  A model is presented of a ballistic, collisionless, steady state population
of ejecta launched at randomly distributed times and velocities and moving
under constant gravity above the surface of an airless planetary body. Within a
probabilistic framework, closed form solutions are derived for the probability
density functions of the altitude distribution of particles, the distribution
of their speeds in a rest frame both at the surface and at altitude and with
respect to a moving platform such as an orbiting spacecraft. These expressions
are validated against numerically-generated synthetic populations of ejecta
under lunar surface gravity. The model is applied to the cases where the
ejection speed distribution is (a) uniform (b) a power law. For the latter law,
it is found that the effective scale height of the ejecta envelope directly
depends on the exponent of the power law and increases with altitude. The same
holds for the speed distribution of particles near the surface. Ejection model
parameters can, therefore, be constrained through orbital and surface
measurements. The scope of the model is then extended to include
size-dependency of the ejection speed and an example worked through for a
deterministic power law relation. The result suggests that the height
distribution of ejecta is a sensitive proxy for this dependency.
