Multifractal Fits to the Observed Main Belt Asteroid Distribution

Dohnanyi's (J. W. Dohnanyi, 1969, J. Geophys. Res.74, 2531-2554) theory predicts that a collisional system such as the asteroidal population of the main belt should rapidly relax to a power-law stationary size distribution of the kind N(m)∝m^−α, with α very close to 11/6, provided all the collisional response parameters are independent of size. The actual asteroid belt distribution at observable sizes, instead, does not exhibit such a simple fractal size distribution.We investigate in this work the possibility that the corresponding cumulative distribution may be instead fairly fitted by multifractal distributions. This multifractal behavior, in contrast with the Dohnanyi fractal distribution, is related to the release of his hypothesis of self-similarity.     

Origin of the Basaltic Asteroid 1459 Magnya: A Dynamical and Mineralogical Study of the Outer Main Belt

The recent discovery of a relatively small basaltic asteroid in the outer main belt with no apparent link to (4) Vesta raised several hypotheses on its origin. We present the results of a dynamical and mineralogical study of the region near (1459) Magnya intended to establish its origin. The dynamical analysis shows that the region is filled with high-order two-body and three-body mean motion resonances and nonlinear secular resonances, which can lead to slow chaotic diffusion. The mineralogical analysis has not identified any other asteroid with a composition similar to Magnya, nor the presence of fragments that could be securely related to the catastrophic disruption of a differentiated parent body. The various scenarios for the origin of Magnya are also discussed in the face of both the results presented here and recently published results.     

Stable Chaos versus Kirkwood Gaps in the Asteroid Belt: A Comparative Study of Mean Motion Resonances

We have shown, in previous publications, that stable chaos is associated with medium/high-order mean motion resonances with Jupiter, for which there exist no resonant periodic orbits in the framework of the elliptic restricted three-body problem. This topological “defect” results in the absence of the most efficient mechanism of eccentricity transport (i.e., large-amplitude modulation on a short time scale) in three-body models. Thus, chaotic diffusion of the orbital elements can be quite slow, while there can also exist a nonnegligible set of chaotic orbits which are semiconfined (stable chaos) by “quasi-barriers” in the phase space. In the present paper we extend our study to all mean motion resonances of order q≤9 in the inner main belt (1.9-3.3 AU) and q≤7 in the outer belt (3.3-3.9 AU). We find that, out of the 34 resonances studied, only 8 possess resonant periodic orbits that are continued from the circular to the elliptic three-body problem (regular families), namely, the 2/1, 3/1, 4/1, and 5/2 in the inner belt and the 7/4, 5/3, 11/7, and 3/2 in the outer belt. Numerical results indicate that the 7/3 resonance also carries periodic orbits but, unlike the aforementioned resonances, 7/3-periodic orbits belong to an irregular family. Note that the five inner-belt resonances that carry periodic orbits correspond to the location of the main Kirkwood gaps, while the three outer-belt resonances correspond to gaps in the distribution of outer-belt asteroids noted by Holman and Murray (1996, Astron. J.112, 1278-1293), except for the 3/2 case where the Hildas reside. Fast, intermittent eccentricity increase is found in resonances possessing periodic orbits. In the remaining resonances the time-averaged elements of chaotic orbits are, in general, quite stable, at least for times t∼250 Myr. This slow diffusion picture does not change qualitatively, even if more perturbing planets are included in the model.     

