Masatoshi Hirabayashi

CONSTRAINTS ON THE PHYSICAL PROPERTIES OF MAIN BELT COMET P/2013 R3 FROM ITS BREAKUP EVENT

Jewitt et al. (2014) recently reported that main belt comet P/2013 R3 experienced a breakup, probably due to rotational disruption, with its components separating on mutually hyperbolic orbits. We propose a technique for constraining physical properties of the proto-body, especially the initial spin period and cohesive strength, as a function of the bodys estimated size and density. The breakup conditions are developed by combining mutual orbit dynamics of the smaller components and the failure condition of the proto-body. Given a proto-body with a bulk density ranging from 1000 kg/m3 to 1500 kg/m3 (a typical range of the bulk density of C-type asteroids), we obtain possible values of the cohesive strength (40 - 210 Pa) and the initial spin state (0.48 - 1.9 hr). From this result, we conclude that although the proto-body could have been a rubble pile, it was likely spinning beyond its gravitational binding limit and would have needed cohesive strength to hold itself together. Additional observations of P/2013 R3 will enable stronger constraints on this event, and the present technique will be able to give more precise estimates of its internal structure.

ANALYSIS OF ASTEROID (216) KLEOPATRA USING DYNAMICAL AND STRUCTURAL CONSTRAINTS

This paper evaluates a dynamically and structurally stable size for Asteroid (216) Kleopatra. In particular, we investigate two different failure modes: material shedding from the surface and structural failure of the internal body. We construct zero-velocity curves in the vicinity of this asteroid to determine surface shedding, while we utilize a limit analysis to calculate the lower and upper bounds of structural failure under the zero-cohesion assumption. Surface shedding does not occur at the current spin period (5.385 hr) and cannot directly initiate the formation of the satellites. On the other hand, this body may be close to structural failure; in particular, the neck may be situated near a plastic state. In addition, the necks sensitivity to structural failure changes as the body size varies. We conclude that plastic deformation has probably occurred around the neck part in the past. If the true size of this body is established through additional measurements, this method will provide strong constraints on the current friction angle for the body.

Fission and reconfiguration of bilobate comets as revealed by 67P/Churyumov–Gerasimenko

The solid, central part of a comet--its nucleus--is subject to destructive processes, which cause nuclei to split at a rate of about 0.01 per year per comet. These destructive events are due to a range of possible thermophysical effects; however, the geophysical expressions of these effects are unknown. Separately, over two-thirds of comet nuclei that have been imaged at high resolution show bilobate shapes, including the nucleus of comet 67P/Churyumov-Gerasimenko (67P), visited by the Rosetta spacecraft. Analysis of the Rosetta observations suggests that 67Ps components were brought together at low speed after their separate formation. Here, we study the structure and dynamics of 67Ps nucleus. We find that sublimation torques have caused the nucleus to spin up in the past to form the large cracks observed on its neck. However, the chaotic evolution of its spin state has so far forestalled its splitting, although it should eventually reach a rapid enough spin rate to do so. Once this occurs, the separated components will be unable to escape each other; they will orbit each other for a time, ultimately undergoing a low-speed merger that will result in a new bilobate configuration. The components of four other imaged bilobate nuclei have volume ratios that are consistent with a similar reconfiguration cycle, pointing to such cycles as a fundamental process in the evolution of short-period comet nuclei. It has been shown that comets were not strong contributors to the so-called late heavy bombardment about 4 billion years ago. The reconfiguration process suggested here would preferentially decimate comet nuclei during migration to the inner solar system, perhaps explaining this lack of a substantial cometary flux.

