Low-speed impacts between rubble piles modeled as collections of polyhedra

We present results of modeling rubble piles as collections of polyhedra. The use of polyhedra allows more realistic (irregular) shapes and interactions (e.g. collisions), particularly for objects of different sizes. Rotational degrees of freedom are included in the modeling, which may be important components of the motion. We solved the equations of rigid-body dynamics, including frictional/inelastic collisions, for collections of up to several hundred elements. As a demonstration of the methods and to compare with previous work by other researchers, we simulated low-speed collisions between km-scale bodies with the same general parameters as those simulated by Leinhardt et al. [Leinhardt, Z.M., Richardson, D.C., Quinn, T., 2000. Icarus 146, 133-151]. High-speed collisions appropriate to present-day asteroid encounters require additional treatment of shock effects and fragmentation and are the subject of future work; here we study regimes appropriate to planetesimal accretion and re-accretion in the aftermath of catastrophic events. Collisions between equal-mass objects at low speeds () were simulated for both head-on and off-center collisions between rubble piles made of a power-law mass spectrum of sub-elements. Very low-speed head-on collisions produce single objects from the coalescence of the impactors. For slightly higher speeds, extensive disruption occurs, but re-accretion produces a single object with most of the total mass. For increasingly higher speeds, the re-accreted object has smaller mass, finally resulting in complete catastrophic disruption with all sub-elements on escape trajectories and only small amounts of mass in re-accreted bodies. Off-center collisions at moderately low speeds produce two re-accreted objects of approximately equal mass, separating at greater than escape speed. At high speed, complete disruption occurs as with the high-speed head-on collisions. Head-on collisions at low to moderate speeds result in objects of mostly oblate shape, while higher speed collisions produce mostly prolate objects, as do off-center collisions at moderate and high speeds. Collisions carried out with the same dissipative coefficients (coefficient of restitution ?n=0.8, zero friction) as used by Leinhardt et al. [Leinhardt, Z.M., Richardson, D.C., Quinn, T., 2000. Icarus 146, 133-151] result in a value for specific energy for disruption , somewhat lower than the value of 2 J/kg found by them, while collisions with a lower coefficient of restitution and friction [?n=0.5, ?t=0, μ=0.5, similar to those used by Michel, et al. [Michel, P., Benz, W., Richardson, D.C., 2004. Planet. Space Sci. 52, 1109-1117] for SPH + N-body calculations] yield .     

Numerical experiments with rubble piles: equilibrium shapes and spins

We present numerical experiments investigating the shape and spin limits of self-gravitating “perfect” rubble piles that consist of identical, smooth, rigid, spherical particles with configurable normal coefficient of restitution and no sliding friction. Such constructs are currently employed in a variety of investigations, ranging from the formation of asteroid satellites to the dynamical properties of Saturn's densest rings. We find that, owing to cannonball stacking behavior, rubble piles can maintain non-spherical shapes without bulk spin, unlike a fluid, and can spin faster than a perfect fluid before shedding mass, consistent with the theory for the more general continuum rubble pile model (Holsapple, 2004, Icarus 172, 272-303). Rubble piles that reassemble following a catastrophic disruption reconfigure themselves to lie within stability limits predicted by the continuum theory. We also find that coarse configurations consisting of a small number of particles are more resistant to tidal disruption than fine configurations with many particles. Overall this study shows that idealized rubble piles behave qualitatively in a manner similar to certain granular materials, at least in the limit where global shape readjustments and/or mass shedding begins. The limits obtained here may provide constraints on the possible internal structure of some small Solar System bodies that have extreme shapes or are under high stress. Amalthea is presented as a case study.     

