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Impact craters are among the most prominent topographic features on planetarybodies. Crater scaling laws allow us to extract information about the impacthistories on the host bodies. The pi-group scaling laws have been constructedbased on the point-source approximation, dimensional analysis, and the resultsfrom impact experiments. Recent impact experiments, however, demonstrated thatthe scaling parameters themselves exhibits complex behavior against the changein the impact conditions and target properties. Here, we propose analternative, fully analytical method to predict impact outcomes based on impactcratering mechanics. This approach is based on the Maxwell Z-model and theresidual velocity. We present analytical expressions of (1) the proportionalityrelation between the ejection velocity and the ejection position, (2) theradius of a growing crater as a function of time, and (3) the transient craterradii. Since we focused on obtaining analytical solutions, a number ofsimplifications are employed. Due to the simplifications in the strength model,the accuracy of the prediction in the strength-dominated regime is relativelylow. Our model reproduces the power-law behavior of the ejecta velocitydistribution and the approximate time variation of a growing crater. Thepredicted radii under typical impact conditions mostly converge to a regionbetween the two typical scaling lines by the pi-group scaling laws, stronglysupporting the notion that the new method is one of the simplest ways topredict impact outcomes, as it provides analytical solutions. Our model couldserve as a quick-look tool to estimate the impact outcome under a given set ofconditions, and it might provide new insights into the nature of impactexcavation processes.

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