On the Family of the Binary Asteroid 423 Diotima

We identified the family of the binary asteroid 423 Diotima consisting of 411 members in the phase space of orbital elements—semimajor axes a (or mean motions n), eccentricities e, and inclinations i—by using an electronic version of the ephemerides of minor planets EMP-2003 containing osculating orbital elements for 34992 asteroids of the main belt. The 9/4 resonance with Jupiter clearly separates the family of 423 Diotima from the family of Eos, which, according to EMP for 2003, contains 1204 asteroids.     

An analysis of the region of the Phocaea dynamical family

In this work, I conduct a preliminary analysis of the Phocaea family region. I obtain families and clumps in the space of proper elements and proper frequencies, study the taxonomy of the asteroids for which this information is available, analyse the albedo and absolute magnitude distribution of objects in the area, obtain a preliminary estimate of the possible family age, study the cumulative size distribution and collision probabilities of asteroids in the region, the rotation rate distribution and obtain dynamical map of averaged elements and Lyapunov times for grids of objects in the area.
Among my results, I identified the first clump visible only in the frequency domain, the (6246) Komurotoru clump, obtained a higher limit for the possible age of the Phocaea family of 2.2 Byr, identified a class of Phocaea members on Mars-crossing orbits characterized by high Lyapunov times and showed that an apparently stable region on time-scales of 20 Myr near the  ν₆  secular resonance is chaotic, possibly because of the overlapping of secular resonances in the region. The Phocaea dynamical group seems to be a real S-type collisional family, formed up to 2.2 Byr ago, whose members with a large semimajor axis have been dynamically eroded by the interaction with the local web of mean-motion and secular resonances. Studying the long-term stability of orbits in the chaotic regions and the stability of family and clumps identified in this work remain challenges for future works.     

Dynamical portrait of the Lixiaohua asteroid family

In this paper we present a comprehensive analysis of the dynamics in the region of the (3556) Lixiaohua asteroid family. The family lies in a particularly interesting region of the phase space, crossed by several two-body and three-body mean motion resonances. Also, members of this family can have close encounters with large asteroids, such as Ceres. We have identified the mean motion resonances which contribute to the long-term dynamical evolution of the family and our results confirm that the members of this family can be classified into a number of groups, exhibiting different dynamical behavior. We show for the first time that in the Lixiaohua region, apart from the chaotic diffusion in proper eccentricity and inclination (e _p and I _p ), there is at least one extended chaotic zone where several resonances overlap, thus giving rise to chaotic diffusion in proper semi-major axis (a _p ) as well. Using a code of Monte Carlo type, we simulate the evolution of the family, according to the model which combines the chaotic diffusion (in a _p , e _p and I _p ), Yarkovsky/YORP thermal effect and random walk in a _p due to the close encounters with massive asteroids. These simulations show that all these effects should be taken into account in order to accurately explain the observed distribution of family members in the space of proper elements, although a “minimal” model that accounts for chaotic diffusion in (e _p , I _p ), Yarkovsky-induced drift in a _p and random walk in a _p due to the close encounters with the most massive asteroids is enough to grossly characterize the shape of the family.     

Additional criteria for identifying the asteroid families and confirmation of the effect of spatial separation of family members according to their albedos

The D(a) distribution of asteroid sizes by their semimajor axes and the N(p) distribution of the number of asteroids by their albedo values for individual families are used to isolate the asteroid families more clearly. The families identified by Masiero et al. (2013) are analyzed with the use of these distributions, and correctly and incorrectly isolated families are found. A reduction in the mean albedo with increasing semimajor axis is observed for almost all correctly identified families that are not truncated by resonances. This reduction is statistically significant for the majority of these families. Not a single family exhibits a statistically significant increase in albedo. This confirms our previous conclusions that a nongravitational effect acting in the asteroid belt results in the spatial separation of asteroids with different albedos.     