Dynamical erosion of the asteroid belt and implications for large impacts in the inner Solar System

The cumulative effects of weak resonant and secular perturbations by the major planets produce chaotic behavior of asteroids on long timescales. Dynamical chaos is the dominant loss mechanism for asteroids with diameters in the current asteroid belt. In a numerical analysis of the long-term evolution of test particles in the main asteroid belt region, we find that the dynamical loss history of test particles from this region is well described with a logarithmic decay law. In our simulations the loss rate function that is established at persists with little deviation to at least . Our study indicates that the asteroid belt region has experienced a significant amount of depletion due to this dynamical erosion—having lost as much as ∼50% of the large asteroids—since 1 Myr after the establishment of the current dynamical structure of the asteroid belt. Because the dynamical depletion of asteroids from the main belt is approximately logarithmic, an equal amount of depletion occurred in the time interval 10-200 Myr as in 0.2-4 Gyr, roughly ∼30% of the current number of large asteroids in the main belt over each interval. We find that asteroids escaping from the main belt due to dynamical chaos have an Earth-impact probability of ∼0.3%. Our model suggests that the rate of impacts from large asteroids has declined by a factor of 3 over the last 3 Gyr, and that the present-day impact flux of objects on the terrestrial planets is roughly an order of magnitude less than estimates currently in use in crater chronologies and impact hazard risk assessments.     

Compaction and fragmentation of porous gypsum targets from low-velocity impacts

We performed low-velocity impact experiments of gypsum spheres with porosity ranging from 0 to 61% and diameter ranging from 25 to 83 mm. The impact velocity was from 0.2 to 22 m/s. The target was an iron plate. The outcome of gypsum spheres with porosity 31-61% was different from those of non-porous ice [Higa M., Arakawa, M., Maeno, N., 1996. Planet. Space Sci. 44, 917-925; Higa M., Arakawa, M., Maeno, N., 1998. Icarus 133, 310-320] and non-porous gypsum. In between the intact and fragmentation modes, the outcome of the non-porous ice and gypsum was crack growth at the impact point. However, the outcome of the porous gypsum was compaction. We found that the restitution coefficients of the porous gypsum spheres were all in a similar range, in spite of the difference of the porosity and size at impact velocities up to about 10 m/s where they begin to be fragmented in pieces. Moreover, there is not a large difference between the restitution coefficient of porous and non-porous gypsum. These results collectively indicate that restitution coefficient of gypsum spheres of cm-size is not strongly dependent upon the porosity and compaction process.     

The topographic limits of gravitationally bound, rotating sand piles

Rubble pile asteroids can attain shapes that are dramatically different from those of rotating, self-gravitating equilibrium fluids. A new numerical technique, called “seed growth,” is demonstrated for calculating three-dimensional bodies that are self-gravitating and rotating, and whose every surface is approximately at a constant angle, ?, with respect to the local horizontal. By altering the configuration of cusps, which are points along a constant longitude path where the surface angle changes sign but not magnitude, multiple solution shapes that satisfy the condition that all surface slopes are at a constant angle are possible. Five different cusp configurations are explored here, three of which yield solutions for 20°???30°. Rotational effects are explored, and it is found that for some solution shapes, the ratios of their shortest to longest dimensions, c/a, can fall outside the limits published in the literature for rotating, cohesionless, spheroidal bodies. Solution shapes show some similarities to observed small bodies, such as the saturnian satellite Atlas, the near-Earth Asteroid 1999 KW4, and some contact binary asteroids.     

Significance analysis of asteroid pairs

We have studied statistical significance of asteroid pairs residing on similar heliocentric orbits with distances (approximately the current relative encounter velocity between orbits) up to in the five-dimensional space of osculating elements. We found candidate pairs from the Hungaria zone through the entire main belt as well as outside the main belt, one among Hildas and one in the Cybele zone. We first determined probability that the candidate pairs are just coincidental couples from the background asteroid population. Those with estimated probability <0.3 were further investigated. In particular we computed synthetic proper elements for the relevant asteroids and used them to determine the three-dimensional distance of the members in candidate pairs. We consider small separation in the proper-element space as a signature of a real asteroid pair; conversely, cases with large separation in the proper-element space were rejected as spurious. Finally, we provide a list of candidate pairs that appear real, genetically related, to facilitate targeted studies, such as photometric and spectroscopic observations. As a by-product, we discovered six new compact clusters of three or more asteroids. Initial backward orbit integrations suggest that they are young families with ages <2 Myr.     

