Secondary craters of Tycho: Size‐frequency distributions and estimated fragment size–velocity relationships

Abstract

We examined the size‐frequency distribution and the spatial distribution of secondary craters around the lunar crater Tycho. Secondary crater diameters were found to range from 0.55 to 4.0 km, and their distance from Tycho to range from 130 to 370 km. The diameter and ejection velocity of the secondary‐forming fragments were also estimated from the crater size and the distance from the primary using the scaling relationships for cratering. The power law index of the size‐frequency distribution of the Tycho secondary craters ranges from 3.3 to 4.0, the same as the steep slope of the typical size‐frequency distribution for lunar craters of less than 4 km diameter. The decay index of secondary crater densities with distance from the primary craters is not constant and is small at large distances (less than 2.5 for r > 2.5R). The total number of secondaries forming ejecta fragments is more than twice larger than for other lunar primaries previously studied. These results imply that there are many small secondary craters in fields far from the primary crater. A dominant contribution of secondaries to the size‐frequency distribution of all lunar craters is thus strongly suggested. The index range of 2.6 to 3.0 for estimated fragment size distributions is not only close to other natural and experimental craters, but also to those of blocks on asteroids. The relative fragment size distributions are independent of the ejection velocity. This result is the first observational confirmation of the theoretical assumption, and agrees with a recent result from laboratory experiments.