Asteroidal binary systems: Detection and formation

Recent occultation data and an analysis of some photometric lightcurves have shown the possible existence of asteroidal binary systems.A simple geometrical model taking into account mutual shadowing effects shows some peculiar features of the lightcurve which can be recovered in several previously observed objects; therefore the hypothesis of a relatively high frequency of binary asteroids should be seriously considered.On the other hand, while the rotational period distribution of large asteroids (D>200 km) is sharply peaked at about 5–8 hours, the surprisingly higher dispersion towards longer periods for intermediate size objects (50<D<150 km) could be connected with a larger probability of binary nature within this class.From a theoretical point of view, the collisional fragmentation of asteroids could originate gravitationally bound fragments, with a tidal transfer of rotational into orbital angular momentum, causing a rapid synchronization of the system. This kind of processes could more easily occur for intermediate objects since: (a) for large ones, very massive colliding bodies are needed for fragmentation, that means a very rare event; (b) for smaller asteroids, solid state interactions are stronger than the gravitational ones, so that a breakage probably causes a complete disruption of the gravitational binding. Further collisional events could disintegrate some systems, so that the present frequency of binary asteroids could be lower than that of the objects whose rotational period was increased by such processes.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Shock melting of ordinary chondrite powders and implications for asteroidal regoliths

Abstract— A series of 59 impacts in the laboratory reduced a coherent 460 g piece of the L6 ordinary chondrite ALH 85017 to a coarse‐grained “regolith.” We then subjected the 125–250 μm fines from this sample to reverberation shock stresses of 14.5–67 GPa in order to delineate the melting behavior of porous, unconsolidated, chondritic asteroid surfaces during meteorite impact. The initial pore space (40–50%) was completely closed at 14.5 GPa and a dense aggregate of interlocking grains resulted. Grain‐boundary melting commenced at <27 GPa and ?50% of the total charge was molten at 67 GPa; this stress corresponds to typical asteroid impacts at ?5 km/sec. Melting of the entire sample most likely mandates >80 GPa, which is associated with impact velocities >8 km/sec. The Fe‐Ni and troilite clasts of the original meteorite melted with particular ease, forming immiscible melts that are finely disseminated throughout the silicate glass. These metal droplets are highly variable in size, extending to <100 nm and most likely to superparamagnetic domains; such opaques are also observed in the natural melt veins of ordinary chondrites. It follows that melting and dissemination of pre‐existing, Fe‐rich phases may substantially affect the optical properties of asteroidal surfaces. It seems unnecessary to invoke reduction of Fe²⁺ (or Fe³⁺) by sputtering or impact‐processes—in analogy to the lunar surface—to produce “space weathering” effects on S‐type asteroids. We note that HED meteorites contain ample FeO (comparable to that in lunar basalts) for reduction processes to take place, yet their probable parent object(s), Vesta and its collisional fragments, display substantially unweathered surfaces. Howardites, eucrites, and diogenites (HEDs), however, contain little native metal (typically <0.5%), in contrast to ordinary chondrites (commonly 10–15%) and their S‐type parent objects. These considerations suggest that the modal content of native metal and sulfides is more important for space weathering on asteroids than total FeO.     

Bulk density of ordinary chondrite meteorites and implications for asteroidal internal structure

Abstract— The bulk densities of 82 samples of 72 ordinary chondrites (OCs) were measured to an accuracy of ～1% using a modified Archimedian method. We found the average bulk density to be 3.44 ± 0.19 g/cm³ for the H group, 3.40 ± 0.15 g/cm³ for the L group, and 3.29 ± 0.17 g/cm³ for the LL group (± represent 1σ). Bulk density measurements of 11 pieces of one fall, Pultusk (H group), were also found to vary considerably (3.31 to 3.63 g/cm³). To investigate controls on bulk density within the OCs, we compared density with bulk chemical composition (the ratio of Fe metal to total Fe; the ratio of total Fe to SiO₂; the ratio of FeO to total Fe and MgO). Within each OC group, bulk chemical composition is nearly invariant whereas bulk density varies from about 3.0 to 3.8 g/cm³. Slight but systematic differences in average density between the H, L, and LL groups presumably relate to differences in metallic Fe abundance. However, considerable overlap between OC groups and the wide range of bulk densities within each group suggest differences in porosity dominantly control variations of density within the OC subgroups.     

