On the origin of the asteroids

Initial temperature distribution of the nebulous disk around the sun led to the bordering region between the asteriods and Jupiter becoming a transition region, in which the “icy” matter changed from uncondensed to condensed state. This continuity in chemical constitution makes the projected surface density of solid condensate in the inner portion of the Jupiter region greater than the mean value in the asteriod region, and the time taken for dust particles to precipitate to become comparable to that in the asteriod region. Owing to gravitational instability, the dust layer then broke up into clusters of particles, each cluster transforming into a planetesimal. The mass of such a planetesimal and the rate of its growth in the Jupiter region are greater than those in the asteriod region. Perturbations and mutual encounters between the larger planetesimals in the inner portion of the Jupiter region changed their orbits and produced rather large relative velocities. Some of these entered the asteriod region, drew out most of the matter there, and increased the random velocity of the asteriods that remained, so that they could not combine to form a planet. We prove the above view by a quantitative analysis in this paper.     

On the Laplacian orbit determination of asteroids

A modified Laplacian technique is described for initial orbit determination of asteroids from CCD observations and its applications for orbit determination of the main belt asteroids and near Earth asteroids. The proposed modification is based on a simultaneous improvement of both the orbital elements and the derivatives of spherical coordinates in frames of Laplace's method. It provides an orbit which represents the used observations with the residuals comparable with errors of these observations. The improved values of the derivatives might be used as ephemeris parameters for identification of newly discovered objects.     

On the deflection of asteroids with mirrors

This paper presents an analysis of an asteroid deflection method based on multiple solar concentrators. A model of the deflection through the sublimation of the surface material of an asteroid is presented, with simulation results showing the achievable impact parameter with, and without, accounting for the effects of mirror contamination due to the ejected debris plume. A second model with simulation results is presented analyzing an enhancement of the Yarkovsky effect, which provides a significant deflection even when the surface temperature is not high enough to sublimate. Finally the dynamical model of solar concentrators in the proximity of an irregular celestial body are discussed, together with a Lyapunov-based controller to maintain the spacecraft concentrators at a required distance from the asteroid.     

On the spin rate of the s-type asteroids

A relation between the radii and rotation rates of S-type asteroids is discussed. According to this relation these objects do not rotate with the same spin rate.     

Collisional history of asteroids: Evidence from Vesta and the Hirayama families

Collisional evolution studies of asteroids indicate that the initial asteroid population at the time mean collisional velocities were pumped up to ～5 km/sec was only modestly larger than it is today; i.e., the asteroid belt was already depleted relative to the mean surface density elsewhere in the planetary region. Numerical simulations of the collisional evolution of hypothetical initial asteroid populations have been run, subject to three constraints: they must (a) evolve to the present observed asteroid size distribution, (b) preserve Vesta's basaltic crust, and (c) produce at least the observed number of major Hirayama families. A “runaway growth” initial asteroid population distribution is found to best satisfy these constraints. A new model is presented for calculating the fragmental size distribution for the disruption of large, gravitationally bound bodies in which the material strength is increased by hydrostatic self-compression. This model predicts that large asteroid behave as intrinsically strong bodies, even if they have had a history of being collisionally fractured. This model, when applied to the breakup of the Themis and Eos family parent bodies, gives size distributions in reasonably good agreement with those observed.     

