Figure 10. Distribution of the speed w of ejecta (bold curve) relative to a platform moving with a horizontal speed of 1650 m/s and at an altitude h=30 km above the lunar surface. The assumed distribution of the ejection speeds at the surface is a power law with a low cutoff value of 100 m/s and an exponent of 1.2. The two-pronged-shape of the distribution is due to the ejection zenith angle of the particles, set here at 30 and 10 degrees (left and right panels respectively). As the value of this parameter decreases, the two peaks approach each other and merge into a single peak for particles ejected along the surface normal (zero zenith angle). The grey bars represent the results of a numerical simulation with 10^7 particles for the same ejection law assumed in the model.
Abstract
We present a model of a ballistic, collisionless, steady state population of ejecta above the surface of an airless planetary body. We derive closed form solutions for the probability density functions of the altitude distribution of particles as well as for the distribution of their speeds. This is done in (i) a rest frame both at the surface and at altitude and, (ii) with respect to a moving platform such as an orbiting spacecraft. We use numerically-generated synthetic populations of ejecta under lunar surface gravity to validate these expressions and apply the model to the cases where the ejection speed distribution is (a) uniform (b) a power law. For the latter law, we find that the effective scale height of the ejecta envelope directly depends on the exponent of ejection speed law and increases with altitude. The same conclusion holds for the speed distribution of particles near the surface. At altitude, we find that orbiting spacecraft will encounter a speed distribution of particles that is strongly dependent on the ejection angle (see Figure). 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 altitude distribution of ejecta is a sensitive proxy for the dependency between speed and size of the particles.
Last Revised: 2015 March 23rd |