Creep stability of the proposed AIDA mission target 65803 Didymos: I. Discrete cohesionless granular physics model

Abstract

As the target of the proposed Asteroid Impact & Deflection Assessment (AIDA) mission, the near-Earth binary asteroid 65803 Didymos represents a special class of binary asteroids, those whose primaries are at risk of rotational disruption. To gain a better understanding of these binary systems and to support the AIDA mission, this paper investigates the creep stability of the Didymos primary by representing it as a cohesionless self-gravitating granular aggregate subject to rotational acceleration. To achieve this goal, a soft-sphere discrete element model (SSDEM) capable of simulating granular systems in quasi-static states is implemented and a quasi-static spin-up procedure is carried out. We devise three critical spin limits for the simulated aggregates to indicate their critical states triggered by reshaping and surface shedding, internal structural deformation, and shear failure, respectively. The failure condition and mode, and shear strength of an aggregate can all be inferred from the three critical spin limits. The effects of arrangement and size distribution of constituent particles, bulk density, spin-up path, and interparticle friction are numerically explored. The results show that the shear strength of a spinning selfgravitating aggregate depends strongly on both its internal configuration and material parameters, while its failure mode and mechanism are mainly affected by its internal configuration. Additionally, this study provides some constraints on the possible physical properties of the Didymos primary based on observational data and proposes a plausible formation mechanism for this binary system. With a bulk density consistent with observational uncertainty and close to the maximum density allowed for the asteroid, the Didymos primary in certain configurations can remain geo-statically stable without including cohesion.

Rubble Pile Asteroids

“…Models with simplistic or no surface forces mimic shear strength by hexagonal closest packing of similar sized spheres, or bi-modal distributions of spheres, finding that the spin-up process produces material flow towards the equator of spherical bodies that are qualitatively similar to the observed equatorial ridges observed (Walsh et al ,2012. With better surface forces by way of the soft-sphere discrete element models (SSDEM) that allow modeling frictional material with a high (~37 deg) angle of friction, the results become less straightforward as some failure modes appear internally in the evolving body, rather than just on the surface (Sánchez & Scheeres 2012, Zhang et al 2017. While some of these outcomes can result in equatorial bulging, they often end up far more extreme than the sometimes subtle bulge seen in so many radar images.…”

“…[ Figure 12: Near-Earth asteroid Geographos was found to have a highly irregular shape, which was matched in N-body simulations of a tidal disruption ).] Including more realistic surface interactions between the constituent particles, by way of a softsphere discrete element model (SSDEM; see Sanchez & Scheeres 2011,2012Schwartz et al 2012;Zhang et al 2017), actually generate more highly elongated shapes than found in the first generation of tidal disruption models . In some cases a few pieces in the fragment train are bound due to the slight increase in frictional forces during disruption (a contrast to some previous models with minimal or no friction) and result in very low velocity collisions between fragments leading to some bifurcated shapes that resemble asteroids such as Itokawa, Toutatis etc., and could possibly account for some of the large population of contact binaries.…”

“…Similar N-body tools used for tidal disruption models were deployed to model how rubble piles would respond to the gradual torques provided by YORP spinup (Walsh et al ,2012Sanchez and Scheeres 2012, Zhang et al 2017). Models with simplistic or no surface forces mimic shear strength by hexagonal closest packing of similar sized spheres, or bi-modal distributions of spheres, finding that the spin-up process produces material flow towards the equator of spherical bodies that are qualitatively similar to the observed equatorial ridges observed (Walsh et al ,2012.…”

The solar nebula origin of (486958) Arrokoth, a primordial contact binary in the Kuiper Belt

“…Particles are either frictionless or given gravel-like friction parameters-a static friction coefficient of 1.0, a rolling friction coefficient of 1.05, a twisting friction coefficient of 1.3, and a shape parameter of 0.5; the friction parameters mimic the shear strength of irregular particle shapes in contact (101). The normal and tangential coefficients of restitution are 0.2.…”

Rotationally induced failure of irregularly shaped asteroids

“…Soft-sphere discrete element methods have shown that a randomly packed sphere might have internal deformation at fast spin (e.g. Scheeres, 2012, 2016) although a heterogeneity in the internal structure would control the failure modes and conditions (Zhang et al, 2017).…”