On YORP-induced spin deformations of asteroids

The alteration of the spin states of small Solar-System bodies by the YORP thermal effect has recently become a plausible and, for some, the favorite candidate for the formation of binary asteroids. The idea is that if an asteroid is slowly spun up to a state where some strength measure is exceeded; it can no longer remain rigid and adjusts to a new configuration. Such a process might involve global fission, global shape changes without fission, or gradual surface mass loss with subsequent mass re-accumulations forming a secondary body.Here I analyze the changes in the shape, spin, and state during slowly increasing angular momentum of rubble-pile, self-gravitating, homogeneous ellipsoidal bodies undergoing homogeneous motions. I use, as appropriate for rubble-pile asteroids, the strength models of granular materials with zero tensile strength (cohesionless but arbitrary dilatancy); those are characterized by the “angle of friction” material constant. There are distinct limit spins depending on that angle of friction and the shape, which were previously presented [Holsapple, K.A., 2001. Icarus 154, 432-448; Holsapple, K.A., 2004. Icarus 172, 272-303]. Here the deformations and state changes when the angular momentum is slowly increased from that of a limit spin state are determined, to study the YORP processes. When a body is at its limit spin and the angular momentum increases further, the body deforms in a unique way along definite paths in the ellipsoidal shape space: it evolves as an elongating shape with an increasing rotational inertia, which in most cases produces a decreasing spin. I give exact analytical solutions for those shape and spin histories, as well as the histories of the mass density, angular momentum and energy. Comparison to other approaches is made.     

On spectral dependence of polarization of asteroids

From the analysis of all of the data available on the spectral dependence of polarization of light reflected by asteroids, it has been shown that the slope of the spectral dependence of polarization of asteroids changes its sign, when moving from the negative branch of the phase curve of polarization to the positive one. This effect also manifests itself in the spectral behavior of polarization of the Moon and, probably, in the polarization of the other atmosphereless bodies. From the analysis of a population of asteroids of different types, a weak correlation between the spectral slopes of the polarization degree and the albedo has been found.     

Meteoritic and other constraints on the internal structure and impact history of small asteroids

Studies of the internal structure of asteroids, which are crucial for understanding their impact history and for hazard mitigation, appear to be in conflict for the S-type asteroids, Eros, Gaspra, and Ida. Spacecraft images and geophysical data show that they are fractured, coherent bodies, whereas models of catastrophic asteroidal impacts, family and satellite formation, and studies of asteroid spin rates, and other diverse properties of asteroids and planetary craters suggest that such asteroids are gravitationally bound aggregates of rubble. These conflicting views may be reconciled if 10-50 km S-type asteroids formed as rubble piles, but were later consolidated into coherent bodies. Many meteorites are breccias that testify to a long history of impact fragmentation and consolidation by alteration, metamorphism, igneous and impact processes. Ordinary chondrites, which are the best analogs for S asteroids, are commonly breccias. Some may have formed in cratering events, but many appear to have formed during disruption and reaccretion of their parent asteroids. Some breccias were lithified during metamorphism, and a few were lithified by injected impact melt, but most are regolith and fragmental breccias that were lithified by mild or moderate shock, like their lunar analogs. Shock experiments show that porous chondritic powders can be consolidated during mild shock by small amounts of silicate melt that glues grains together, and by friction and pressure welding of silicate and metallic Fe,Ni grains. We suggest that the same processes that converted impact debris into meteorite breccias also consolidated asteroidal rubble. Internal voids would be partly filled with regolith by impact-induced seismic shaking. Consolidation of this material beneath large craters would lithify asteroidal rubble to form a more coherent body. Fractures on Ida that were created by antipodal impacts and are concentrated in and near large craters, and small positive gravity anomalies associated with the Psyche and Himeros craters on Eros, are consistent with this concept. Spin data suggest that smaller asteroids 0.6-6 km in size are unconsolidated rubble piles. C-type asteroids, which are more porous than S-types, and their analogs, the volatile-rich carbonaceous chondrites, were probably not lithified by shock.     

