Internal structure and physical properties of the Asteroid 2008 TC3 inferred from a study of the Almahata Sitta meteorites

The density measurements of Almahata Sitta ureilites reveal a bulk density of ∼3.1 g/cm³. This value, together with the 2008 TC₃ asteroid shape model and albedo, was used to estimate the asteroid’s mass. Based on the study of recovered meteorites and atmospheric entry observations Asteroid 2008 TC₃ is compositionally heterogeneous and of low mechanical strength. Thus we consider the presence of significant macroporosity likely, lowering asteroid’s bulk density compared to that of the Almahata Sitta ureilites. Most realistic albedos lie in a range of 0.09-0.2 and the presence of significant macroporosity leads to mass estimates below 20 × 10³ kg, which is lower than previously estimated. The presence of a non-ureilitic fraction and space weathering may affect the albedo and also influence the mass estimates. However, from current data it is not possible to quantify this effect.     

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”.     

Detailed prediction for the BYORP effect on binary near-Earth Asteroid (66391) 1999 KW4 and implications for the binary population

A previous theory by the authors for detailed modeling of the binary YORP effect is reviewed and expanded to accommodate doubly-synchronous binary systems, as well as a method for non-dimensionalizing the coefficients for application to binary systems where a shape model to compute its own coefficients is not available. The theory is also expanded to account for the effects of primary J₂ and the Sun’s 3rd body perturbation on the secular orbit evolution. The newly expanded theory is applied to the binary near-Earth Asteroid 1999 KW4, for which a detailed shape model is available. The result of simulation of the secular evolutionary equations shows that the KW4 orbit will be double in size in approximately 22,000 years, and will reach the Hill radius in approximately 54,000 years. The simulation also shows that the eccentricity will alternate growing and shrinking in magnitude, depending on the location of the solar node in the body-fixed frame. Therefore the eccentricity is not fixed to evolve in the opposite sign as the semi-major axis unless the circulation of the node (with a period of 500 years) is averaged out as well. The current orbit expansion rate for KW4 of 7 cm per year is shown to be detectable with observations of the mean anomaly which grows quadratically in time with an expanding orbit. Finally, the KW4 results are scaled for application to a number of other binary systems for which detailed shape models are not available. This application shows that the orbits considered can expand to their Hill radius in the range of 10⁴-10⁶ years. This implies rapid formation of binary systems is necessary to support the large percentage of binaries observed in the NEA population.     

Physical modeling of near-Earth Asteroid (29075) 1950 DA

Near-Earth Asteroid (29075) 1950 DA may closely encounter Earth in 2880. The probability of Earth impact may be as high as 1/300, but the outcome of the encounter depends critically on the physical properties of the asteroid [Giorgini et al., 2002. Science 196, 132-136]. We have used Arecibo and Goldstone radar data and optical lightcurves to estimate the shape, spin state, and surface structure of 1950 DA. The data allow two distinct models. One rotates prograde and is roughly spheroidal with mean diameter 1.16±0.12 km. The other rotates retrograde and is oblate and about 30% larger. Both models suggest a nickel-iron or enstatite chondritic composition. Ground-based observations should be able to determine which model is correct within the next several decades.     

The statistics of flight opportunities to accessible near-Earth asteroids

A statistical study has been carried out of the availability of favourable flight opportunities to near-Earth asteroids with orbits similar to the Earth's. Emphasis is given to rendezvous-type mission profiles employing two-burn impulsive transfers. Velocity-optimized Lambert trajectories for a sample of 27 actual objects were calculated and compiled in a database. The velocity and flight time statistics of the resulting 1200 different solutions covering a period of 11 years have been investigated and discussed. Comparison with typical flight profiles to the Moon and near planets has revealed flight opportunities to 5 objects within a decade from the present requiring less ΔV than favourable flight opportunities to Mars or Venus. One of the objects involved, 1999 AO10, can be rendezvoused with using a total velocity increment that is smaller than that required to establish a lunar orbiter. The use of slow flybys for the most scientifically appealing targets is illustrated through an example trajectory involving the C-class binary object 1996 FG3. The challenges and opportunities for doing science in proximity to such small objects are also discussed.     

Characterization of the near-Earth Asteroid 2002 NY40

In August 2002, the near-Earth Asteroid 2002 NY₄₀, made its closest approach to the Earth. This provided an opportunity to study a near-Earth asteroid with a variety of instruments. Several of the telescopes at the Maui Space Surveillance System were trained at the asteroid and collected adaptive optics images, photometry and spectroscopy. Analysis of the imagery reveals the asteroid is triangular shaped with significant self-shadowing. The photometry reveals a 20-h period and the spectroscopy shows that the asteroid is a Q-type.     

