Using a discrete element method to investigate seismic response and spin change of 99942 Apophis during its 2029 tidal encounter with Earth

Abstract Near-Earth Asteroid 99942 Apophis presents a unique opportunity to study the dynamics, bulk properties, and interior structure of a rubble-pile asteroid when it makes its close encounter with the Earth in 2029. In order to better understand the potential outcomes of a tidal encounter between Earth and Apophis, and to support a potential future mission to Apophis, we perform numerical simulations of the encounter. We represent Earth as a single rigid sphere and the target body as a cohesionless, self-gravitating granular aggregate of identical spheres in a hexagonal-close-packed configuration subject only to gravitational and soft-sphere (elastic) contact forces. We use a radar-derived shape model for the asteroid, along with current best estimates for the orbital solution of Apophis to simulate the encounter trajectory, and perform a large parameter sweep over different potential encounter orientations and bulk densities for the body. We find that the median change in the rotational period for Apophis, sampled for a range of different initial body and spin orientations, is −1.9 h (mean −0.1 ± 6.0 (1- σ ) hours) during the encounter. Additionally, we measure that the mean of the largest change in axis length among the 3 primary body axes, also sampled over trials with different initial body and spin orientations, is 0.132 ± 0.066 mm during the encounter, assuming a bulk Young's Modulus of 10 6  Pa. Such strains on the timescale of peak stress during the encounter may be large enough to be detected by an in-situ seismometer.