On de-Sitter geometry in crater statistics

TL;DR

This paper explains the universal inverse square distribution of small impact crater sizes using de-Sitter geometry, linking crater statistics to geometric properties of circle configurations on planes and spheres.

Contribution

It introduces a geometric framework based on de-Sitter geometry to understand crater size distributions, accounting for overlap effects.

Findings

Crater size distributions follow an inverse square law for small radii.

De-Sitter geometry provides a natural explanation for the universal distribution.

Overlap effects influence the observed crater size-frequency patterns.

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 article, 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.