On the shapes and spins of “rubble pile” asteroids

We examine the shape of a “rubble pile” asteroid as it slowly gains angular momentum by YORP torque, to the point where “landsliding” occurs. We find that it evolves to a “top” shape with constant angle of repose from the equator up to mid-latitude, closely resembling the shapes of several nearly critically spinning asteroids imaged by radar, most notably (66391) 1999 KW4 [Ostro, S.J., Margot, J.-L., Benner, L.A.M., Giorgini, J.D., Scheeres, D.J., Fahnestock, E.G., Broschart, S.B., Bellerose, J., Nolan, M.C., Magri, C., Pravec, P., Scheirich, P., Rose, R., Jurgens, R.F., De Jong, E.M., Suzuki, S., 2006. Science 314, 1276-1280]. Similar calculations for non-spinning extremely prolate or oblate “rubble piles” show that even loose rubble can sustain shapes far from fluid equilibrium, thus inferences based on fluid equilibrium are generally useless for inferring bulk properties such as density of small bodies. We also investigate the tidal effects of a binary system with a “top shape” primary spinning at near the critical limit for stability. We find that very close to the stability limit, the tide from the secondary can actually levitate loose debris from the surface and re-deposit it, in a process we call “tidal saltation.” In the process, angular momentum is transferred from the primary spin to the satellite orbit, thus maintaining the equilibrium of near-critical spin as YORP continues to add angular momentum to the system. We note that this process is in fact dynamically related to the process of “shepherding” of narrow rings by neighboring satellites.     

A dynamical solution of the triple asteroid system (45) Eugenia

We present the first dynamical solution of the triple asteroid system (45) Eugenia and its two moons Petit–Prince (diameter ∼ 7 km) and S/2004 (45) 1 (diameter ∼ 5 km). The two moons orbit at 1165 and 610 km from the primary, describing an almost-circular orbit (e ∼ 6 × 10⁻³ and e ∼ 7 × 10⁻² respectively). The system is quite different from the other known triple systems in the main belt since the inclinations of the moon orbits are sizeable (9° and 18° with respect to the equator of the primary respectively). No resonances, neither secular nor due to Lidov–Kozai mechanism, were detected in our dynamical solution, suggesting that these inclinations are not due to excitation modes between the primary and the moons. A 10-year evolution study shows that the orbits are slightly affected by perturbations from the Sun, and to a lesser extent by mutual interactions between the moons. The estimated J₂ of the primary is three times lower than the theoretical one, calculated assuming the shape of the primary and an homogeneous interior, possibly suggesting the importance of other gravitational harmonics.     

