English

On de-Sitter geometry in crater statistics

Earth and Planetary Astrophysics 2015-06-11 v2 General Relativity and Quantum Cosmology Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.1209.0525,
  title  = {On de-Sitter geometry in crater statistics},
  author = {Gary W. Gibbons and Marcus C. Werner},
  journal= {arXiv preprint arXiv:1209.0525},
  year   = {2015}
}

Comments

6 pages, 2 figures, accepted by MNRAS. Version 2: title modified, appendix added, some small changes

R2 v1 2026-06-21T21:59:17.958Z