  This study is carried out in the framework of sample-return missions to
asteroids that use a low-speed projectile as the primary component of its
sampling mechanism (e.g., JAXA's Hayabusa and Hayabusa2 missions). We perform
numerical simulations of such impacts into granular materials using different
projectile shapes under Earth's gravity. We then compare the amounts of ejected
mass obtained in our simulations against what was found in experiments that
used similar setups, which allows us to validate our numerical approach. For
the targets, we consider 2 different monodisperse grain-diameter sizes: 5 mm
and 3 mm. The impact speed of the projectile is 11 m s$^{-1}$ directed
downward, perpendicular to the surface of the targets. Using an implementation
of the soft-sphere discrete element method (SSDEM) in the $N$-Body gravity tree
code PKDGRAV, previously validated in the context of low-speed impacts into
sintered glass bead agglomerates, we find a noticeable dependence of the amount
of ejected mass on the projectile shape. As found in experiments, in the case
of the larger target grain size (5 mm), a conically shaped projectile ejects a
greater amount of mass than do projectiles of other shapes, including disks and
spheres. We then find that numerically the results are sensitive to the normal
coefficient of restitution of the grains, especially for impacts into targets
comprised of smaller grains (3 mm). We also find that static friction plays a
more important role for impacts into targets comprised of the larger grains. As
a preliminary demonstration, one of these considered setups is simulated in a
microgravity environment. As expected, a reduction in gravity increases both
the amount of ejected mass and the timescale of the impact process. Our
methodology is also adaptable to the conditions of sampling mechanisms included
in specific mission designs.
