Analytic rock abundance distributions and their application to spacecraft landing hazards

The abundances of protrusion hazards (“rocks”) on planetary surfaces, and the analytic functions used to describe them, are reviewed in the context of spacecraft landing system design. Power laws appear most successful in impact-dominated surfaces such as the Moon and small bodies, whereas where Aeolian and fluvial sorting processes contribute (e.g., Mars, Titan), a depletion at small and large particle sizes is seen, making exponential and related (e.g., log-normal, Weibull, Golombek-Rapp) functions better descriptors of the population. A useful empirical relation is that the number density per m2 of 50cm diameter rocks N(>50) = 0.0015 * CFAˆ1.5 (to±30%) where CFA is the cumulative area fraction in per cent. Obstacle specifications on prior missions are reviewed – an emergent relationship of clearance = 0.1 * vehicle width is found ( ± a factor of 2). For typical lander scales and rock abundances, a 1cm increase in clearance (rock diameter tolerance) leads to a 10% reduction in contact probability. Applications to the Dragonfly mission are considered.