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

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 spin-shape parameter space that allow equilibrium solutions to exist. At present, only a graphical illustration of these solutions for a prolate ellipsoid following the Drucker-Prager failure law is available [Sharma, I., Jenkins, J.T., Burns, J.A., 2005a. Bull. Am. Astron. Soc. 37, 643; Sharma, I., Jenkins, J.T., Burns, J.A., 2005b. Equilibrium shapes of ellipsoidal soil asteroids. In: García-Rojo, R., Hermann, H.J., McNamara, S. (Eds.), Proceedings of the 5th International Conference on Micromechanics of Granular Media, vol. 1. A.A. Balkema, UK; Holsapple, K.A., 2007. Icarus 187, 500-509]. Here, we obtain the equilibrium landscapes for general triaxial ellipsoids, as well as provide the requisite governing formulae. In addition, we demonstrate that it may be possible to better interpret the results of Richardson et al. [Richardson, D.C., Elankumaran, P., Sanderson, R.E., 2005. Icarus 173, 349-361] within the context of a Drucker-Prager material. The graphical result for prolate ellipsoids in the static limit is the same as those of Holsapple [Holsapple, K.A., 2007. Icarus 187, 500-509] because, when worked out, his final equations will match ours. This is because, though the formalisms to reach these expressions differ, in statics, at the lowest level of approximation, volume-averaging and the approach of Holsapple [Holsapple, K.A., 2007. Icarus 187, 500-509] coincide. We note that the approach applied here was obtained independently [Sharma, I., Jenkins, J.T., Burns, J.A., 2003. Bull. Am. Astron. Soc. 35, 1034; Sharma, I., 2004. Rotational Dynamics of Deformable Ellipsoids with Applications to Asteroids. Ph.D. thesis, Cornell University] and it provides a general, though approximate, framework that is amenable to systematic improvements and is flexible enough to incorporate the dynamical effects of a changing shape, different rheologies and complex rotational histories. To demonstrate our technique, we investigate the non-equilibrium dynamics of rigid-plastic, spinning, prolate asteroids to examine the simultaneous histories of shape and spin rate for rubble piles. We have succeeded in recovering most results of Richardson et al. [Richardson, D.C., Elankumaran, P., Sanderson, R.E., 2005. Icarus 173, 349-361], who obtained equilibrium shapes by studying numerically the passage into equilibrium of aggregates containing discrete, interacting, frictionless, spherical particles. Our mainly analytical approach aids in understanding and quantifying previous numerical simulations.     

Dynamics of the Hungaria asteroids

To try to understand the dynamical and collisional evolution of the Hungaria asteroids we have built a large catalog of accurate synthetic proper elements. Using the distribution of the Hungaria, in the spaces of proper elements and of proper frequencies, we can study the dynamical boundaries and the internal structure of the Hungaria region, both within a purely gravitational model and also showing the signature of the non-gravitational effects. We find a complex interaction between secular resonances, mean motion resonances, chaotic behavior and Yarkovsky-driven drift in semimajor axis. We also find a rare occurrence of large scale instabilities, leading to escape from the region. This allows to explain the complex shape of a grouping which we suggest is a collisional family, including most Hungaria but by no means all; we provide an explicit list of non-members of the family. There are finer structures, of which the most significant is a set of very close asteroid couples, with extremely similar proper elements. Some of these could have had, in a comparatively recent past, very close approaches with low relative velocity. We argue that the Hungaria, because of the favorable observing conditions, may soon become the best known sub-group of the asteroid population.     

Radar observations and the shape of near-Earth asteroid 2008 EV5

We observed the near-Earth ASTEROID 2008 EV5 with the Arecibo and Goldstone planetary radars and the Very Long Baseline Array during December 2008. EV5 rotates retrograde and its overall shape is a 400 ± 50 m oblate spheroid. The most prominent surface feature is a ridge parallel to the asteroid’s equator that is broken by a concavity about 150 m in diameter. Otherwise the asteroid’s surface is notably smooth on decameter scales. EV5’s radar and optical albedos are consistent with either rocky or stony-iron composition. The equatorial ridge is similar to structure seen on the rubble-pile near-Earth asteroid (66391) 1999 KW4 and is consistent with YORP spin-up reconfiguring the asteroid in the past. We interpret the concavity as an impact crater. Shaking during the impact and later regolith redistribution may have erased smaller features, explaining the general lack of decameter-scale surface structure.     

Initial sizes of planetesimals and accretion of the asteroids

The present size frequency distribution (SFD) of bodies in the asteroid belt appears to have preserved some record of the primordial population, with an excess of bodies of diameter D ∼ 100 km relative to a simple power law. The survival of Vesta’s basaltic crust also implies that the early SFD had a shallow slope in the range ∼10-100 km. (Morbidelli, A., Bottke, W.F., Nesvorny, D., Levison, H.F. [2009]. Icarus 204, 558-573) were unable to produce these features by accretion from an initial population of km-sized planetesimals. They concluded that bodies with sizes in the range ∼100-1000 km and a SFD similar to the current population were produced directly from solid particles of sub-meter scale, without experiencing accretion through intermediate sizes. We present results of new accretion simulations in the primordial asteroid region. The requisite SFD can be produced from an initial population of planetesimals of sizes ?0.1 km, smaller than the usual assumption of km-sized bodies. The bump at D ∼ 100 km is produced by a transition from dispersion-dominated runaway growth to a regime dominated by Keplerian shear, before the formation of large protoplanetary embryos. Thus, accretion of the asteroids from an initial population of small (sub-km) planetesimals cannot be ruled out.     

