One such 'scaling law' for craters was published in 1987 by Schmidt and Housen in the International Journal of Impact Engineering vol. 5 page 543. It goes like this:
1/3 0.78 0.44 -0.22
D = 1.16 ( Pp/Pt) Dp V G
Where D is the crater diameter in centimeters, Pp and Pt are the densities
( gm /cubic centimeter) of the projectile and the target, Dp is the diameter
in centimeters of the projectile, V is the impact velocity in centimeters/sec,
and G is the acceleration of gravity at the surface in centimeters/sec/sec.
The impact kinetic energy, in ergs, is of course 1/2 m V-squared where m is
the projectile mass in grams.