Keck adaptive optics imaging of near-Earth Asteroid 2004 XP14

We present resolved near-infrared images of near-Earth Asteroid 2004 XP14, obtained with the adaptive optics system on Keck II during July 2006. This is the first time a near-Earth asteroid has been directly imaged from the ground. Our result illustrates the capabilities of adaptive optics and complements radar and spectral observations.     

Extreme sensitivity of the YORP effect to small-scale topography

Radiation recoil (YORP) torques are shown to be extremely sensitive to small-scale surface topography, using numerical simulations. Starting from a set of “base objects” representative of the near-Earth object population, random realizations of three types of small-scale topography are added: Gaussian surface fluctuations, craters, and boulders. For each, the expected relative errors in the spin and obliquity components of the YORP torque caused by the observationally unresolved small-scale topography are computed. Gaussian power, at angular scales below an observational limit, produces expected errors of order 100% if observations constrain the surface to a spherical harmonic order l?10. For errors under 10%, the surface must be constrained to at least l=20. A single crater with diameter roughly half the object's mean radius, placed at random locations, results in expected errors of several tens of percent. The errors scale with crater diameter D as D² for D>0.3 and as D³ for D<0.3 mean radii. Objects that are identical except for the location of a single large crater can differ by factors of several in YORP torque, while being photometrically indistinguishable at the level of hundredths of a magnitude. Boulders placed randomly on identical base objects create torque errors roughly 3 times larger than do craters of the same diameter, with errors scaling as the square of the boulder diameter. A single boulder comparable to Yoshinodai on 25143 Itokawa, moved by as little as twice its own diameter, can alter the magnitude of the torque by factors of several, and change the sign of its spin component at all obliquities. Most of the total torque error produced by multiple unresolved craters is contributed by the handful of largest craters; but both large and small boulders contribute comparably to the total boulder-induced error. A YORP torque prediction derived from groundbased data can be expected to be in error by of order 100% due to unresolved topography. Small surface changes caused by slow spin-up or spin-down may have significant stochastic effects on the spin evolution of small bodies. For rotation periods between roughly 2 and 10 h, these unpredictable changes may reverse the sign of the YORP torque. Objects in this spin regime may random-walk up and down in spin rate before the rubble-pile limit is exceeded and fissioning or loss of surface objects occurs. Similar behavior may be expected at rotation rates approaching the limiting values for tensile-strength dominated objects.     

Current bombardment of the Earth-Moon system: Emphasis on cratering asymmetries

We calculate the current spatial distribution of projectile delivery to the Earth and Moon using numerical orbital dynamics simulations of candidate impactors drawn from a debiased Near-Earth Object (NEO) model. We examine the latitude distribution of impactor sites and find that for both the Earth and Moon there is a small deficiency of time-averaged impact rates at the poles. The ratio between deliveries within 30° of the pole to that of a 30° band centered on the equator is small for Earth (<5%) (0.958±0.001) and somewhat greater for the Moon (∼10%) (0.903±0.005). The terrestrial arrival results are examined to determine the degree of AM/PM asymmetry to compare with the PM excess shown in meteorite fall times. We find that the average lunar impact velocity is 20 km/s, which has ramifications in converting observed crater densities to impactor size distributions. We determine that current crater production on the leading hemisphere of the Moon is 1.28±0.01 that of the trailing when considering the ratio of craters within 30° of the apex to those within 30° of the antapex and that there is virtually no nearside-farside asymmetry, in agreement with observations of rayed craters. As expected, the degree of leading-trailing asymmetry increases when the Moon's orbital distance is decreased.     

Solar and planetary destabilization of the Earth-Moon triangular Lagrangian points

In the restricted circular three-body problem, two massive bodies travel on circular orbits about their mutual center of mass and gravitationally perturb the motion of a massless particle. The triangular Lagrange points, L₄ and L₅, form equilateral triangles with the two massive bodies and lie in their orbital plane. Provided the primary is at least 27 times as massive as the secondary, orbits near L₄ and L₅ can remain close to these locations indefinitely. More than 2200 cataloged asteroids librate about the L₄ and L₅ points of the Sun-Jupiter system, and five bodies have been discovered around the L₄ point of the Sun-Neptune system. Small satellites have also been found librating about the L₄ and L₅ points of two of Saturn's moons. However, no objects have been discovered around the Earth-Moon L₄ and L₅ points. Using numerical integrations, we show that orbits near the Earth-Moon L₄ and L₅ points can survive for over a billion years even when solar perturbations are included, but the further addition of the far smaller perturbations from other planets destabilize these orbits within several million years. Thus, the lack of observed objects in these regions cannot be used as a constraint on Solar System formation, nor on the tidal evolution of the Moon's orbit.