Modelling circumplanetary ejecta clouds at low altitudes: a probabilistic approach

TL;DR

This paper develops a probabilistic model for the distribution of ejecta clouds around airless planetary bodies, deriving analytical solutions validated against simulations, and explores how ejection speed laws influence ejecta height and velocity distributions.

Contribution

It introduces a novel probabilistic framework with closed-form solutions for ejecta distributions, including size-dependent ejection speeds, enhancing understanding of planetary ejecta behavior.

Findings

Effective scale height depends on the ejection speed power law exponent.

Height distribution of ejecta can constrain ejection parameters.

Model validated against synthetic lunar ejecta populations.

Abstract

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.