Rock Size-frequency Distributions at the Mars Exploration Rover Landing Sites: Impact Hazard and Accessibility

Introduction: The Viking and Mars Pathfinder landing sites and a wide variety of rocky locations on the Earth show size-frequency distributions that follow an exponential when expressed in cumulative fractional area covered by rocks of a given diameter or larger versus diameter plots. Mars lander rock distributions have been fit by an equation of the form: Fk(D) = k exp [-q(k) D], where Fk(D) is the cumulative fractional area covered by rocks of diameter D or larger, k is the total area covered by all rocks, and an exponential q(k) = 1.79 + 0.152/k, which governs how abruptly the area covered by rocks decreases with increasing diameter [1]. These distributions form a family of non-crossing curves that flatten out at small rock diameter at a total rock abundance of 5-40%. Probability of Impacting Rocks: The probability of the airbag-encased lander impacting rocks of any size is computed assuming that the number of rocks per unit area can be modeled as a Poisson distribution appropriate for the natural processes that produced these distributions. The probability, p, of a single rock in any given area, c, is proportional to c, as p = 1/(c L), where L is the number of rocks per unit area (assumed to be uniform). The probability of exactly n rocks in any area (c L) is then expressed as, P(n, c L) = (c L)