Abstract
We present a theoretical and analytical curve that reproduces essential features of the frequency distributions vs. diameter of the 42,000 impact craters contained in Barlow's Mars Catalog. The model is derived using reasonable simple assumptions that allow us to relate the present craters population with the craters population at each particular epoch. The model takes into consideration the reduction of the number of craters as a function of time caused by their erosion and obliteration, and this provides a simple and natural explanation for the presence of different slopes in the empirical log-log plot of number of craters (N) vs. diameter (D). A mean life for martians craters as a function of diameter is deduced, and it is shown that this result is consistent with the corresponding determination of craters mean life based on Earth data. Arguments are given to suggest that this consistency follows from the fact that a crater mean life is proportional to its volumen. It also follows that in the absence of erosions and obliterations, when craters are preserved, we would have N ∝ 1/D^{4.3}, which is a striking conclusion, since the exponent 4.3 is larger than previously thought. Such an exponent implies a similar slope in the extrapolated impactors size-frequency distribution.