Statistical arguments for asteroidal jet streams

The distribution of asteroid orbits in space is studied and a detailed investigation for Hirayama's Flora family is presented. Some tendencies to (5-dimensional) clustering are found by means of comparing actual with random distribution simulated on a computer.     

Proper elements for highly inclined asteroidal orbits

Based on Williams' work and rewritten in action angle variables, a method for the calculation of proper elements is here presented. The averaging over the long periodic terms is performed by the semi numerical method developed by Henrard (1990); no series expansion in eccentricity or inclination of the asteroid is used which allows calculating proper elements for highly inclined orbits. Conversely, the theory is truncated at the first degree in the eccentricity and the inclination of the perturbing planets. A few tests about accuracy and consistency are presented.     

Chaotic Asteroidal Dynamics and Maximum Lyapunov Exponents

This paper describes the results of studies of dynamical chaos in the problem of the orbital dynamics of asteroids near the 3 : 1 mean-motion resonance with Jupiter. Maximum Lyapunov characteristic exponents (MLCEs) are used as an indicator and a measure of the chaoticity of motion. MLCE values are determined for trajectories calculated by the numerical integration of equations of motion in the planar elliptical restricted three-body problem. The dependence of the MLCE on the problem parameters and on the initial data is analyzed. The inference is made that the domain of chaos in the phase space of the problem considered consists of two components of different nature. The values of the MLCEs observed for one of the components (namely, for the component corresponding to low-eccentricity asteroidal orbits) are compared to the theoretical estimates obtained within the framework of model of the resonance as a perturbed nonlinear pendulum.     

Chaotic behaviour of trajectories for the asteroidal resonances

A systematic study of the main asteroidal resonances of the third and fourth order is performed using mapping techniques. For each resonance one-parameter family of surfaces of section is presented together with a simple energy graph which helps to understand and predict the changes in the surfaces of section within the family. As the truncated Hamiltonian for the planar, elliptic, restricted three-body problem is used for the mapping, the method is expected to fail for high eccentricities. We compared, therefore, the surfaces of section with trajectories calculated by symplectic integrators of the fourth and six order employing the full Hamiltonian. We found a good agreement for small eccentricities but differences for the higher eccentricities (e 0.3).     

On the transfer of radiation at asteroidal surfaces in relation to their orbit deflection – I

One of the methods discussed in deflecting the orbit of an Earth-colliding asteroid is the use of nuclear explosives. In assessing its feasibility, apart from political considerations, it is important to quantify how effective it is in orbit deflection. The transfer of radiation incident at the surface is governed by a non-linear diffusion equation. For low-yield explosions with a slab geometry ( S ₀≃10⁸ kJ μs⁻¹), the temperature at depth x and time t is well approximated by a similarity solution of the form T ( x , t )= T ₀ f (ξ), ξ= x/ ( T ⁿ ₀ t )^1/2, with T ₀ given by ( S ₀/σ)^1/4, where σ is the Stefan–Boltzmann constant, n is an index that specifies the radiation transfer and f (ξ) is the solution of a non-linear differential equation subject to the condition f (0)=1 and lim_ξ→∞ f (ξ)=0. For high-yield explosions ( S ₀≃10¹⁰ kJ μs⁻¹), numerical solutions to the non-linear diffusion equation can be obtained. These solutions have properties similar to the case of low-yield explosions. If the duration of the explosion is d ×10⁻⁸ s, where d is close to 3, the fraction of energy absorbed by the surface is found to be 7, 12 and 23 per cent for S ₀=10⁸, 10⁹ and 10¹⁰ kJ μs⁻¹ respectively.     

