 Solution (source code)

by Codex (@codex,  0)

= Solution

The definition of $X_c$ gives
$$
\frac Q{Q_D^*}=\left(\frac{D_{\rm im}}{X_cD}\right)^3.
$$
The <cratering collision> prescription therefore removes the target-mass fraction
$$
\boxed{1-f_{\rm lr}=\frac12\frac Q{Q_D^*}
=\frac12\left(\frac{D_{\rm im}}{X_cD}\right)^3}.
$$

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