Small Main-Belt Asteroid Spectroscopic Survey in the Near-Infrared

Near-infrared spectra (∼0.90 to ∼1.65 μm) are presented for 181 main-belt asteroids, more than half having diameters less than 20 km. These spectra were measured using a specialized grism at the NASA Infrared Telescope Facility, where the near-infrared wavelength coverage is designed to complement visible wavelength CCD measurements for enhanced mineralogic interpretation. We have focused our analysis on asteroids that appear to have surfaces dominated by olivine or pyroxene since these objects can be best characterized with spectral coverage only out to 1.65 μm. Olivine-dominated A-type asteroids have distinctly redder slopes than olivine found in meteorites, possibly due to surface alteration effects such as micro-meteoroid bombardment simulated by laser irradiation laboratory experiments. K-type asteroids observed within the Eos family tend to be well matched by laboratory spectra of CO3 chondrites, while those independent of the Eos family have a variety of spectral properties. The revealed structure of the 1-μm band for 3628 Bo?němcová appears to refute its previously proposed match to ordinary chondrite meteorites. Bo?němcová displays a 1-μm band that is unlike that for any currently measured meteorite; however, spectra out to 2.5 μm are needed to conclusively argue that Bo?němcová has a surface mineralogy different from that of ordinary chondrites. Extending the spectral coverage of Vestoids out to ∼1.65 μm continues to be consistent with the “genetic” relationship of almost all observed Vestoids with Vesta and the howardites, eucrites, and diogenites. Eucrites/howardites provide the best spectral matches to the observed Vestoids.     

Radar Observations of Asteroid 3908 Nyx

We report Doppler-only (cw) radar observations of basaltic near-Earth asteroid 3908 Nyx obtained at Arecibo and Goldstone in September and October of 1988. The circular polarization ratio of 0.75±0.03 exceeds ∼90% of those reported among radar-detected near-Earth asteroids and it implies an extremely rough near-surface at centimeter-to-decimeter spatial scales. Echo power spectra over narrow longitudinal intervals show a central dip indicative of at least one significant concavity. Inversion of cw spectra yields two statistically indistinguishable shape models that have similar shapes and dimensions but pole directions that differ by ∼100°. We adopt one as our working model and explore its implications. It has an effective diameter of 1.0±0.15 km and radar and visual geometric albedos of 0.15±0.075 and 0.16^+0.08_−0.05. The visual albedo supports the interpretation by D. P. Cruikshank et al. (1991, Icarus89, 1-13) that Nyx has a thermal inertia consistent with that of bare rock. The model is irregular, modestly asymmetric, and topographically rugged.     

Asteroid Models from the Pan-STARRS Photometry

We present simulations on the asteroid photometric data that will be provided by the Pan-STARRS (Panoramic Survey Telescope and Rapid Response System). The simulations were performed using realistic shape and light-scattering models, random orientation of spin axes, and rotation periods in the range 2–24 h. We show that physical models of asteroids can be reconstructed from this data with some limitations (possible multiple pole solutions). We emphasize the potential of sparse photometric data to produce models of a large number of asteroids within the next decade and we outline further tests with fast and slow rotators, tumblers, and binary asteroids.     

Radar Observations of Asteroid 1862 Apollo

Arecibo radar echo spectra show the Q-class asteroid 1862 Apollo to have an elongation within 10% of 1.27, a pole-on silhouette with an average dimension of about 1.7 km, and disc-integrated radar properties that are typical for radar-detected near-Earth asteroids.     

Collisional Rates within Newly Formed Asteroid Families

A statistical analysis of the mutual collisions among members of asteroid families during the very early times after family formation has been performed. The statistical properties of the collisions (probability, distribution of velocity, and so on) have been computed using an algorithm effective even in cases in which the longitude of the nodes and the longitudes of the perihelia of the orbits under consideration are not distributed uniformly. The results show the occurrence of a strong enhancement in the mutual collision rate among family members, immediately after family formation. Nevertheless, this episode lasts for a relatively short time, and it does not affect too severely the overall collisional evolution of the family. The early enhancement of mutual collisions, however, may influence the cratering record exhibited by the surfaces of family members, possibly laying the foundation for the early development of a surface regolith layer.     