On the transfer of radiation at asteroidal surfaces in relation to their orbit deflection — II

The efficiency of absorption of X-rays generated by a nuclear explosion at the surface of an asteroid, estimated earlier, is used to calculate the explosion yield needed to deflect the orbit of an asteroid. Following the work of Ahrens &38; Harris, it is shown that a recoil velocity of 1 cm s⁻¹ is required to deflect an asteroid from a collision course with the Earth, and the necessary yield of explosion energy is estimated. If it is assumed that the scaling law between the energy and the diameter of the resulting crater, obtained from experiments carried out on the Earth, remains valid on the asteroid surface, where gravity is much weaker, an explosion energy of 8 and 800 megaton (Mton) equivalent of TNT would be required for asteroids of diameter 1 and 10 km respectively. If, on the other hand, the crater diameter is proportional to a certain power of the gravity g , the power being determined from a dimension analysis, 130 kton and 12 Mton would be required to endow asteroids of diameters 1 and 10 km with the required velocity, respectively. The result indicates that in order to estimate the required explosion energy, a better understanding of cratering under gravity much weaker than on the Earth would be required.     

Dynamics of dust in a plasma sheath and injection of dust into the plasma sheath above Moon and asteroidal surfaces

We have examined single dust particle dynamics in a plasma sheath near the surface of solid bodies in space, considering conditions which resemble those of planetary system bodies, when photoelectric effect can be neglected. The forces on the dust particles are assumed to be from the electric field in the sheath and from gravitation only. As the dust particles will charge negatively in the sheath, these forces will act in opposite directions and may balance.The charge delay of a moving dust particle is responsible for many of the interesting dynamical properties, and we show that for a stationary plasma, dust motion is unstable to about one Debye length out from the surface of the solid body. This part of the sheath will therefore be devoid of dust particles as they will either fall down, escape completely from the solid body or collect and make damped oscillations at stable positions in the outer part of the sheath. With increasing plasma bulk speed towards the surface, the inner unstable part of the sheath will decrease in thickness.The sources for the dust in the sheath are assumed to be mainly ejecta from meteorites and micrometeorites, but may also, for the smallest solid bodies, be from electrostatic levitation of very small dust particles. We have for different sizes of solid bodies calculated the sizes of ejecta that can be floated in the sheath. For the solar wind plasma, the suspended dust particles range from less than 1 m for the Moon to about 80 m for an asteroid with radius 1 km. These particles create a dust atmosphere.The results in this paper hold when the dust particle density is so low that the charges on the dust particles do not contribute significantly to the total space charge; a higher density will lead to a modification of the sheath.Our calculations show that ejecta below a certain size will be accelerated in the sheath and totally escape from the body even if they have near zero initial vertical velocity, while ejecta above this size will need a much larger velocity to escape. This is especially significant for the small solid bodies (radius of order km and less) which will therefore act as important sources of micronsized dust. This could be of significance for the dust production and the size distribution of dust in planetary ring systems.     

Scattering Law Analysis Based on Hapke and Lommel-Seeliger Models for Asteroidal Taxonomy

In deriving the physical properties of asteroids from their photometric data, the scattering law plays an important role, although the shape variations of asteroids result in the main variations in lightcurves. By following the physical behaviors of light reflections, Hapke et al. deduced complex functions to represent the scattering process, however, it is very hard to accurately simulate the surface scattering law in reality. For simplicity, other numerical scattering models are presented for efficiently calculating the physical properties of asteroids, such as the Lommel-Seeliger(LS) model. In this article,these two models are compared numerically. It is found that in some numerical applications the LS model in simple form with four parameters can be exploited to replace the Hapke model in complex form with five parameters. Furthermore, the generated synthetic lightcurves by the Cellinoid shape model also show that the LS model can perform as well as the Hapke model in the inversion process. Finally, by applying the Principal Component Analysis(PCA) technique to the parameters of the LS model, we present an efficient method to classify C and S type asteroids, instead of the conventional method using the parameters of the Hapke model.     

