Size‐frequency distributions of rocks on Mars and Earth analog sites: Implications for future landed missions

The size-frequency distribution of rocks at the Viking landing sites and a variety of rocky locations on the Earth that formed from a number of geologic processes all have the general shape of simple exponential curves, which have been combined with remote sensing data and models on rock abundance to predict the frequency of boulders potentially hazardous to future Mars landers and rovers. Rock data from the near field of the Viking landers where dimensions can be measured accurately in stereo images and estimates from the far field of Viking 1 have convex up curved shapes on log-log graphs of cumulative frequency per square meter or cumulative fractional area versus diameter. The rock data show a sharp drop-off at large diameters and a progressive approach to a plateau with decreasing diameter (approaching the total rock coverage), which can be fit well with simple exponential functions. Similar shaped size-frequency distributions of rocks are found at a wide variety of rocky surfaces on the Earth and can be fit well with simple exponential functions. This distribution is compatible with fracture and fragmentation theory, which provides a physical basis for its wide application. A combined fit to rock area data at both Viking sites was made with a general exponential function, in which the pre-exponential is the total area covered by rocks. Simple linear height versus diameter relationships were also derived from height-diameter ratios at the Viking sites, which suggest that rockier areas on Mars have higher standing rocks than less rocky areas. Height was then substituted into the general exponential function derived for diameter, yielding the cumulative fractional area of rocks versus height for any given total rock coverage on Mars. Results indicate that most of Mars is rather benign with regard to hazards from landing on large rocks. For total rock coverage of 8%, equivalent to modal rock coverage on Mars and the Viking 1 site without the outcrops, about 1% of the surface is covered by 20 cm or higher rocks. A lander designed to accommodate landing on 0.5-m-high boulders, such as the Mars Pathfinder airbag system, could land on a surface covered by about 20% rocks, similar to the Viking 2 site (which is rockier than ∼95% of the planet), with ∼1% of the surface covered by rocks of 0.5 m or higher.