Comparing the roughness of the Moon from Lunar Orbiter Laser Altimeter (LOLA) to asteroids and planets

The Lunar Orbiter Laser Altimeter (LOLA) is a unique instrument that measures the topography of Moon at vertical resolutions of 10 cm and horizontal resolutions of 25 m over 1000s of km. These data are used to compute the fractal roughness of the surface of the Moon at horizontal scales that overlap similar altimetry collected at the asteroids 25143 Itokawa and 433 Eros, and the planets Mercury and Mars. This comparative analysis provides new insights on the processes that create fractal versus non-fractal topography on the Moon. 2>0.5 where e is the elevation, and s is the distance between altimetric points. For fractal structures, σ obeys σ= Ch(B/Bo)H where Bo = 1 m, and Ch is a normalizing constant. The quantity H is called the Hurst exponent. 50 m, the Moon is significantly rougher than the rubble pile asteroid Itokawa. However, extrapolating the fractal distributions observed on the Moon to B~1m, the value of σ approximates those computed for the very smooth Muses-C regio on Itokawa, where on average <1m changes in elevation are seen over 5 m of lateral displacements. This is equivalent to slopes<12°. 10km). One possible explanation for this loss may be due to gravitational forces that limit the formation of topography in excess of 3-5 km. Gravity slows the construction of large topography by volcanism and enhances any fluvial erosional processes on Mars for example. Furthermore, the formation of broad (>15km) but shallow complex craters relative to small but simple bowl shaped ones occurs because the topography of large transient craters (>10 km on the Moon) cannot be maintained by the strength of the crustal rocks and collapse due to gravity.