On the observability of radiation forces acting on near-Earth asteroids

We consider the perturbations on near-earth asteroid orbits due to various forces stemming from solar radiation. We find that the existence of precise radar astrometric observations at multiple apparitions, spanning periods on the order of 10 years, allows the detection of such forces on bodies as large as kilometer across. Indeed, the perturbations are so substantial that certain of the forces can be essential to fit an orbit to the observations. In particular, we show that the recoil force of thermal radiation from the asteroid, known as the Yarkovsky effect, is the most important of these unmodeled perturbations. We also show that the effect of reflected light can be important if even moderate albedo variations are present, while moderate changes in oblateness appear to have a far smaller effect. An unexpected result is that the Poynting–Robertson effect, typically only considered for submillimeter dust particles, could be observable on smaller asteroids with high eccentricity, such as 1566 Icarus. Finally, we also study the possibility of improving the orbit uncertainty through well-timed optical observations which might help in better detection of these nongravitational perturbations.     

On the accuracy of indirect methods for estimating the sizes of asteroids

We have shown that the least reliable data source for estimating the albedo of asteroids is the maximal value of the degree of negative polarization. To increase the accuracy of the method that uses the data on the slope of the positive branch of polarization, the values of the approximating coefficient should be selected in accordance with a specified type of asteroids. The similar situation is in the shadow method, where the value of the phase integral q should be selected in accordance with each of the types. Moreover, the estimates obtained by both methods will be more reliable if the phase dependences of brightness that are characteristic of a specified type of asteroids, including the range of the opposition effect, are used in transforming from A(0) to A(α). The modeling performed with the Irvine-Yanovitskii modification of the shadow model of Hapke showed that the values of the phase coefficient β (10° ≤ α ≤ 20°) and q are, respectively, in the ranges of 0.016–0.030 and 0.6–1.0 for the E-type asteroids, 0.026–0.033 and 0.42–0.52 for the M-type asteroids, and 0.031–0.039 and 0.42–0.52 for the C-type asteroids.     

On the implausibility of a cometary origin for most Apollo-Amor asteroids

As the rate of replenishment of short-lived Apollo-Amor asteroids from the main belt seems to be insufficient to compensate for their losses, the idea was put forward that most of them are inactive cometary nuclei. However, the observational and theoretical evidence is inconclusive about whether it is possible to transform cometary nuclei into asteroid-like objects. There is good evidence that Apollo-Amor asteroids represent the last parent bodies of most, or even all, classes of meteorites. But meteorites cannot be formed within cometary nuclei having a constitution like Whipple's classical model, and alternative models seem to be unsatisfactory. Therefore, it is concluded that the cometary origin of most Apollo-Amor asteroids is implausible and they are genuine asteroids coming from the main belt. The process of their losses and replenishment must be studied further.     

A satellite-asteroid mystery and a possible early flux of scattered C-class asteroids

Spectrophotometric measurements of the subset of satellites thought to be of capture origin, orbiting Saturn, Jupiter, and Mars, indicate that they typically (all?) have neutral spectra and low albedo, indicating spectral class C. This finding is puzzling in light of evidence that class-C objects are native only to the outer half of the asteroid belt. How did C-like objects approach, and get captured by, planets? Probably Jupiter resonances scattered a high flux of C-type objects out of the belt and throughout much of the primordial solar system. Such scattering could occur only at the close of planet accretion when extended atmospheres could affect capture. The largest flux of scattered objects came from resonances in the most heavily populated regions of the belt near 2.8 AU: in particular, the 7:3 and 5:2 resonance regions primarily populated by C's. Hence, most captured satellites are C's, not D's, S's, etc. This scenario supports and expands upon the capture scenario involving extended protoatmospheres, proposed by J. B. Pollack, J. Burns, and M. Tauper (1979, Icarus 37, 587–611) and D. Hunten (1979, Icarus 37,113–123).     

The delivery of organic matter from asteroids and comets to the early surface of Mars

Carbon delivered to the Earth by interplanetary dust particles may have been an important source of pre-biotic organic matter (Anders, 1989). Interplanetary dust is shown to deliver an order-of-magnitude higher surface concentration of carbon onto Mars than onto Earth, suggesting interplanetary dust may be an important source of carbon on Mars as well.     