Vesta fragments from v6 and 3:1 resonances: Implications for V-type near-Earth asteroids and howardite,eucrite and diogenite meteorites

Abstract— A large body of evidence, including the presence of a dynamical family associated with 4 Vesta, suggests that this asteroid might be the ultimate source of both the V-type near-Earth asteroids (NEAs) and howardite, eucrite and diogenite (HED) meteorites. Dynamical routes from Vesta to the inner regions of the solar system are provided by both the 3:1 mean-motion resonance with Jupiter and the V₆, secular resonance. For this reason, numerical integrations of the orbits of fictitious Vesta fragments injected in both of these resonances have been performed. At the same time, the orbital evolution of the known V-type NEAs has been investigated. The results indicate that the dynamical half lifetimes of Vesta fragments injected in both the 3:1 and the V₆, resonances are rather short ('2 Ma). The present location of the seven known V-type NEAs is better explained by orbital evolutions starting from the v₆ secular resonance. The most important result of the present investigation, however, is that we now face what we call the “Vesta paradox.” Roughly speaking, the paradox consists of the fact that the present V-type NEAs appear to be too dynamically young to have originated in the event that produced the family, but they are too big to be plausible second-generation fragments from the family members. The cosmic-ray exposure (CRE) age distribution of HED meteorites also raises a puzzle, since we would expect an overabundance of meteorites with short CRE ages. We propose different scenarios to explain these paradoxes.     

Third-order secular Solution of the variational equations of motion of a satellite in orbit around a non-spherical planet

We constructed an analytical theory of satellite motion up to the third order relative to the oblateness parameter of the Earth (J ₂). Equations of secular variations was developed for the first three orbital elements (a, e, i) of an artificial satellite. The secular variations are solved in a closed form.     

Asteroids with large secular orbital variations

As the classical linear theory of secular perturbations for asteroids is known not to be adequate for computing the perturbations of asteroids with high eccentricities and/or inclinations, a seminumerical method to calculate the secular perturbations by including higher-degree terms in the disturbing function has been developed. It is here applied to asteroids with small values of $\text{(1 ? e}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{cos}\text{i}$, since the secular variations as well as their deviations from the results derived by the classical linear theory are generally large for such asteroids. It is found that the arguments of perihelion for five of the numbered asteroids are librating around 90 or 270°. For asteroids with $\text{(1 ? e}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext><mtext>cos</mtext><mtext>\; i</mtext>}}$ less than 0.85 the results of the secular variations are tabulated. Also the stability of such orbits is discussed by comparing the orbital properties of short-periodic comets with them. Generally speaking, orbits of the asteroids are more stable than those of the short-periodic comets, and asteroids with librating arguments of perihelion are more stable than those with circular coplanar orbits although their orbital elements are changed more by secular perturbations.     

Generalized Calibration of the Polarimetric Albedo Scale of Asteroids

Six different calibrations of the polarimetric albedo scale of asteroids have been published so far. Each of them contains its particular random and systematic errors and yields its values of geometric albedo. On the one hand, this complicates their analysis and comparison; on the other hand, it becomes more and more difficult to decide which of the proposed calibrations should be used. Moreover, in recent years, new databases on the albedo of asteroids obtained from the radiometric surveys of the sky with the orbital space facilities (the InfraRed Astronomical Satellite (IRAS), the Japanese astronomical satellite AKARI (which means “light”), the Wide-field Infrared Survey Explorer (WISE), and the Near-Earth Object Wide-field Survey Explorer (NEOWISE)) have appeared; and the database on the diameters and albedos of asteroids obtained from their occultations of stars has substantially increased. Here, we critically review the currently available calibrations and propose a new generalized calibration derived from the interrelations between the slope h and the albedo and between P_min and the albedo. This calibration is based on all of the available series of the asteroid albedos and the most complete data on the polarization parameters of asteroids. The generalized calibration yields the values of the polarimetric albedo of asteroids in the system unified with the radiometric albedos and the albedos obtained from occultations of stars by asteroids. This, in turn, removes the difficulties in their comparison, joint analysis, etc.     

