On a Test of Randomness of Lunar Craters.

Abstract

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On a Test of Randomness of Lunar Craters. Marcus, Allan H. Abstract The apparent randomness in the distribution of centers of lunar craters is an important argument in favor of the meteoroidal impact hypothesis for the origin of craters. The usual test of randomness is based on goodness of fit of the Poisson distribution to the numbers of crater centers in equi-areal subregions of a region of the lunar surface. It is shown that even if the underlying distribution of crater centers is completely random, the distribution of centers of ol)seri'ablo craters is not. In particular, in finite regions in which a very large crater is found we would expect to find a dearth of small craters, since the large crater would have obliterated older small craters in its neighbo4~ood. The distribution of the number of crater centers is therefore a mixture of F)oisson distributions, with the density of craters in a region being treated as a random variable. It is possible to determine the mixing distribution of crater density from a model of the formation and survival of lunar craters. Under the meteoroidal impact hypothesis, the coefficient of variation of the crater density is less than 4%. Large variations in crater density may then be due to differences in the amount of crater-filling activity among various regions of the lunar surface. Empirical counts of continental craters show these effects clearly. Simulated plots of randomly formed craters are used to study the probability levels to be expected on applying the test of goodness of fit of the Poisson distribution. It is concluded that there is no reason to reject the hypothesis of randomness of formation of craters of moderate and large size. Publication: The Astronomical Journal Pub Date: June 1965 DOI: 10.1086/109737 Bibcode: 1965AJ.....70..325M full text sources ADS |