Neutral exospheres of large airless bodies consist of atoms or molecules on ballistic trajectories. An import example is the lunar water exosphere, thought to transport water to cold traps. In anticipation of future observational measurements, the theory of thermalized surface-bounded gravitationally-bound exospheres is further developed. The vertical density profile is calculated using thermodynamic averages of an ensemble of ballistic trajectories. When the launch velocities follow the Maxwell-Boltzmann Flux distribution, the classical density profile results. For many other probability distributions, including thermal desorption from a vertical wall, the density diverges logarithmically near the surface. Hence, an exosphere resulting from thermal desorption from a rough surface includes a ground-hugging population that appears to be colder than the surface. Another insight derived from the thermodynamic perspective is that cold traps can be interpreted in terms of the frostpoint of the water exosphere, if the long-term average of the pressure of the exosphere is considered. Ice in lunar caves is long-lasting only if the cave interior is below the cold trap temperature threshold.
