The bearing capacity of asteroid (65803) Didymos estimated from boulder tracks

Article https://doi.org/10.1038/s41467-024-50149-8 The bearing capacity of asteroid (65803) Didymos estimated from boulder tracks Received: 15 November 2023 Accepted: 14 May 2024 J. Bigot1, P. Lombardo1, N. Murdoch 1 , D. J. Scheeres 2, D. Vivet1, Y. Zhang 3, J. Sunshine 4, J. B. Vincent 5, O. S. Barnouin 6, C. M. Ernst R. T. Daly 6, C. Sunday4, P. Michel 7, A. Campo-Bagatin 8, A. Lucchetti M. Pajola 9, A. S. Rivkin 6 & N. L. Chabot 6 6 , 9 , The bearing capacity - the ability of a surface to support applied loads - is an important parameter for understanding and predicting the response of a surface. Previous work has inferred the bearing capacity and trafficability of specific regions of the Moon using orbital imagery and measurements of the boulder tracks visible on its surface. Here, we estimate the bearing capacity of the surface of an asteroid for the first time using DART/DRACO images of suspected boulder tracks on the surface of asteroid (65803) Didymos. Given the extremely low surface gravity environment, special attention is paid to the underlying assumptions of the geotechnical approach. The detailed analysis of the boulder tracks indicates that the boulders move from high to low gravitational potential, and provides constraints on whether the boulders may have ended their surface motion by entering a ballistic phase. From the 9 tracks identified with sufficient resolution to estimate their dimensions, we find an average boulder track width and length of 8.9 ± 1.5 m and 51.6 ± 13.3 m, respectively. From the track widths, the mean bearing capacity of Didymos is estimated to be 70 N/m2, implying that every 1 m2 of Didymos’ surface at the track location can support only ~70 N of force before experiencing general shear failure. This value is at least 3 orders of magnitude less than the bearing capacity of dry sand on Earth, or lunar regolith. 1234567890():,; 1234567890():,; Check for updates Geotechnical properties of asteroids affect their geology and evolution1 and are important parameters in numerical models of the formation and history of small bodies. Moreover, they are also important for any space mission involving surface operations or interactions2. Direct measurements of the geotechnical properties made in the extremely low-gravity environment of the asteroid surface have the potential to inform the design of future space missions and instrumentation, and to reduce operational risk. One such geotechnical property is the ultimate bearing capacity or load bearing strength, which corresponds to the maximum pressure that a surface can withstand without experiencing general shear failure3,4. The bearing capacity provides a means to determine if the surface of the considered celestial body is able to support the weight of a lander, rover, instrument or even an astronaut, and is also a potential measure for the trafficability of the surface material, i.e., whether the soil can provide traction and propulsion5–8. In preparation for the crewed Apollo missions, the geotechnical properties of the lunar soil were an important cause of concern5. On 1 Institut Supérieur de l’Aéronautique et de l’Espace (ISAE-SUPAERO), Université de Toulouse, Toulouse, France. 2University of Colorado, Boulder, CO, USA. Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, MI, USA. 4University of Maryland, College Park, MD, USA. 5 DLR, Cologne, Germany. 6Johns Hopkins Applied Physics Laboratory, Laurel, MD, USA. 7Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Nice, France. 8University of Alicante, Alicante, Spain. 9INAF-OAPD Astronomical Observatory of Padova, Padova, Italy. e-mail: 3 Nature Communications | (2024)15:6204 1 Article https://doi.org/10.1038/s41467-024-50149-8 100 m 100 m 15 14 13 12 11 10 9 1 2 8 3 4 5 6 7 (a) (b) Fig. 1 | Identification of suspected boulder tracks on asteroid Didymos. a The approximate equator (dashed magenta line), example boulder tracks (magenta arrows) and likely boulders (white arrows) on the surface of Didymos. b The 15 boulder tracks identified on the surface of Didymos are indicated by the magenta lines. The image used here is a cropped section of DRACO image 22206, after Laplacian filtering. Earth, the ultimate bearing capacity of a specific terrain can be deduced using in situ measurements such as plate loading tests (e.g., ref. 9) combined with the Terzaghi equation10. In lieu of being able to perform such experiments on the Moon prior to the Surveyor and Apollo missions, the load bearing strength of the lunar soil was derived from images of boulder tracks formed by rockfalls. Two major types of studies, with different assumptions, have been carried out, considering either the static boulder7,8 or the rolling boulder11 to compute the bearing capacity of the lunar soil from Lunar Orbiter photographs7,8,10,11. These studies found that the lunar surface load bearing strength ranges from approximately 102 to 103 kN/m2. More recently, these Apollo-era methods have been refined and applied to high-resolution imagery to determine whether different types of soils in the pyroclastic deposits and in the permanently shadowed regions of the Moon can be traversed by a vehicle12,13. Remote sensing images from the Lunar Reconnaissance Orbiter were used to determine the lunar bearing capacity using boulder track measurements12,13 and the approach was adapted to be applicable to polar regions of the Moon and their illumination conditions14. Specifically, the Terzaghi geotechnical equation12 gives the bearing capacity of the surface as a function of the local gravity, the soil properties (cohesion, internal friction angle, density), and the boulder track parameters (depth, width). Another approach is to use the Hansen equation which also depends on the slope and the boulder shape12. The values of bearing capacity derived from the boulder tracks12 were found to correlate well with the known values of the highlands and mare regions provided by the Apollo missions7,8,10,11. On the 26th September 2022 (UTC), NASA’s Double Asteroid Redirection Test (DART15) mission performed a kinetic impact into the 151-meter-size asteroid Dimorphos, the secondary asteroid orbiting around the 780-meter-diameter primary asteroid Didymos16,17. The DART impact reduced the orbit period of Dimorphos by 33 min18, produced a large amount of ejecta19, and was highly effective in deflecting the asteroid20. In the seconds before impact, DRACO (Didymos Reconnaissance and Asteroid Camera for Optical navigation21) took images of the binary system at a constant phase angle of ~59°16,17. These images showed, at the pixel scale of the available images, Didymos to have a relatively smooth equatorial region compared to the polar terrains. Linear groove-like features perpendicular to the equator can be seen, some of which appear to contain boulders (see Fig. 1). Applying the estimated values for Didymos’ s (...truncated)