Modelling circumplanetary ejecta clouds at low altitudes: A probabilistic approach

• Published in: Icarus (New York, N.Y. 1962) N.Y. 1962), 2015-04, Vol.250, p.268-279
• Main Author: Christou, Apostolos A.
• Format: Article
• Language: English
• Subjects: Altitude; Ejecta; Ejection; Gravitation; Impact processes; Interplanetary dust; Mathematical models; Moon; Moon, surface; Power law; Probabilistic methods; Probability theory; Satellites, surfaces
• ISSN: 0019-1035; 1090-2643
• DOI: 10.1016/j.icarus.2014.11.033

•We construct a steady state model of the impact ejecta cloud above an airless surface.•Altitude and speed distributions of the ejecta are derived for different ejection laws.•The methodology can be used to link the ejection process to measurements. 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.