  Neutral exospheres of the Moon, Mercury, and several other solar system
bodies consist of particles on ballistic trajectories. Here, the vertical
density profile of a surface-bounded exosphere is calculated using
thermodynamic averages of an ensemble of ballistic trajectories. When the
initial velocities follow the so-called "Maxwell-Boltzmann Flux" (MBF)
distribution, the classical density profile results. For many other probability
distributions, the density approaches infinity near the surface and has a more
ground-hugging vertical profile than the classical solution. Even MBF on a
rough surface results in a ground-hugging component. Observed vertical density
profiles that were interpreted as a superposition of a hot and a cold (ground
hugging) population may in fact be consistent with a population at a single
temperature.
