Photometric and Colorimetric Observations of Asteroid 423 Diotima and Their Analysis

Series of photometric and colorimetric observations of the Main-Belt asteroid 423 Diotima during its five oppositions were obtained at the Crimean Astrophysical Observatory. It was concluded, based on the results of a frequency analysis of the V-band photometry obtained in 1990, that the asteroid is a binary system: the rotation period of the primary component is equal to 4_. ^h56, and the period of rotation and the orbital period of the satellite are equal to 14_. ^h90. An analysis of simultaneous BV and BVR observations made in 1993 and 1998–1999 yielded a rotation period of 4_. ^h54 ± 0_. ^h01 for the primary component. An analysis of the sets of V-band observations of the asteroid made from 1982 through 2000 allowed us to find the period of forced precession, which was equal to 113^d (or 226^d). It was suggested that the axis of the primary component of the binary asteroid precesses and the large amplitude of brightness variations (about 1 ^m ) is due to its lenticular shape.     

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.     

Dynamical study of the Hilda asteroids

Schubart's model of a planar, elliptic restricted three-body problem is used to study the orbital motion of the Hilda asteroids from thePalomar-Leiden Survey. The 3:2 resonant coupling to Jupiter of some of these small asteroids are found to be stable. However, some of the small asteroids with absolute magnitudeg>15 have large amplitude of variation in their orbital elements in one libration period. Since the lifetime scales against catastrophic collision of the Hilda asteroids are estimated to be several times larger than those of the main belt objects, a significant portion of these resonant asteroids could be the original members of the Hilda group. From this point of view, it is suggested that such size-dependence of resonant orbital motions might be the result of the cosmogonic effects ofjet stream accretion.     

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.     

Orbital evolution of asteroids with the effects of mutual gravitational attraction

The effects of the mutual gravitational attraction between asteroids were analyzed by two N-body calculations, in which N=4,516 (the Sun, the nine planets, and 4,506 asteroids). In one calculation the gravity of the asteroids was taken into account, and in the other it was ignored. These calculations were carried out for a time period of about 100 years. The largest difference in the positions of the asteroids between these two calculations is about 10^–3 AU. For the orbital elements of the semimajor axis, the eccentricity, and the inclination, the largest differences were 9 × 10^–6 AU, 4 × 10^–6, and 5 × 10^–4 degrees, respectively. It was found that the distribution of the differences of the semimajor axis between the two calculations is quite similar to the Cauchy distribution.     

Study on the Spin Characteristics of the Flora Asteroid Family

Asteroid families are the remnants of catastrophic collisions, and their fundamental physical properties provide us the information of their parent bodies and thereafter dynamical evolutions. Especially, the orbit and spin characteristics can reveal the influences of the Yarkovsky effect and the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect on the evolution of the asteroid family, respectively. Based on the Asteroid Lightcurve Database (LCDB), the spin rate distribution of the Flora asteroid family is studied, and a tendency that the spin rates of the small Flora family members concentrate primarily in the range of 3–5 d^?1 is found. The analysis on the spin states of the Flora family asteroids tells that most of these asteroid family members are in the prograde spinning state. However, for the Flora family members with an orbital semi-major axis smaller than 2.2 au, the ratio between the number of prograde spinning members and that of retrograde ones is close to that of the near-Earth asteroids, namely 1 : 3. Furthermore, for those prograde spinning Flora family asteroids with an orbital semi-major axis larger than 2.2 au, a portion of them exhibit the aggregation in the distribution of orbital semi-major axis against the absolute magnitude, and in which nine members show the features similar to the Slivan state.     

On the character of evolution of orbits in the vicinity of the 1 : 3 Kirkwood gap

The character of orbital evolution for bodies moving near the if 1 : 3 commensurability with Jupiter was studied by model calculations for the time interval of ～500 years. A comparison of oscillations of the orbital elements a, e, q and q′ is made for ensembles of bodies along three starting orbits in the vicinity of the sharp commensurability with Jupiter. These orbits are eccentric ones of low inclinations having perihelia near the Earth's orbit. Examples of a deceleration of the rate of orbital evolution near the sharp commensurability are revealed. The existence of a group of asteroids connected with the Kirkwood gap, i.e., being in a resonant motion with Jupiter, is suggested. A connection of asteroids 887 Alinda and 1915 Quetzalcoatl with this gap is confirmed.     

