We used the smooth, roughly exponential decay, of lunar cratering rates, K(t), relatively to the present-day value (Fig. 3.4), given by Hartmann (1999). This curve gives a monitoring of the dominant population of crater forming bodies with sizes >500 m existing in the interplanetary medium at any given time.

Fig. 3.4. Variation with time of relative lunar cratering rates, K(t). This curve represents the conjuncture of the late heavy bombardment, proposed by Hartmann. Such rates refer to the number of impact craters with size >4 km, per unit time and unit area, relatively to the present-day value. Beyond 3.9 Gyr ago, they cannot be measured and have to be conjectured with models (Courtesy W.K. Hartmann).

Fig. 3.4. Variation with time of relative lunar cratering rates, K(t). This curve represents the conjuncture of the late heavy bombardment, proposed by Hartmann. Such rates refer to the number of impact craters with size >4 km, per unit time and unit area, relatively to the present-day value. Beyond 3.9 Gyr ago, they cannot be measured and have to be conjectured with models (Courtesy W.K. Hartmann).

The basic assumption of EMMA is that these bodies were also the dominant parent bodies of early micrometeorites. Therefore, if the flux of lunar impactors was multiplied by K(t), the micrometeorite flux, x K(t), was increased by the same factor, relative to the present-day annual flux before atmospheric entry, $0. In brief, K(t) would directly scale to the variation with time of the amplification factor of the micrometeorite flux, relative to the present-day value.

The approximate exponential variation of K (t) allows the integration of x K(t). Gounelle (2000) noted that the integrant is always larger than 1 during the LHBomb. He showed that the integration from an upper limit, ti, just reduces to a simple multiplication of three terms:

where K(t1) — 2 x 106 is the value directly read on Fig. 3.4 at t1 — 4.45 Gyr; t = 70 Myr is a reasonable average value of the "mean life" of the population of impactors that rules the slope of the K(t); is the present-day micrometeorite flux measured at the Earth's orbit, of about 40,000 tons per year for the whole Earth (Love and Brownlee, 1993).

For the Earth, this formula gives an integrated micrometeoric flux since the formation of the Moon, ~ 5.6 x 1024g. This value is astonishingly similar to the average value (~4.7 x 1024 g) directly inferred from the neon and nitrogen contents of micrometeorites. This striking fit is still hard to believe!

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