Analysis of the Hungaria asteroid population

There are approximately 5000 known asteroids in the Hungaria orbital space, a region defined by orbits with high inclination (16° < i < 34°), low eccentricities (e < 0.18), and semi-major axes 1.78 < a < 2.0 AU. We argue that this region is populated by a large number of asteroids formed after a catastrophic collision involving (434) Hungaria, the presumptive largest fragment of the Hungaria collisional family. The remaining objects form a background population that share orbital characteristics with the family members. Due to the general dynamic stability of the region, it is likely that most asteroids in Hungaria space (the Hungaria “group”) have been in this region since the formation of the Solar System or at least since the planets assumed their current orbital configuration. Our examination of the Hungaria group included comparing rotation rates, taxonomic classification, and orbital dynamics to determine the characteristics of the family and background populations. We first found there is an excess of slow rotators among the group but, otherwise, the distribution of spin frequencies is essentially uniform, i.e., that a plot of the cumulative number of objects over the range of 1 d⁻¹ < f < 9 d⁻¹ is nearly a straight line or, put another way, if the distribution over the range is binned by equal intervals of f (1-2 d⁻¹, 2-3 d⁻¹, etc.), the number of objects in each bin is statistically the same.There is a distinct family within the Hungaria group, centered at a semi-major axis of 1.940 AU, with a dispersion range that increases with decreasing size of members, as expected of an evolved collisional family. The larger members with well-determined taxonomic class, including (434) Hungaria itself, have flat spectra, mostly likely type E or similar. The degree of spreading versus size of family members is consistent with that expected from Yarkovsky thermal drift in roughly 0.5 Gyr, suggesting that age for the family. The Asteroid (434) Hungaria is displaced in semi-major axis by 0.004 AU from the center of the Hungaria family. The collision event that produced the family should not have left the largest body displaced by more than 0.001 AU from the original orbit, thus we infer that the displacement of (434) Hungaria is mainly due to Yarkovsky drift, and is consistent with the expected drift for that size body in ∼0.5 Gyr. Below ∼1.93 AU heliocentric distance the Hungaria family is perturbed by at least two secular resonances, 2g − g₅ − g₆ and one of the family of 4th or 6th order secular resonances near s ∼ −22.25 ″/year. Their combined effect results in larger inclination dispersion of the family members.     

Some peculiarities in the Asteroidal Belt

The analysis of the fine structure of the Asteroidal Belt evidenciates a group of asteroids next to the resonance 4/9 with Jupiter. In this group and in other groups associated to the Hirayama families there are indications that their orbital parameters can be represented by quantum numbers as defined here and in two of our previous works. Together with this the distribution of the eccentricities and inclinations of the orbital planes of short period comets and diverse type of asteroids indicates that they can be classified as objects with e > sin i and objects with e > sin i with a limit e = sin i which determinates geometrical properties of the orbits related with discrete states in the solar system. This study lets open the possibility of following studies in order to confirm the quantum characteristics of the Asteroidal Belt being these characteristics common to all the solar system and depending of the same fundamental constant of action per mass unit H ₀ = 1/2 ₀ × T ₀ (potential × time) because only a small part of all the available data in the Asteroid Belt is used here.     

Vesta,Vestoids, and the howardite,eucrite, diogenite group: Relationships and the origin of spectral differences

Abstract— Spectra of asteroid 4 Vesta and 21 small (estimated diameters less than 10 km) asteroids with Vesta‐like spectral properties (Vestoids) were measured at visible and near‐infrared wavelengths (～0.44 to ～1.65 μm). All of the measured small asteroids (except for 2579 Spartacus) have reflectance spectra consistent with surface compositions similar to eucrites and howardites and consistent with all being derived from Vesta. None of the observed asteroids have spectra similar to diogenites. We find no spectral distinction between the 15 objects tabulated as members of the Vesta dynamical family and 6 of the 7 sampled “non‐family” members that reside just outside the semi‐major axis (a), eccentricity (e), and inclination (i) region of the family. The spectral consistency and close orbital (a‐e‐i) match of these “non‐family” objects to Vesta and the Vesta family imply that the true bounds of the family extend beyond the subjective cut‐off for membership. Asteroid 2579 Spartacus has a spectrum consistent with a mixture of eucritic material and olivine. Spartacus could contain olivine‐rich material from Vesta's mantle or may be unrelated to Vesta altogether. Laboratory measurements of the spectra of eucrites show that samples having nearly identical compositions can display a wide range of spectral slopes. Finer particle sizes lead to an increase in the slope, which is usually referred to as reddening. This range of spectral variation for the best‐known meteoritic analogs to the Vestoids, regardless of whether they are actually related to each other, suggests that the extremely red spectral slopes for some Vestoids can be explained by very fine‐grained eucritic material on their surfaces.     

A simple analytical model for the secular resonance ν6 in the asteroidal belt

When asteroids are in the secular resonance ₆, the variation of the eccentricity becomes very large. In this paper, the dynamics of this secular resonance ₆ is investigated by a simple analytical model, in which the third degree terms of the eccentricity and inclination are taken into account. The eccentricity variations of asteroids located near this resonance are represented clearly by the diagrams of equi-Hamiltonian curves on the plane of versuse ( the longitude of perihelion of asteroids and Saturn,e: the eccentricity of asteroids). These diagrams predict that the eccentricity of these asteroids suffers a large increase or decrease, and that the secular resonance argument librates about 0° and 180°. In order to confirm these predictions, numerical integrations are carried out over one million years. By these integrations, it is found that the eccentricity of secular resonant asteroids becomes more than 0.8, and that the libration about 0° also exists, as well as the libration about 180°. The strongly depopulated region in the asteroidal belt, which corresponds to the position of the secular resonance ₆, is also explained well by this analytical model.     