Linear stability of collinear equilibrium points around an asteroid as a two-connected-mass: Application to fast rotating Asteroid 2000EB14

This note discusses the stability of collinear equilibrium points around a rotating system composed of two masses rigidly connected by a massless rod in the case, where the centripetal force outweighs the gravitational force. It is found that a stable region appears at L₁ when the ratio of gravitational to centripetal acceleration is less than 0.125, and that there is always no stable area at L₂ and L₃; the result is applied to the fast rotating Asteroid 2000EB₁₄.     

Equilibrium shapes of rubble-pile binaries: The Darwin ellipsoids for gravitationally held granular aggregates

Binaries are in vogue; many minor-planets like asteroids are being found to be binary or contact-binary systems. Even ternaries like 87 Sylvia have been discovered. The densities of these binaries are often estimated to be very low, and this, along with suspected accretionary origins, hints at a rubble interior. As in the case of fluid objects, a rubble-pile is unable to sustain all manners of spin, self-gravitation, and tidal interactions. This motivates the present study of the possible ellipsoidal shapes and mutual separations that members of a rubble-pile binary system may achieve. Conversely, knowledge of a granular binary’s shape and separation will constrain its internal structure - the ability of the binary’s members to sustain elongated shapes and/or maintain contact will hint at appreciable internal frictional strength. Because the binary’s members are allowed to be of comparable mass, the present investigation constitutes an extension of the second classical Darwin problem to granular aggregates.General equations defining the ellipsoidal rubble-pile binary system’s equilibrium are developed. These are then specialized to a pair of spin-locked, possibly unequal, prolate ellipsoidal granular aggregates aligned along their long axes. We observe that contact rubble-pile binaries can indeed exist. Further, depending on the binary’s geometry, an equilibrium contact binary’s members may, in fact, disrupt if separated. These results are applied to four suspected or known binaries: 216 Kleopatra, 25143 Itokawa, 624 Hektor and 90 Antiope. This exercise helps to bound the shapes and/or provide information about the interiors of these binaries.The binary’s interior will be modeled as a rigid-plastic, cohesionless material with a Drucker-Prager yield criterion. This rheology is a reasonable first model for rubble piles. We employ an approximate volume-averaging procedure that is based on the classical method of moments, and is an extension of the virial method (Chandrasekhar, S., 1969. Ellipsoidal Figures of Equilibrium. Yale University Press, New Haven, CT) to granular solid bodies. The present approach also helps us present an incrementally consistent approach to investigate the equilibrium shapes of fluid binaries, while highlighting the inconsistencies and errors inherent in the popular “Roche binary approximation”.     

Origin and sustainability of the population of asteroids captured in the exterior resonance 1:2 with Mars

At present, approximately 1500 asteroids are known to evolve inside or sticked to the exterior 1:2 resonance with Mars at a ? 2.418 AU, being (142) Polana the largest member of this group. The effect of the forced secular modes superposed to the resonance gives rise to a complex dynamical evolution. Chaotic diffusion, collisions, close encounters with massive asteroids and mainly orbital migration due to the Yarkovsky effect generate continuous captures to and losses from the resonance, with a fraction of asteroids remaining captured over long time scales and generating a concentration in the semimajor axis distribution that exceeds by 20% the population of background asteroids. The Yarkovsky effect induces different dynamics according to the asteroid size, producing an excess of small asteroids inside the resonance. The evolution in the resonance generates a signature on the orbits, mainly in eccentricity, that depends on the time the asteroid remains captured inside the resonance and on the magnitude of the Yarkovsky effect. The greater the asteroids, the larger the time they remain captured in the resonance, allowing greater diffusion in eccentricity and inclination. The resonance generates a discontinuity and mixing in the space of proper elements producing misidentification of dynamical family members, mainly for Vesta and Nysa-Polana families. The half-life of resonant asteroids large enough for not being affected by the Yarkovsky effect is about 1 Gyr. From the point of view of taxonomic classes, the resonant population does not differ from the background population and the excess of small asteroids is confirmed.     