小天体离散元仿真软件的搭建与测试

小天体探测是当今太阳系探测的一大热点, 对小行星演化的研究有助于人们了解太阳系的起源. 演化研究的一项重要内容是小天体结构的演化, 即小天体在多种力学机制作用下自身形状与结构的演化. 在小天体碎石堆结构的假设之下, 一种比较常见的模拟小天体结构演化的方法是离散元仿真算法(Discrete Element Method, DEM), 目前国内外有数个团队开发了相关算法软件. 本文介绍了团队开发的《基于DEM仿真算法的多粒子系统模拟软件》的基础理论、实现方法以及加速算法, 并使用二体接触模型、声速传播仿真、小行星内部压强、小行星旋转稳定性仿真算例验证了算法的可靠性.     

NEAR Magnetic Field Observations at 433 Eros: First Measurements from the Surface of an Asteroid

The magnetometer investigation aboard the NEAR-Shoemaker spacecraft has obtained extensive magnetic field observations throughout the 433 Eros environment, from distances in excess of 100,000 km to those conducted after landing on 12 February 2001. We report the apparent absence of global scale magnetization at this asteroid (H<0.005 A·m⁻¹; natural remanent magnetization per kilogram <1.9×10⁻⁶ A·m² ·kg⁻¹), orders of magnitude less than the intense magnetization attributed to S-class asteroids Gaspra and Braille. The extremely low magnetization state of 433 Eros places this object significantly below the levels generally associated with LL chondrites and undifferentiated primitive bodies, challenging our current understanding of the meteorite-asteroid connection.     

Asteroid 522 Helga is chaotic and stable

Celestial Mechanics and Dynamical Astronomy -     

Formation of Asteroid Families by Catastrophic Disruption: Simulations with Fragmentation and Gravitational Reaccumulation

This paper builds on preliminary work in which numerical simulations of the collisional disruption of large asteroids (represented by the Eunomia and Koronis family parent bodies) were performed and which accounted not only for the fragmentation of the solid body through crack propagation, but also for the mutual gravitational interaction of the resulting fragments. It was found that the parent body is first completely shattered at the end of the fragmentation phase, and then subsequent gravitational reaccumulations lead to the formation of an entire family of large and small objects with dynamical properties similar to those of the parent body. In this work, we present new and improved numerical simulations in detail. As before, we use the same numerical procedure, i.e., a 3D SPH hydrocode to compute the fragmentation phase and the parallel N-body code pkdgrav to compute the subsequent gravitational reaccumulation phase. However, this reaccumulation phase is now treated more realistically by using a merging criterion based on energy and angular momentum and by allowing dissipation to occur during fragment collisions. We also extend our previous studies to the as yet unexplored intermediate impact energy regime (represented by the Flora family formation) for which the largest fragment's mass is about half that of the parent body. Finally, we examine the robustness of the results by changing various assumptions, the numerical resolution, and different numerical parameters. We find that in the lowest impact energy regime the more realistic physical approach of reaccumulation leads to results that are statistically identical to those obtained with our previous simplistic approach. Some quantitative changes arise only as the impact energy increases such that higher relative velocities are reached during fragment collisions, but they do not modify the global outcome qualitatively. As a consequence, these new simulations confirm previous main results and still lead to the conclusion that: (1) all large family members must be made of gravitationally reaccumulated fragments; (2) the original fragment size distribution and their orbital dispersion are respectively steeper and smaller than currently observed for the real families, supporting recent studies on subsequent evolution and diffusion of family members; and (3) the formation of satellites around family members is a frequent and natural outcome of collisional processes.     