Evidence for the existence of groups of meteorite-producing asteroidal fragments

Abstract— The MORP camera network in western Canada observed 56 events which we associate with meteorites larger than 0.1 kg. An additional 33 Prairie Network (central USA) fireballs with published orbits were previously identified as the sources of meteorites of at least 0.25 kg. A comparison of the MORP orbits with each other and with the PN orbits, using the D′ criterion of orbital similarity, exhibits a surprising number of small values. This suggests there are groups of related objects among the 89 events. We evaluate the probability of small values of D′ arising by chance from a group of random orbits that has the distribution of orbital elements expected for meteorites. There is an excess of small values of D′ among the 89 meteoritic objects over the expectation for random orbits and a marked excess of very small values. Four groups comprising a total of 16 objects account for this excess. These groups exhibit a preference for the larger masses of the population and a very strong concentration of perihelia just slightly inside the Earth's orbit. Although it has been shown by others that gravitational perturbations will disperse Earth-crossing streams in times that are much less than cosmic-ray exposure ages, the properties of the four groups suggest they may be streams of fragments that crossed the Earth's orbit only recently. Such streams may include a considerable fraction of meteorites falling at a given time. Orbital evolution of these streams could alter the sample of meteorites arriving on Earth over time intervals that are less than the accumulation time of the Antarctic collections.     

Relative Effect of Inclinations for Moonlets in the Triple Asteroidal Systems

We present the analysis and computational results for the inclination relative effect of moonlets of triple asteroidal systems. Perturbations on moonlets due to the primary’s non-sphericity gravity, the solar gravity, and moonlets’ relative gravity are discussed. The inclination vector for each moonlet follows a periodic elliptical motion; the motion period depends on the moonlet’s semi-major axis and the primary’s J2 perturbations. Perturbation on moonlets from the Solar gravity and moonlet’s relative gravity makes the motion of the x component of the inclination vector of moonlet 1 and the y component of the inclination vector of moonlet 2 to be periodic. The mean motion of x component and the y component of the inclination vector of each moonlet forms an ellipse. However, the instantaneous motion of x component and the y component of the inclination vector may be an elliptical disc due to the coupling effect of perturbation forces. Furthermore, the x component of the inclination vector of moonlet 1 and the y component of the inclination vector of moonlet 2 form a quasi-periodic motion. Numerical calculation of dynamical configurations of two triple asteroidal systems (216) Kleopatra and (153591) 2001 SN263 validates the conclusion.     

The frequency of compound chondrules and implications for chondrule formation

Abstract— The properties of compound chondrules and the implications that they have for the conditions and environment in which chondrules formed are investigated. Formulae to calculate the probability of detecting compound chondrules in thin sections are derived and applied to previous studies. This reinterpretation suggests that at least 5% of chondrules are compounds, a value that agrees well with studies in which whole chondrules were removed from meteorites. The observation that adhering compounds tend to have small contact arcs is strengthened by application of these formulae. While it has been observed that the secondaries of compound chondrules are usually smaller than their primaries, these same formulae suggest that this could be an observation bias. It is more likely than not that thin section analyses will identify compounds with secondaries that are smaller than their primaries. A new model for chondrule collisional evolution is also developed. From this model, it is inferred that chondrules would have formed, on average, in areas of the solar nebula that had solids concentrated at least 45 times over the canonical solar value.     

Periodicity in the crater formation rate and implications for astronomical modeling

Claim for periodicity in the crater formation rate is reinvestigated using a criterion proposed by Broadbent, and data sets of Rampino and Stothers and of Grieve are shown to satisfy the periodicity criterion (P 30 Myr).On the other hand, currently observed impactors are mainly asteroids, while long and short periodic comets whose fluxes may vary by external disturbances occupy only a small fraction. Using a Monte Carlo simulation, constraints are obtained for the dispersion Q(Myr) from an exact periodicity and for the periodic components (F _tp) in the signals for their periodicity to be detected. It is found that for = 5, 6 and 7 Myr, F _tp, would have to be 40% or greater, 60% or greater and 80% or greater, respectively. These constraints are used to discuss whether the giant molecular cloud perturbations can give rise to the periodicity in the impact events. The amplitude of the solar Z-motion need to be some 100pc for = 6 Myr, which requires the periodic component (SP and LP comets, if the former originate from the latter) to be 60%, while for = 7 Myr, the periodic component need to be 80%. The GMC perturbation model consistent with the periodicity appears to be the one where the amplitude is 100pc and the periodic component - 60% of the impactors. If SP comets mainly originate from a source such as the hypothetical Kuiper belt, the GMC perturbation would not be consistent with the periodicity.     

