  The final sizes, composition, and angular momenta of solid planetary bodies
depend on the outcomes of collisions between planetary embryos. The most common
numerical method for simulating embryo collisions is to combine a gravity
solver with a hydrodynamic solver, allowing pressure gradients, shock waves,
and gravitational torques to loft material into orbit. Here, we perform the
first direct comparison between hydrodynamic methods and a simplified method
employing only gravity and a quadratic repulsive force. The formation of
Earth's Moon, perhaps the most heavily simulated planetary collision, is used
as a test case. Many of the main features of a collision between two planetary
embryos, including collisions in which an orbiting disc of material and/or
intact moons are formed, are controlled solely by gravitational forces.
Comparison of the methods shows that the mass and orbit of the satellite, as
well as the extent of physical mixing between the protoearth and impactor, are
similar regardless of the inclusion of the inclusion of hydrodynamic effects or
the equation of state employed. The study of thermal and chemical effects of
the impact, and determining the time scale for lunar accretion, still require a
full hydrodynamic calculation. The simplified gravity plus quadratic repulsive
force approach allows rapid testing of various initial conditions to identify
cases for further detailed study.
