99942 Apophis’ closest encounter with the Earth in 2029: Contribution of rigidity and dissipation to its rotational evolution

99942 Apophis’s encounter with the Earth in 2029 is known to cause its unique rotational evolution [e.g., 1]. Such variations may induce surface movements at some levels [e.g., 2-4]. Another issue is how Apophis responds to the encounter mechanically. Work was performed using Soft-Sphere Discrete Element Modeling (SSDEM) [5] and Finite Element Modeling (FEM) [6]. We extended the FEM approach by [6] to simulate the dynamics of Apophis during this encounter by accounting for the interactions of translation, rotation, and deformation under energy dissipation based on viscoelasticity. Our selection of viscoelasticity was based on typical application in soil continuum mechanics. We considered one of the simulation cases from [6], which was generated for the rotational state 2 hr before the closest encounter based on its uncertainty [7]. We reprocessed the FEM mesh used by [6], who used the radar-driven shape model [8], to generate a newFEM mesh consisting of 84 nodes and 264 elements, though we have not observed significant variations in the dynamical behavior.

We ran three cases by changing the rigidity: 1.e4 Pa, 1.e6 Pa, and infinity (i.e., perfectly rigid body). The viscosity was kept as 1.e5 Pa s. Figure 1 shows the perfectly rigid case. The angular velocity component changes ~1.e-5 1/s, which is consistent with earlier work [1]. Figure 2 then shows how the roll, pitch, and yaw angles deviate from the rigid case for each non-rigid case. The results show that while the deviation immediately starts after the start of simulation, the trend changes dramatically during and after the closest encounter. Depending on the magnitude of rigidity, the variation may reach 10 deg after 13 hr. This level of deviation promises that if the rotation, shape, and gravity during the encounter are measured by planned missions and observations [9-13], a state estimation technique with this model can determine the rigidity and dissipation factor of this asteroid, those not well known for small bodies as of today.

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