59 research outputs found
On de-Sitter geometry in crater statistics
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.Comment: 6 pages, 2 figures, accepted by MNRAS. Version 2: title modified,
appendix added, some small change
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