A Specific Nongravitational Effect in the Asteroid Belt

The evolution of orbits of asteroids found in the IRAS and WISE albedo databases was calculated numerically from 2005 to 2016. It follows from the analysis of the obtained results that a certain nongravitational effect (NGE) currently affects the motion of a considerable fraction of main-belt asteroids with diameters up to 40 km. This conclusion agrees with the available data regarding the axial rotation of asteroids. The NGE manifests itself in an increase in the semimajor axes of orbits of low-albedo asteroids relative to the semimajor axes of orbits of high-albedo bodies. The NGE-induced rate of elongation of semimajor axes of asteroids with albedos р_v < 0.1 may be as high as (2–8) × 10^–8 AU/year. Errors in orbital elements of asteroids (unrelated to the accuracy of observational data used to determine these orbital elements) were found in one of the MPC catalogues for 2003 in the process of estimation of the accuracy of calculations.     

The peculiar case of the Agnia asteroid family

The Agnia asteroid family, a cluster of asteroids located near semimajor axis a=2.79 AU, has experienced significant dynamical evolution over its lifetime. The family, which was likely created by the breakup of a diameter D∼50 km parent body, is almost entirely contained within the high-order secular resonance z₁. This means that unlike other families, Agnia's full extent in proper eccentricity and inclination is a byproduct of the large-amplitude resonant oscillations produced by this resonance. Using numerical integration methods, we found that the spread in orbital angles observed among Agnia family members would have taken at least 40 Myr to create; this sets a lower limit on the family's age. To determine the upper bound on Agnia's age, we used a Monte Carlo model to track how the small members in the family evolve in semimajor axis by Yarkovsky thermal forces. Our results indicate the family is no more than 140 Myr old, with a best-fit age of 100⁺³⁰₋₂₀ Myr. Using two independent methods, we also determined that the D∼5 km fragments were ejected from the family-forming event at a velocity near 15 m/s. This velocity is consistent with results from numerical hydrocode simulations of asteroid impacts and observations of other similarly sized asteroid families. Finally, we found that 57% of known Agnia fragments were initially prograde rotators. The reason for this limited asymmetry is unknown, though we suspect it is a fluke produced by the stochastic nature of asteroid disruption events.     

Families among high-inclination asteroids

We present a new classification of families identified among the population of high-inclination asteroids. We computed synthetic proper elements for a sample of 18,560 numbered and multi-opposition objects having sine of proper inclination greater than 0.295. We considered three zones at different heliocentric distances (inner, intermediate and outer region) and used the standard approach based on the Hierarchical Clustering Method (HCM) to identify families in each zone. In doing so, we used slightly different approach with respect to previously published methodologies, to achieve a more reliable and robust classification. We also used available SDSS color data to improve membership and identify likely family interlopers. We found a total of 38 families, as well as a significant number of clumps and clusters deserving further investigation.     

The elliptic restricted problem at the 3 : 1 resonance

Four 3 : 1 resonant families of periodic orbits of the planar elliptic restricted three-body problem, in the Sun-Jupiter-asteroid system, have been computed. These families bifurcate from known families of the circular problem, which are also presented. Two of them, I _c , II _c bifurcate from the unstable region of the family of periodic orbits of the first kind (circular orbits of the asteroid) and are unstable and the other two, I _e , II _e , from the stable resonant 3 : 1 family of periodic orbits of the second kind (elliptic orbits of the asteroid). One of them is stable and the other is unstable. All the families of periodic orbits of the circular and the elliptic problem are compared with the corresponding fixed points of the averaged model used by several authors. The coincidence is good for the fixed points of the circular averaged model and the two families of the fixed points of the elliptic model corresponding to the families I _c , II _c , but is poor for the families I _e , II _e . A simple correction term to the averaged Hamiltonian of the elliptic model is proposed in this latter case, which makes the coincidence good. This, in fact, is equivalent to the construction of a new dynamical system, very close to the original one, which is simple and whose phase space has all the basic features of the elliptic restricted three-body problem.     

