytical monotonic fit to cumulative lunar crater density as a function of surface age, with a decay time constant t=144 Myr (100 Myr half-life). From Chyba (1991). No attempt is made in this figure to model a possible terminal lunar cataclysm, but see the discussion in Sect. 6.4 of the text.

where

In this model, the decay constant t is 144 Myr. The relevant value for m(0) may be chosen to be the mass flux appropriate for any particular impact population, be they interplanetary dust particles (IDPs), km-diameter comets, or asteroids. This assumes that the time variation of each subpopulation varies as this model for the overall impactor flux. Of course, this may not have been the case. Chyba and Sagan (1992) discussed this concern for IDPs in particular. At various points in the discussion below, we examine this assumption for particular potential impactor populations.

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