On some long time dynamical features of the Trojan asteroids of Jupiter

The equation of motion of long periodic libration around the Lagrangian point $L_4$ L 4 in the restricted three-body problem is investigated. The range of validity of an approximate analytical solution in the tadpole region is determined by numerical integration. The predictions of the model of libration are tested on the Trojan asteroids of Jupiter. The long time evolution of the orbital eccentricity and the longitude of the perihelion of the Trojan asteroids, under the effect of the four giant planets, is also investigated and a slight dynamical asymmetry is shown between the two groups of Trojans at $L_4$ L 4 and $L_5$ L 5 .     

The delivery of organic matter from asteroids and comets to the early surface of Mars

Carbon delivered to the Earth by interplanetary dust particles may have been an important source of pre-biotic organic matter (Anders, 1989). Interplanetary dust is shown to deliver an order-of-magnitude higher surface concentration of carbon onto Mars than onto Earth, suggesting interplanetary dust may be an important source of carbon on Mars as well.     

Theory of the Trojan asteroids

In the previously published Parts I and II of the paper, the author has constructed a formal long-periodic solution for the case of 11 resonance in the restricted problem of three bodies to 0(m ^3/2), wherem is the small mass parameter of the system. The time-dependencet(, ,m), where is the mean synodic longitude and is related to the Jacobi constant, has been expressed by ahyperelliptic integral. It is shown here that with the approximationm=0 in the integrand, the functiont(, , 0) can be expanded in a series involving standardelliptic functions. Then the problem of inversion can be formally solved, yielding the function (t, , 0).Similarly, the normalized period (,m) of the motion can be approximated by theHagihara hyperelliptic integral (, 0), corresponding tom=0. This integral is also expanded into elliptic functions. Asymptotic forms for (, 0) are derived for 0 and for 1, corresponding to the extreme members of thetadpole branch of the family of orbits.     

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.     

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.     

Tumbling asteroids

We present both a review of earlier data and new results on non-principal axis rotators (tumblers) among asteroids. Among new tumblers found, the best data we have are for 2002 TD₆₀, 2000 WL₁₀₇, and (54789) 2001 MZ₇—each of them shows a lightcurve with two frequencies (full terms with linear combinations of the two frequencies are present in the lightcurve). For 2002 TD₆₀, we have constructed a physical model of the NPA rotation. Other recent objects which have been found to be likely tumblers based on their lightcurves that do not fit with a single periodicity are 2002 NY₄₀, (16067) 1999 RH₂₇, and (5645) 1990 SP. We have done a statistical analysis of the present sample of the population of NPA rotators. It appears that most asteroids larger than ∼0.4 km with estimated damping timescales (Harris, 1994, Icarus 107, 209) of 4.5 byr and longer are NPA rotators. The statistic of two short-period tumblers (D=0.04 and 0.4 km) with non-zero tensile strength suggests that for them the quantity μQ/T, where μ is the mechanical rigidity, Q is the elastic dissipation factor, and T is a spin excitation age (i.e., a time elapsed since the last significant spin excitation event), is greater by two to four orders of magnitude than the larger, likely rubble-pile tumblers. Among observational conditions and selection effects affecting detections of NPA rotations, there is a bias against detection of low-amplitude (small elongation) tumblers.     

Near-Sun asteroids

As follows from dynamical studies, in the course of evolution, most near-Earth objects reach orbits with small perihelion distances. Changes of the asteroids in the vicinity of the Sun should play a key role in forming the physical properties, size distribution, and dynamical features of the near-Earth objects. Only seven of the discovered asteroids are currently moving along orbits with perihelion distances q < 0.1 AU. However, due to the Kozai–Lidov secular perturbations, the asteroids, having recently passed near the Sun, could by now have moved to orbits farther from the Sun. In this study, we found asteroids that have been recently orbiting with perihelion distances q < 0.1 AU. Asteroids may be on such orbits for hundreds to tens of thousands of years. To carry out astrophysical observations of such objects is a high priority.