Impact cratering mechanics: A forward approach to predicting ejecta velocity distribution and transient crater radii

TL;DR

This paper introduces an analytical model based on impact cratering mechanics to predict ejecta velocity distribution and transient crater radii, offering a simpler alternative to traditional scaling laws with potential for quick impact outcome estimates.

Contribution

The paper develops a fully analytical approach using the Maxwell Z-model and residual velocity to predict impact outcomes, expanding beyond traditional empirical scaling laws.

Findings

Model reproduces power-law ejecta velocity distribution

Predicts crater growth and transient radii with simplified assumptions

Results align with traditional pi-group scaling laws

Abstract

Impact craters are among the most prominent topographic features on planetary bodies. Crater scaling laws allow us to extract information about the impact histories on the host bodies. The pi-group scaling laws have been constructed based on the point-source approximation, dimensional analysis, and the results from impact experiments. Recent impact experiments, however, demonstrated that the scaling parameters themselves exhibits complex behavior against the change in the impact conditions and target properties. Here, we propose an alternative, fully analytical method to predict impact outcomes based on impact cratering mechanics. This approach is based on the Maxwell Z-model and the residual velocity. We present analytical expressions of (1) the proportionality relation between the ejection velocity and the ejection position, (2) the radius of a growing crater as a function of time, and (3) the transient crater radii. Since we focused on obtaining analytical solutions, a number of simplifications are employed. Due to the simplifications in the strength model, the accuracy of the prediction in the strength-dominated regime is relatively low. Our model reproduces the power-law behavior of the ejecta velocity distribution and the approximate time variation of a growing crater. The predicted radii under typical impact conditions mostly converge to a region between the two typical scaling lines by the pi-group scaling laws, strongly supporting the notion that the new method is one of the simplest ways to predict impact outcomes, as it provides analytical solutions. Our model could serve as a quick-look tool to estimate the impact outcome under a given set of conditions, and it might provide new insights into the nature of impact excavation processes.