  During planet formation, numerous small impacting bodies result in cratering
impacts on large target bodies. A fraction of the target surface is eroded,
while a fraction of the impactor material accretes onto the surface. These
fractions depend upon the impact velocities, the impact angles, and the escape
velocities of the target. This study uses smoothed particle hydrodynamics
simulations to model cratering impacts onto a planar icy target for which
gravity is the dominant force and material strength is neglected. By evaluating
numerical results, scaling laws are derived for the escape mass of the target
material and the accretion mass of the impactor material onto the target
surface. Together with recently derived results for rocky bodies in a companion
study, a conclusion is formulated that typical cratering impacts on terrestrial
planets, except for those on Mercury, led to a net accretion, while those on
the moons of giant planets, e.g., Rhea and Europa, led to a net erosion. Our
newly derived scaling laws would be useful for predicting the erosion of the
target body and the accretion of the impactor for a variety of cratering
impacts that would occur on large rocky and icy planetary bodies during planet
formation and collisional evolution from ancient times to today.
