On de-Sitter geometry in crater statistics

Abstract

The cumulative size-frequency distributions of impact craters on planetary bodies in the Solar system appear to approximate a universal inverse square power law for small crater radii. In this paper, we show how this distribution can be understood easily in terms of geometrical statistics, using a de-Sitter geometry of the configuration space of circles on the Euclidean plane and on the unit sphere. The effect of crater overlap is also considered. © 2012 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.