Accretion among preplanetary bodies: The many faces of runaway growth

When preplanetary bodies reach proportions of ∼1 km or larger in size, their accretion rate is enhanced due to gravitational focusing (GF). We have developed a new numerical model to calculate the collisional evolution of the gravitationally-enhanced growth stage. The numerical model is novel as it attempts to preserve the individual particle nature of the bodies (like N-body codes); yet it is statistical in nature since it must incorporate the very large number of planetesimals. We validate our approach against existing N-body and statistical codes. Using the numerical model, we explore the characteristics of the runaway growth and the oligarchic growth accretion phases starting from an initial population of single planetesimal radius R₀. In models where the initial random velocity dispersion (as derived from their eccentricity) starts out below the escape speed of the planetesimal bodies, the system experiences runaway growth. We associate the initial runaway growth phase with increasing GF-factors for the largest body. We find that during the runaway growth phase the size distribution remains continuous but evolves into a power-law at the high-mass end, consistent with previous studies. Furthermore, we find that the largest body accretes from all mass bins; a simple two-component approximation is inapplicable during this stage. However, with growth the runaway body stirs up the random motions of the planetesimal population from which it is accreting. Ultimately, this feedback stops the fast growth and the system passes into oligarchy, where competitor bodies from neighboring zones catch up in terms of mass. We identify the peak of GF with the transition between the runaway growth and oligarchy accretion stages. Compared to previous estimates, we find that the system leaves the runaway growth phase at a somewhat larger radius, especially at the outer disk. Furthermore, we assess the relevance of small, single-size fragments on the growth process. In classical models, where the initial velocity dispersion of bodies is small, these do not play a critical role during the runaway growth; however, in models that are characterized by large initial relative velocities due to external stirring of their random motions, a situation can emerge where fragments dominate the accretion, which could lead to a very fast growth.     

Orbital and thermal evolutions of four potential targets for a sample return space mission to a primitive near-Earth asteroid

In this paper, we present our study of the orbital and thermal evolutions, due to solar radiative heating, of four near-Earth asteroids (NEAs) considered as potential target candidates for sample return space missions to primitive asteroids. We used a dynamical model of the NEA population to estimate the most likely source region and orbital history of these objects. Then, for each asteroid, we integrated numerically over their entire lifetime a set of 14 initially indistinguishable orbit (clones), obtained by small variations of the nominal initial conditions. Using a thermal model, we then computed surface and sub-surface temperatures of these bodies during their dynamical history. Our aim is to determine whether these bodies are likely to have experienced high temperature level, and whether great temperature changes can be expected due to the orbital changes as well as their maximum and minimum values. Such information is important in the framework of sample return space missions whose goal is to bring back pristine materials. The knowledge of the temperature range of materials at different depth over the orbital evolution of potential targets can help defining sampling strategies that ensure the likelihood that unaltered material will be brought back. Our results suggest that for all the considered potential targets, the surface has experienced for some time temperatures greater than 400 K and at most 500 K with 50% probability. This probability drops rapidly with increasing temperature. Sub-surface materials at a depth of only 3 cm are much more protected from high temperature and generally do not reach temperatures exceeding 450 K (with 50% probability). They should thus be unaltered at this depth at least from a Sun-driven heating point of view. On the other hand, surface material for some of the considered objects can have a range of temperature which can make them less reliable as pristine materials. However, it is assumed here that the same material is constantly exposed to solar heat, while regolith turnover may occur. The latter can be caused by different processes such as seismic shaking and/or impact cratering. This would reduce the total time that materials are exposed to a certain temperature. Thus, it is very likely that a sample collected from any of the four considered targets, or any primitive NEA with similar dynamical properties, will have components that will be thermally unaltered as long as some of it comes from only 3 to 5 cm depth. Such a depth is not considered difficult to reach with some of the current designs of sampling devices.     