Asteroid motion near the 3 : 1 resonance

A mapping model is constructed to describe asteroid motion near the 3 : 1 mean motion resonance with Jupiter, in the plane. The topology of the phase space of this mapping coincides with that of the real system, which is considered to be the elliptic restricted three body problem with the Sun and Jupiter as primaries. This model is valid for all values of the eccentricity. This is achieved by the introduction of a correcting term to the averaged Hamiltonian which is valid for small values of the ecentricity.We start with a two dimensional mapping which represents the circular restricted three body problem. This provides the basic framework for the complete model, but cannot explain the generation of a gap in the distribution of the asteroids at this resonance. The next approximation is a four dimensional mapping, corresponding to the elliptic restricted problem. It is found that chaotic regions exist near the 3 : 1 resonance, due to the interaction between the two degrees of freedom, for initial conditions close to a critical curve of the circular model. As a consequence of the chaotic motion, the eccentricity of the asteroid jumps to high values and close encounters with Mars and even Earth may occur, thus generating a gap. It is found that the generation of chaos depends also on the phase (i.e. the angles andv) and as a consequence, there exist islands of ordered motion inside the sea of chaotic motion near the 3 : 1 resonance. Thus, the model of the elliptic restricted three body problem cannot explain completely the generation of a gap, although the density in the distribution of the asteroids will be much less than far from the resonance. Finally, we take into account the effect of the gravitational attraction of Saturn on Jupiter's orbit, and in particular the variation of the eccentricity and the argument of perihelion. This generates a mixing of the phases and as a consequence the whole phase space near the 3 : 1 resonance becomes chaotic. This chaotic zone is in good agreement with the observations.     

小行星主带上单个行星的质量上限

介绍了N体模拟的Hermite算法,并利用该算法研究了不同质量行星在小行星主带上轨道的演化情况．采用的演化模型是太阳系N体模型(N=7),即把水星、金星、地球的质量加到太阳上,忽略冥王星,同时在小行星主带附近增加一个假想行星,系统演化时间为1亿年．数值模拟显示能够稳定存在于小行星主带上的单个天体的质量上限其量级为10~(25)kg．模拟同时还显示在某些情况下,假想行星与木星之间的低阶共振可以增强系统的稳定性．     

On Stable Chaos in the Asteroid Belt

The twenty most chaotic objects found among first hundred of numbered asteroids are studied. Lyapunov time calculated with and without inner planets indicates that for eleven of those asteroids the strongest chaotic effect results from the resonances with Mars. The filtered semimajor axis displays an abrupt variation only when a close approach to Mars takes place. The study of the behaviour of the critical argument for candidate resonances can reveal which is responsible for the semimajor axis variation. We have determined these resonances for the asteroids in question. For the asteroids chaotic even without the inner planets we have determined the most important resonances with Jupiter, or three-body resonances. This revised version was published online in July 2006 with corrections to the Cover Date.     

An Upper Limit of Mass for a Stable Minor Planet in the Main Asteroid Belt

The stability of an imaginary planet located in the present main asteroid belt is studied with a 7-body model (Sun, Mars, Jupiter, Saturn, Uranus, Neptune and the imaginary planet). The fourth-order Hermite algorithm P(EC)³ is used, which has a very small secular energy error for the integration of periodic orbits with a constant time-step. The evolution of orbits is followed up to 10⁸ years. Our numerical results show that the low-order resonances with Jupiter can enhance the stability of the imaginary planet in some cases. The survival probability of the imaginary planet decreases with the planet mass. The upper limit of the imaginary planet's mass that can survive in the main belt is around 10²⁵ kg, i.e., about the Earth's mass.     

Scientific Value of the Laser Ranging of Asteroid Icarus

The space mission of the laser ranging of asteroid Icarus is that a laser reflector and a timer are placed on the No.1566 asteroid and the laser interference ranging is conducted between the asteroid and the ground-based station for making the precise measurements of the PPN parameters γ and β, solar quadrupolar moment J₂, time rate of change ?/G of the gravitational constant and barycentric gravitational constant of the solar system objects. With the development of laser techniques, the timing accuracy of 10 ps (or 3 mm expressed by the amount of ranging) can be realized. In 2015 the asteroid Icarus will be close to the earth, which provides a better launch window for the Icarus lander. In the present article the 2003 interplanetary ephemeris frame of the PMOE is adopted to simulate the laser ranging between the ground-based station and the asteroid for 800 days from 2015 September 25 on and obtain the indeterminacies of 18 parameters, among which those of γ, β, J₂ and ?/G are respectively 7.8 × 10⁻⁸, 9.0 × 10⁻⁷, 9.8 × 10⁻¹¹ and 7.0 × 10−15yr⁻¹, with each being 1 to 3 orders higher than the available experimental accuracy. The simulated result shows that this space mission is of scientific significance to the test of the theory of relativity, determination of the fundamental parameters of solar system and test of the space-time fundamental laws.     