STRESS AND FAILURE ANALYSIS OF RAPIDLY ROTATING ASTEROID (29075) 1950 DA

Rozitis et al. recently reported that near-Earth asteroid (29075) 1950 DA, whose bulk density ranges from 1.0 g/cm3 to 2.4 g/cm3, is a rubble pile and requires a cohesive strength of at least 44 Pa to 74 Pa to keep from failing due to its fast spin period. Since their technique for giving failure conditions required the averaged stress over the whole volume, it discarded information about the asteroids failure mode and internal stress condition. This paper develops a finite element model and revisits the stress and failure analysis of 1950 DA. For the modeling, we do not consider material-hardening and softening. Under the assumption of an associated flow rule and uniform material distribution, we identify the deformation process of 1950 DA when its constant cohesion reaches the lowest value that keeps its current shape. The results show that to avoid structural failure the internal core requires a cohesive strength of at least 75 Pa - 85 Pa. It suggests that for the failure mode of this body, the internal core first fails structurally, followed by the surface region. This implies that if cohesion is constant over the whole volume, the equatorial ridge of 1950 DA results from a material flow going outward along the equatorial plane in the internal core, but not from a landslide as has been hypothesized. This has additional implications for the likely density of the interior of the body.

Failure modes and conditions of a cohesive, spherical body due to YORP spin-up

This paper presents transition of the failure mode of a cohesive, spherical body due to YORP spin-up. On the assumption that the distribution of materials in the body is homogeneous, failed regions first appearing in the body at different spin rates are predicted by comparing the yield condition of an elastic stress in the body. It is found that as the spin rate increases, the locations of the failed regions move from the equatorial surface to the central region. To avoid such failure modes, the body should have higher cohesive strength. The results by this model are consistent with those by a plastic finite element model. Then, this model and a two-layered-cohesive model first proposed by Hirabayashi et al. are used to classify possible evolution and disruption of a spherical body. There are three possible pathways to disruption. First, because of a strong structure, failure of the central region is dominant and eventually leads to a breakup into multiple components. Second, a weak surface and a weak interior make the body oblate. Third, a strong internal core prevents the body from failing and only allows surface shedding. This implies that observed failure modes may highly depend on the internal structure of an asteroid, which could provide crucial information for giving constraints on the physical properties.

Structural failure of two-density-layer cohesionless biaxial ellipsoids

Abstract This paper quantitatively evaluates structural failure of biaxial cohesionless ellipsoids that have a two-density-layer distribution. The internal density layer is modeled as a sphere, while the external density layer is the rest of the part. The density is supposed to be constant in each layer. The present study derives averaged stresses over the whole volume of these bodies and uses limit analysis to determine their global failure. The upper bound of global failure is considered in terms of the size of the internal layer and the aspect ratio of the shape. The result shows that the two-density-layer causes the body to have different strength against structural failure.

An analytical model of crater count equilibrium

Abstract Crater count equilibrium occurs when new craters form at the same rate that old craters are erased, such that the total number of observable impacts remains constant. Despite substantial efforts to understand this process, there remain many unsolved problems. Here, we propose an analytical model that describes how a heavily cratered surface reaches a state of crater count equilibrium. The proposed model formulates three physical processes contributing to crater count equilibrium: cookie-cutting (simple, geometric overlap), ejecta-blanketing, and sandblasting (diffusive erosion). These three processes are modeled using a degradation parameter that describes the efficiency for a new crater to erase old craters. The flexibility of our newly developed model allows us to represent the processes that underlie crater count equilibrium problems. The results show that when the slope of the production function is steeper than that of the equilibrium state, the power law of the equilibrium slope is independent of that of the production function slope. We apply our model to the cratering conditions in the Sinus Medii region and at the Apollo 15 landing site on the Moon and demonstrate that a consistent degradation parameterization can successfully be determined based on the empirical results of these regions. Further developments of this model will enable us to better understand the surface evolution of airless bodies due to impact bombardment.

