Squicciarini, Vito (2017) Modello analitico per il conteggio dei crateri all'equilibrio. [Laurea triennale]
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Crater counting has become a powerful tool to gain information about the history of the Solar System. The more cratered a surface looks, the older it is. However, as cratering density increases, erosion by newly emplaced craters starts playing an important role in surface evolution. It has long been known that, at some point, cratered surfaces tend to reach an equilibrium, i.e. the number of visible craters stops growing. The aim of this thesis is to develop an analytical model attempting to explain the equilibrium problem. The three erosive processes considered (cookie-cutting, ejecta blanketing, sandblasting) are modelled through a degradation parameter, k, related to the efficiency of the erosion process. It is then derived a first order differential equation describing the evolution of the observed CSFD. Its analytical solution correctly recovers the observation that, when the slope of the crater production function is steeper than 2, the slope of the equilibrium is independent of it. The observed crater population then evolves towards such a steady state, so that, for an old surface, small craters have already achieved equilibrium, while large ones keep following the production function. The transition radius between these behaviours grows with time and it can be used to compute relative dating. Combined with a production function, the model can successfully estimate the absolute age of the studied surface, which in turn gives clues about the geological history of its planet. In the last section, the model is applied to observational data from two lunar surfaces, giving constraints on the degradation parameter and allowing, thanks to radiometric dating of lunar samples from Apollo 15, an accurate estimate of the absolute ages and the average impactor rate.
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