From Magnitudes to Diameters: The Albedo Distribution of Near Earth Objects and the Earth Collision Hazard

A recently published model of the Near Earth Object (NEO) orbital-magnitude distribution (Bottke et al., 2002, Icarus156, 399-433.) relies on five intermediate sources for the NEO population: the ν₆ resonance, the 3:1 resonance, the outer portion of the main belt (i.e., 2.8-3.5 AU), the Mars-crossing population adjacent to the main belt, and the Jupiter family comet population. The model establishes the relative contribution of these sources to the NEO population. By computing the albedo distribution of the bodies in and/or near each of the five sources, we can deduce the albedo distribution of the NEO population as a function of semimajor axis, eccentricity, and inclination. A problem with this strategy, however, is that we do not know a priori the albedo distribution of main belt asteroids over the same size range as observed NEOs (diameter D<10 km). To overcome this problem, we determined the albedo distribution of large asteroids in and/or near each NEO source region and used these results to deduce the albedo distribution of smaller asteroids in the same regions. This method requires that we make some assumptions about the absolute magnitude distributions of both asteroid families and background asteroids. Our solution was to extrapolate the observed absolute magnitude distributions of the families up to some threshold value H_thr, beyond which we assumed that the families' absolute magnitude distributions were background-like.We found that H_thr=14.5 provides the best match to the color vs heliocentric distance distribution observed by the Sloan Digital Sky Survey. With this value of H_thr our model predicts that the debiased ratio between dark and bright (albedo smaller or larger than 0.089) objects in any absolute-magnitude-limited sample of the NEO population is 0.25±0.02. Once the observational biases are properly taken into account, this agrees very well with the observed C/S ratio (0.165 for H<20). The dark/bright ratio of NEOs increases to 0.87±0.05 if a size-limited sample is considered. We estimate that the total number of NEOs larger than a kilometer is 855±110, which, compared to the total number of NEOs with H<18 (963±120), shows that the usually assumed conversion H=18?D=1 km slightly overestimates the number of kilometer-size objects.Combining our orbital distribution model with the new albedo distribution model, and assuming that the density of bright and dark bodies is 2.7 and 1.3 g/cm³, respectively, we estimate that the Earth should undergo a 1000 megaton collision every 63,000±8000 years. On average, the bodies capable of producing 1000 megaton of impact energy are those with H<20.6. The NEOs discovered so far carry only 18±2% of this collision probability.     

The main mean motion commensurabilities in the planar circular and elliptic problem

We study the motion of asteroids in the main mean motion commensurabilities in the frame of the planar restricted three-body problem. No assumption is made about the size of the eccentricity of the asteroid. At small to moderate eccentricity, we recover existing results (shape of the phase space and location of secondary resonances). We also provide global pictures of the dynamics in the region of secondary resonances. At high eccentricity, the phase space portraits of the integrable part of the Hamiltonian show new families of stable orbits for the 3:2 and 2:1 cases and the secular resonances ₅ and ₆ are located.     

Polarimetric evidence of close similarity between members of the Karin and Koronis dynamical families

We present the results of a campaign of polarimetric observations of small asteroids belonging to the Karin and Koronis families, carried out at the ESO Cerro Paranal Observatory using the VLT-Kueyen 8-m telescope. The Karin family is known to be very young, having likely been produced by the disruption of an original member of the Koronis family less than 6 Myr ago. The purpose of our study was to derive polarimetric properties for a reasonable sample of objects belonging to the two families, in order to look for possible systematic differences between them, to be interpreted in terms of differences in surface properties, in particular albedo. In turn, systematic albedo differences might be caused by different times of exposure to space weathering processes experienced by the two groups of objects. The results of our analysis indicate that no appreciable difference exists between the polarimetric properties of Karin and Koronis members. We thus find that space-weathering mechanisms may be very efficient in affecting surface properties of S-class asteroids on very short timescales. This result complements some independent evidence found by recent spectroscopic studies of very young families.     

Complete fragmentation of the parent bodies of Themis,Eos, and Koronis families

The fragmentation of the parent asteroids of the Themis, Eos, and Koronis families is investigated by considering mutual gravitational effects among the fragmented bodies. The masses of the parent asteroids and the kinetic and gravitational energies of the fragmented bodies are estimated. Comparison of these results and data from the laboratory impact experiments leads to the conclusion that the parent asteroids of the three families were completely fragmented at E_p/M of 10⁸ erg/g or more (E_p, impact energy; M, parent mass). However, since most of the fragments had low relative velocities many reaccumulated through mutual gravitation. The larger members in these families should have the rubble pile structures and hydrostatic equilibrium figures.