Dynamical evolution of Earth’s quasi-satellites: 2004 GU9 and 2006 FV35

We study the dynamical evolution of Asteroids (164207) 2004 GU₉ and 2006 FV₃₅, which are currently Earth quasi-satellites (QS). Our analysis is based on numerical computation of their orbits, and we also applied the theory of co-orbital motion developed in Wajer (Wajer, P. [2009]. Icarus 200, 147-153) to describe and analyze the objects’ dynamics. 2004 GU₉ stays as an Earth QS for about a 1000 years. In the present epoch it is in the middle of its stay in this regime. After leaving the QS orbit near 2600 this asteroid will move inside the Earth’s co-orbital region on a regular horseshoe (HS) orbit for a few 1000 years. Later, either HS-QS or HS-P transitions are possible, where P means “passing”. Although 2004 GU₉ moves primarily under the influence of the Sun and Earth, Venus plays a significant role in destabilizing the object’s orbit. Our analysis showed that the guiding center of 2006 FV₃₅ moves deep inside the averaged potential well, and since the asteroid’s argument of perihelion precesses at a rate of approximately , it prevents the QS state begin left for a long period of time; consequently the asteroid has occupied this state for about 10⁴ years and will stay in this orbit for about 800 more years. Near 2800 the asteroid’s close approach with Venus will cause it to exit the QS state, but probably it will still be moving inside the Earth’s co-orbital region and will experience transitions between HS, TP (tadpole) and P types of motion.     

Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems

We present a model of near-Earth asteroid (NEA) rotational fission and ensuing dynamics that describes the creation of synchronous binaries and all other observed NEA systems including: doubly synchronous binaries, high-e binaries, ternary systems, and contact binaries. Our model only presupposes the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect, “rubble pile” asteroid geophysics, and gravitational interactions. The YORP effect torques a “rubble pile” asteroid until the asteroid reaches its fission spin limit and the components enter orbit about each other (Scheeres, D.J. [2007]. Icarus 189, 370-385). Non-spherical gravitational potentials couple the spin states to the orbit state and chaotically drive the system towards the observed asteroid classes along two evolutionary tracks primarily distinguished by mass ratio. Related to this is a new binary process termed secondary fission - the secondary asteroid of the binary system is rotationally accelerated via gravitational torques until it fissions, thus creating a chaotic ternary system. The initially chaotic binary can be stabilized to create a synchronous binary by components of the fissioned secondary asteroid impacting the primary asteroid, solar gravitational perturbations, and mutual body tides. These results emphasize the importance of the initial component size distribution and configuration within the parent asteroid. NEAs may go through multiple binary cycles and many YORP-induced rotational fissions during their approximately 10 Myr lifetime in the inner Solar System. Rotational fission and the ensuing dynamics are responsible for all NEA systems including the most commonly observed synchronous binaries.     

Earth impact probability of the Asteroid (25143) Itokawa to be sampled by the spacecraft Hayabusa

The Japanese spacecraft Hayabusa is planed to reach the Asteroid Itokawa in September 2005, and to bring back some samples of its surface to Earth in 2007. We have studied the future possible evolution of this asteroid by integrating numerically over 100 Myr a set of 39 initially indistinguishable orbits (clones), obtained either by small variations of the nominal initial conditions, or by using different computers (introducing different round-off errors). The results indicate that an Earth impact of this 500-m-size asteroid is likely within a million years, which is only a factor of four larger than the average impact frequency of asteroids of this size. The mission Hayabusa may thus sample a good candidate for being among the next 500-m-size Earth impactors.