Progressive alteration in CV3 chondrites: More evidence for asteroidal alteration

Abstract— The oxidized CV3 chondrites can be divided into two major subgroups or lithologies, Bali-like (CV3_oxB) and Allende-like (CV3_oxA), in which chondrules, calcium-aluminum-rich inclusions (CAIs) and matrices show characteristic alteration features (Weisberg et al, 1997; Krot et al, 1997d; Kimura and Ikeda, 1997). The CV3_oxB lithology is present in Bali, Kaba, parts of the Mokoia breccia and, possibly, in Grosnaja and Allan Hills (ALH) 85006. It is characterized by the presence of the secondary low-Ca phyllosilicates (saponite and sodium phlogopite), magnetite, Ni-rich sulfides, fayalite (Fa>₉₀), Ca-Fe-rich pyroxenes (Fs_10–50Wo_45–50) and andradite. Phyllosilicates replace primary Ca-rich minerals in chondrules and CAIs, which suggests mobilization of Ca during aqueous alteration. Magnetite nodules are replaced to various degrees by fayalite, Ca-Fe-rich pyroxenes and minor andradite. Fayalite veins crosscut fine-grained rims around chondrules and extend into the matrix. Thermodynamic analysis of the observed reactions indicates that they could have occurred at relatively low temperatures (<300 °C) in the presence of aqueous solutions. Oxygen isotopic compositions of the coexisting magnetite and fayalite plot close to the terrestrial fractionation line with large Δ¹⁸O_{fayalite-magnetite} fractionation (～20%). We infer that phyllosilicates, magnetite, fayalite, Ca-Fe-rich pyroxenes and andradite formed at relatively low temperatures (<300 °C) by fluid-rock interaction in an asteroidal environment. Secondary fayalite and phyllosilicates are virtually absent in chondrules and CAIs in the CV3_oxA lithology, which is present in Allende and its dark inclusions, Axtell, ALHA81258, ALH 84028, Lewis Cliff (LEW) 86006, and parts of the Mokoia and Vigarano breccias. Instead secondary nepheline, sodalite, and fayalitic olivine are common. Fayalitic olivine in chondrules replaces low-Ca pyroxenes and rims and veins forsterite grains; it also forms coarse lath-shaped grains in matrix. Secondary Ca-Fe-rich pyroxenes are abundant. We infer that the CV3_oxA lithology experienced alteration at higher temperatures than the CV3_oxB lithology. The presence of the reduced and CV3_oxA lithologies in the Vigarano breccia and CV3_oxA and CV3_oXB lithologies in the Mokoia breccia indicates that all CV3 chondrites came from one heterogeneously altered asteroid. The metamorphosed clasts in Mokoia (Krot and Hutcheon, 1997) may be rare samples of the hotter interior of the CV asteroid. We conclude that the alteration features observed in the oxidized CV3 chondrites resulted from the fluid-rock interaction in an asteroid during progressive metamorphism of a heterogeneous mixture of ices and anhydrous materials mineralogically similar to the reduced CV3 chondrites.     

