Dynamical passage to approximate equilibrium shapes for spinning, gravitating rubble asteroids

Abstract

Many asteroids are thought to be particle aggregates held together principally by self-gravity. Here we study-for static and dynamical situations-the equilibrium shapes of spinning asteroids that are permitted for rubble piles. As in the case of spinning fluid masses, not all shapes are compatible with a granular rheology. We take the asteroid to always be an ellipsoid with an interior modeled as a rigid-plastic, cohesion-less material with a Drucker-Prager yield criterion. Using an approximate volume-averaged procedure, based on the classical method of moments, we investigate the dynamical process by which such objects may achieve equilibrium. We first collapse our dynamical approach to its statical limit to derive regions in spinshape parameter space that allow equilibrium solutions to exist. At present, only a graphical illustration of these solutions for a prolate ellipsoid following the DruckerPrager failure law is available (Sharma et al. BAAS 37 [2005a]

Granular cohesion and fast rotators in the NEA population

“…In addition, given that the particles are, in general, not aligned with the vertical, only a component of the force will be used. Hence, we multiply the cohesive force by 3 π sin(π/3), the average value of cos(x) in the interval [−π/3, π/3]. Eq.…”

“…Now we overlay the fission criterion spin rates corresponding to weak and strong lunar regolith over the spin/size data. The criterion are scaled so that their asymptotes equal the spin limit, which correspond to densities of 2.1 up to 2.7 g/cm 3 , depending on the assumed friction angle. Neither of these strengths span all of the fast rotators.…”

“…This paper continues previous research on the topic of rubble pile asteroids, and strives to integrate theoretical results, simulations and observations of the small asteroid population. Much of the theory of how a rubble pile asteroid may evolve given an increase in its spin rate over time (due to the YORP effect) has been developed in a series of papers by Holsapple [1,2] and by Sharma [3].…”

Stability of binaries. Part 1: Rigid binaries

“…The tensor A is diagonalized in the principal coordinate system of a member, and its components in that frame are available in Sharma et al (2009). We next determine the tidal moment tensor applied on one binary member by the other, say the moment M Q S exerted on the secondary by the primary.…”

An implementation of the soft-sphere discrete element method in a high-performance parallel gravity tree-code

“…An alternative to treating all particles separately is to average the physics across many particles and thereby treat the material as a continuum. In the case of solid-like granular behavior, the continuum approach usually treats the material as elastic or elasto-plastic and models it with the finite element method or a mesh-free method (e.g., [7]; also see [8][9][10] for use of analytical and continuum approaches in modeling asteroid shapes). In the case of liquid-like or gas-like granular flow, the continuum approach may treat the material as a fluid and use computational fluid dynamics.…”