Rotationally induced surface slope-instabilities and the activation of CO2 activity on comet 103P/Hartley 2

Comet 103P/Hartley 2 has diurnally controlled, CO2-driven activity on the tip of the small lobe of its bilobate nucleus. Such activity is unique among the comet nuclei visited by spacecraft, and suggests that CO2 ice is very near the surface, which is inconsistent with our expectations of an object that thermophysically evolved for ∼45 million years prior to entering the Jupiter Family of comets. Here we explain this pattern of activity by showing that a very plausible recent episode of rapid rotation (rotation period of ∼11 [10-13] h) would have induced avalanches in Hartley 2’s currently active regions that excavated down to CO2-rich ices and activated the small lobe of the nucleus. At Hartley 2’s current rate of spindown about its principal axis, the nucleus would have been spinning fast enough to induce avalanches ∼3–4 orbits prior to the DIXI flyby (∼1984–1991). This coincides with Hartley 2’s discovery in 1986, and implies that the initiation of CO2 activity facilitated the comets discovery. During the avalanches, the sliding material would either be lofted off the surface by gas activity, or possibly gained enough momentum moving downhill (toward the tip of the small lobe) to slide off the tip of the small lobe. Much of this material would have failed to reach escape velocity, and would reimpact the nucleus, forming debris deposits. The similar size frequency distribution of the mounds observed on the surface of Hartley 2 and chunks of material in its inner coma suggest that the 20–40 m mounds observed by the DIXI mission on the surface of Hartley 2 are potentially these fallback debris deposits. As the nucleus spun down (rotation period increased) from a period of ∼11–18.34 h at the time of the DIXI flyby, the location of potential minima, where materials preferentially settle, migrated about the surface, allowing us to place relative ages on most of the terrains on the imaged portion of the nucleus.

Constraints on the perturbed mutual motion in Didymos due to impact-induced deformation of its primary after the DART impact

Binary near-Earth asteroid (65803) Didymos is the target of the proposed NASA Double Asteroid Redirection Test (DART), part of the Asteroid Impact & Deflection Assessment (AIDA) mission concept. In this mission, the DART spacecraft is planned to impact the secondary body of Didymos, perturbing mutual dynamics of the system. The primary body is currently rotating at a spin period close to the spin barrier of asteroids, and materials ejected from the secondary due to the DART impact are likely to reach the primary. These conditions may cause the primary to reshape, due to landslides, or internal deformation, changing the permanent gravity field. Here, we propose that if shape deformation of the primary occurs, the mutual orbit of the system would be perturbed due to a change in the gravity field. We use a numerical simulation technique based on the full two-body problem to investigate the shape effect on the mutual dynamics in Didymos after the DART impact. The results show that under constant volume, shape deformation induces strong perturbation in the mutual motion. We find that the deformation process always causes the orbital period of the system to become shorter. If surface layers with a thickness greater than ~0.4 m on the poles of the primary move down to the equatorial region due to the DART impact, a change in the orbital period of the system and in the spin period of the primary will be detected by ground-based measurement.

Rotationally induced failure of irregularly shaped asteroids

Abstract Many asteroids are rubble piles with irregular shapes. While the irregular shapes of large asteroids may be attributed to collisional events, those of small asteroids may result from not only impact events but also rotationally induced failure, a long-term consequence of small torques caused by, for example, solar radiation pressure. A better understanding of shape deformation induced by such small torques will allow us to give constraints on the evolution process of an asteroid and its structure. However, no quantitative study has been reported to provide the relationship between an asteroid’s shape and its failure mode due to its fast rotation. Here, we use a finite element model (FEM) technique to analyze the failure modes and conditions of 24 asteroids with diameters less than 30–40 km, which were observed at high resolution by ground radar or asteroid exploration missions. Assuming that the material distribution is uniform, we investigate how these asteroids fail structurally at different spin rates. Our FEM simulations describe the detailed deformation mode of each irregularly shaped asteroid at fast spin. The failed regions depend on the original shape. Spheroidal objects structurally fail from the interior, while elongated objects experience structural failure on planes perpendicular to the minimum moment of inertia axes in the middle of their structure. Contact binary objects have structural failure across their most sensitive cross-sections. We further investigate if our FEM analysis is consistent with earlier works that theoretically explored a uniformly rotating triaxial ellipsoid. The results show that global shape variations may significantly change the failure condition of an asteroid. Our work suggests that it is critical to take into account the actual shapes of asteroids to explore their failure modes in detail.