  We examine the mechanisms by which atmosphere can be eroded by giant impacts
onto Earth-like planets with thin atmospheres, using 3D smoothed particle
hydrodynamics simulations with sufficient resolution to directly model the fate
of low-mass atmospheres. We present a simple scaling law to estimate the
fraction lost for any impact angle and speed in this regime. In the canonical
Moon-forming impact, only around 10% of the atmosphere would have been lost
from the immediate effects of the collision. There is a gradual transition from
removing almost none to almost all of the atmosphere for a grazing impact as it
becomes more head-on or increases in speed, including complex, non-monotonic
behaviour at low impact angles. In contrast, for head-on impacts, a slightly
greater speed can suddenly remove much more atmosphere. Our results broadly
agree with the application of 1D models of local atmosphere loss to the ground
speeds measured directly from our simulations. However, previous analytical
models of shock-wave propagation from an idealised point-mass impact
significantly underestimate the ground speeds and hence the total erosion. The
strong dependence on impact angle and the interplay of multiple non-linear and
asymmetrical loss mechanisms highlight the need for 3D simulations in order to
make realistic predictions.