On the Stochasticity of the Asteroid Belt

The study of the stochasticity of the asteroid belt requires the analysis of a large number of orbits. We detect the dynamical character of a set of 5 400 asteroids using the Fast Lyapunov Indicator, a method of analysis closely related to the computation of the Lyapunov Characteristic Exponents, but cheaper in computational time. For both regular and chaotic orbits we try to associate the motion to the underlying resonances network. For it we consider different methods of classification of rational numbers proposed by number theory, and we choose the one which seems to be strictly related to the dynamical behaviour of a system. This revised version was published online in July 2006 with corrections to the Cover Date.     

Near-IR imaging of Asteroid 4 Vesta

The Keck Observatory's adaptive optics (AO) system has been used to observe Asteroid 4 Vesta during its 2003 closest approach to Earth. Broadband K^′- and L^′-band images, centered at 2.1 and 3.6 μm, respectively, are presented here. The sharpness of the images was improved by applying a deconvolution algorithm, MISTRAL, to the images. The K^′- and L^′-band images at spatial resolutions of 53 km (^0.055″) and 88 km (^0.085″), respectively, display albedo features on the surface of the asteroid that can also be seen in the HST images (673 nm) presented by Thomas et al. [1997. Impact excavation on Asteroid 4 Vesta: Hubble Space Telescope results. Science 277, 1492-1495] and Binzel et al. [1997. Geologic mapping of Vesta from 1994 Hubble Space Telescope images. Icarus 128, 95-103] at the same latitudes and longitudes. While we cannot determine the morphology of these features, we can speculate that some of the albedo features may be impact craters filled with dark material. Spectra, centered at 1.65 and 2.1 μm, were also obtained. Spectra were corrected for the solar flux and are similar to those published by Gaffey [1997. Surface lithologic heterogeneity of Asteroid 4 Vesta. Icarus 127, 130-157], along the same wavelength range.     

Asteroid 2002NY40 as a source of meteorite-dropping bolides

The existence of asteroidal meteoroid streams capable of producing meteorite-dropping bolides has long being invoked, but evidence is scarce. Recent modelling of previously reported associations suggests that the time-scales to keep the orbital coherence of these streams producing meteorites are too short. We present an unequivocal association between near earth object (NEO) 2002NY40 and at least one bright fireball detected over Finland in 2006 August. Another two additional fireballs recorded from Spain and Finland seem to be related, together producing a fireball-producing stream (β Aquarids). On the basis of historical data, the 2006 finding suggests the existence of a meteoroid complex capable of producing meteorites. Taking into account present time-scales for orbital decoherence, if 2002NY40 has large meteoroids associated with it, such behaviour would be the consequence of a relatively recent asteroidal fragmentation. Supporting our claim, the heliocentric orbits of two recently discovered NEOs, 2004NL8 and 2002NY40, were found to exhibit a good similarity to each other and also to the orbits of the three bolides. The fireball spectra of the two Finish bolides showed that the chemical abundances of these objects are consistent with the main elements found in chondrites. This result is consistent with the probable Low iron, Low metal (LL) chondritic mineralogy of asteroid 2002NY40. Consequently, this asteroid may be delivering LL chondrites to the Earth. Additional fireball reports found in the literature suggest that the associated β Aquarid complex may have been delivering meteorites to the Earth during, at least, the last millennium.