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.
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