A Bayesian statistical assessment of representative samples for asteroidal or meteoritical material

Primitive substances in asteroid and meteorite materials represent a record of early solar system evolution. To allow the study of these materials, they must be collected and transferred to the laboratory. Collection during sample return missions requires an assessment of the size of samples needed. Meteorite falls or finds must be subdivided into appropriate subsamples for analysis by successive generations of scientists. It is essential, therefore, to determine a representative mass or volume at which the collected or allocated sample is representative of the whole. For the first time, we have used a Bayesian statistical approach and a selected meteorite sample, Murchison, to identify a recommended smallest sample mass that can be used without interferences from sampling bias. Enhancing background knowledge to inform sample selection and analysis is an effective means of increasing the probability of obtaining a positive scientific outcome. The influence of the subdivision mechanism when preparing samples for distribution has also been examined. Assuming a similar size distribution of fragments to that of the Murchison meteorite, cubes can be similarly representative as fragments, but at orders of magnitude smaller sizes. We find that: (1) at all defined probabilities (90%, 95%, and 99%), nanometer‐sized particles (where the axes of a three‐dimensional sample are less that a nanometer in length) are never representative of the whole; (2) at the intermediate and highest defined probabilities (95% and 99%), micrometer‐sized particles are never representative of the whole; and (3) for micrometer‐sized samples, the only sample that is representative of the whole is a cube and then only at a 90% probability. The difference between cubes and fragments becomes less important as sample size increases and any >0.5 mm‐sized sample will be representative of the whole with a probability of 99.9%. The results provide guidance for sample return mission planners and curators or advisory boards that must distribute valuable samples for analysis.     

The Paris CM chondrite: Secondary minerals and asteroidal processing

We report a petrographic and mineralogical survey of Paris, a new CM chondrite considered to be the least‐altered CM identified so far (Hewins et al. 2014 ). Compared to other CMs, Paris exhibits (1) a higher concentration of Fe‐Ni metal beads, with nickel contents in the range 4.1–8.1 wt%; (2) the systematic presence of thin lamellae and tiny blebs of pentlandite in pyrrhotite grains; and (3) ubiquitous tochilinite/cronstedtite associations with higher FeO/SiO₂ and S/SiO₂ ratios. In addition, Paris shows the highest concentration of trapped ³⁶Ar reported so far for a CM chondrite (Hewins et al. 2014 ). In combination with the findings of previous studies, our data confirm the reliability of (1) the alteration sequence based on the chemical composition of tochilinite/cronstedtite associations to quantify the fluid alteration processes and (2) the use of Cr content variability in type II ferroan chondrule olivine as a proxy of thermal metamorphism. In contrast, the scales based on (1) the Fe³⁺ content of serpentine in the matrix to estimate the degree of aqueous alteration and (2) the chemical composition of Fe‐Ni metal beads for quantifying the intensity of the thermal metamorphism are not supported by the characteristics of Paris. It also appears that the amount of trapped ³⁶Ar is a sensitive indicator of the secondary alteration modifications experienced by chondrites, for both aqueous alteration and thermal metamorphism. Considering Paris, our data suggest that this chondrite should be classified as type 2.7 as it suffered limited but significant fluid alteration and only mild thermal metamorphism. These results point out that two separated scales should be used to quantify the degree of the respective role of aqueous alteration and thermal metamorphism in establishing the characteristics of CM chondrites.     

Implications for asteroidal regolith properties from comparisons with the lunar phase relation and theoretical considerations

The phase relations of several asteroids. Mercury, and the Moon display the same basic characteristics, but differ slightly in detail. An improved treatment of the photometric function for open-work particulate layers shows that for phase angles greater than about 7°, the shape of the curves is diagnostic of the presence of such layers, and that both the shape and slope of the curves is dependent primarily upon the bulk density of these layers. This treatment also strongly indicates that the “opposition effect” is not due to shadow hiding in a regolith of very low bulk density. Other data support the idea that this effect is unrelated to shadow-hiding phenomena, and that it may thus be a diffraction/scattering effect with or without internal reflection phenomena also.     

Plain formation on mercury: Tectonic implications

Four major plain units, plus intermediates, are distinguished on Mercury. The chronologic relationships between these plains indicate that plains formation was a permanent process on Mercury. Their location and morphology seem to indicate a possible volcanic origin for these plains.The relationships between tectonism and volcanism seems to indicate the global contraction is not the only tectonic process on Mercury.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.CNES Grant No. 77005.