Modelling Bennu's Crater Development
Authors: Smith Peter , DellaGiustina Daniella , Burke Keara , Golish Dathon , Lauretta Dante 
Published: October 2020

Modeling Bennu&#8217;s Crater Development&#160;P.H. Smith (1), D.N. DellaGiustina (1), K.N. Burke (1), D.R. Golish (1), D. S. Lauretta (1)(1) Lunar and Planetary Laboratory, University of Arizona, USA (psmith@lpl.arizona.edu)&#160;IntroductionSeveral hundred craters have been identified and mapped on Bennu [1].&#160; Their spectral properties have been studied using data from the MapCam instrument onboard the OSIRIS-REx spacecraft [2].&#160; The crater frequency versus spectral slope across the wavelength range of 0.550 &#181;m (v band) to 0.860 &#181;m (x band) shows a skewed distribution varying from the median spectral slope of &#8211;0.17 micron&#8211;1 (x/v = 0.948) to a neutral or flat slope (x/v = 1.0).&#160; DellaGiustina et al. [2] attribute this trend to space weathering.&#160; They suggest that freshly formed craters are red, and as they age, they evolve to the bluish slope seen across the asteroidal surface.&#160; This abstract presents the results of an age model of Bennu&#8217;s craters in the size range of 1 to 10 m.&#160; Craters in this size range were selected as having likely been formed during the time that Bennu has orbited in near-Earth space.&#160; Larger craters on Bennu are thought to have formed during its long history in the main asteroid belt [3].&#160;Elements of the Crater ModelOur model covers three stages in the evolution of craters.&#160; First, a creation function produces a small number of craters randomly selected for size according to a power law distribution.&#160; These craters appear each time step.&#160; Because the modeled crater distribution will be compared to the measured one, an uncertainty is introduced into the color slope.&#160; In other words, at each time step, craters form with an x/v of 1.0&#177;0.01 and with sizes randomly drawn from a power law distribution (radius&#8211;3).&#160;Once a crater is created, it is tracked throughout its evolution.&#160; With each time step, the crater weathers toward a bluish slope.&#160; The number of time steps required is determined through an exponential function whose 1/e time is a variable in the model.&#160; The slope decreases rapidly at first but approaches the final Bennu slope asymptotically.&#160; This is the final destination for stages one and two.&#160;The third stage is the erasure of craters.&#160; This can occur through mass wasting that is either gravitationally forced or caused by impact-driven seismic shaking [4].&#160; OSIRIS-REx has observed particles thrown off into orbit that return to the surface, which may also contribute to erasure [5].&#160; Because of the limited observational data concerning these processes, they are modeled together in a linear fashion such that the smaller craters have shorter lifetimes than the larger ones.&#160; The slope of this fill-in rate is a variable in the model.&#160;The code runs time step by time step, and all craters are tracked throughout their lifetime.&#160; The variables are optimized so that the spectral slope distribution matches that observed.&#160;Model Results Figure 1 illustrates a typical output of the model.&#160; The variables are set in the following manner: The 1/e time for weathering is 50 time steps. The erasure algorithm starts eliminating the smallest craters after an age of 160 time steps and will eliminate all craters