Stress analysis of asteroids during atmospheric entry and implications for the breakup criterion

Abstract

Observations of asteroid fragmentation upon atmospheric entry have been used as a basis to estimate asteroid mechanical strength by the simplifying assumption that strength corresponds to ram pressure at burst. However, it is unclear whether ram pressure is a good scalar measure of the stresses that induce fracture. In this work, we study the stress fields prior to break-up in idealized as well as representative irregular asteroids as they enter the atmosphere. We develop a model for elastic, homogeneous, monolithic asteroids subject to aerodynamic, inertial, and centrifugal loads applied via the Meteor Equations and modified Newtonian aerodynamic theory. We obtain an analytical solution to the elasticity boundary value problem for an idealized circular asteroid. Alongside it, detailed finite element solutions are used to both verify the analytical model and to quantify the effects of asteroid shape irregularity on the state of stress. We find that the stresses that drive brittle fracture in asteroids may be an order of magnitude lower than the ram pressure, which could have significant implications for strengths inferred from breakup observations. We also quantify the effect of the spin of the asteroid as it tumbles through the atmosphere and the regimes in which spin-induced stresses dominate. Finally, we find that asteroids with small shape variations are well-approximated as spheres, but that large shape irregularities, like at the necks of elongated or contact binary asteroids, may lead to the appearance of regions of tensile bending stress. Conclusions are drawn about the usefulness of the ram pressure alone as a measure of stress in asteroids.