Family of Minor Bodies Connected with the Prřibram Meteorite

Minor bodies that, at the present stage, have orbital characteristics similar to those of the Pribram meteorite and that differ from it in the date of activity of the radiants by no more than a 1.2-month period in either direction were detected on the basis of catalog data on the orbits of asteroids, individual fireballs, and fireball and meteor streams obtained from photographic observations. The following objects comprising the Prbram family are among such minor bodies: three asteroids (1863, 4486, and J98S70J) of the Apollo group, three fireball streams, five meteor streams, and ten fireballs. This extensive system of bodies consists of three branches: a Northern (N), an Ecliptical (Q), and a Southern (S) Branch. The family of meteor streams associated with the periodic comet Pons–Winnecke appears to be related to this family. Thus, there emerges an intricate complex of small bodies that is similar to the well-known Taurid complex. In the distribution of various populations of minor bodies according to the quantity c of the Tisserand criterion, both of these complexes of minor bodies, like the group of cometoids (or cometlike asteroids), are situated in the region of unstable motion or, to be more exact, near the gap that arises in the L ₂ and L ₃ collinear points of libration.     

Orbital evolution of the Gefion and Adeona asteroid families: close encounters with massive asteroids and the Yarkovsky effect

Asteroid families are groupings of minor planets identified by clustering in their proper orbital elements; these objects have spectral signatures consistent with an origin in the break-up of a common parent body. From the current values of proper semimajor axes a of family members one might hope to estimate the ejection velocities with which the fragments left the putative break-up event (assuming that the pieces were ejected isotropically). However, the ejection velocities so inferred are consistently higher than N-body and hydro-code simulations, as well as laboratory experiments, suggest. To explain this discrepancy between today’s orbital distribution of asteroid family members and their supposed launch velocities, we study whether asteroid family members might have been ejected from the collision at low speeds and then slowly drifted to their current positions, via one or more dynamical processes. Studies show that the proper a of asteroid family members can be altered by two mechanisms: (i) close encounters with massive asteroids, and (ii) the Yarkovsky non-gravitational effect. Because the Yarkovsky effect for kilometer-sized bodies decreases with asteroid diameter D, it is unlikely to have appreciably moved large asteroids (say those with D > 15 km) over the typical family age (1-2 Gyr).For this reason, we numerically studied the mobility of family members produced by close encounters with main-belt, non-family asteroids that were thought massive enough to significantly change their orbits over long timescales. Our goal was to learn the degree to which perturbations might modify the proper a values of all family members, including those too large to be influenced by the Yarkovsky effect. Our initial simulations demonstrated immediately that very few asteroids were massive enough to significantly alter relative orbits among family members. Thus, to maximize gravitational perturbations in our 500-Myr integrations, we investigated the effect of close encounters on two families, Gefion and Adeona, that have high encounter probabilities with 1 Ceres, by far the largest asteroid in the main belt. Our results show that members of these families spreads in a of less than 5% since their formation. Thus gravitational interactions cannot account for the large inferred escape velocities.The effect of close encounters with massive asteroids is, however, not entirely negligible. For about 10% of the simulated bodies, close encounters increased the “inferred” ejection velocities from sub-100 m/s to values greater than 100 m/s, beyond what hydro-code and N-body simulations suggest are the maximum possible initial ejection velocity for members of Adeona and Gefion with D > 15 km. Thus this mechanism of mobility may be responsible for the unusually high inferred ejection speeds of a few of the largest members of these two families.To understand the orbital evolution of the entire family, including smaller members, we also performed simulations to account for the drift of smaller asteroids caused by the Yarkovsky effect. Our two sets of simulations suggest that the two families we investigated are relatively young compared to larger families like Koronis and Themis, which have estimated ages of about 2 Byr. The Adeona and Gefion families seems to be no more than 600 and 850 Myr old, respectively.     

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.     

Shape, size and multiplicity of main-belt asteroids: I. Keck Adaptive Optics survey

This paper presents results from a high spatial resolution survey of 33 main-belt asteroids with diameters >40 km using the Keck II Adaptive Optics (AO) facility. Five of these (45 Eugenia, 87 Sylvia, 107 Camilla, 121 Hermione, 130 Elektra) were confirmed to have satellite. Assuming the same albedo as the primary, these moonlets are relatively small (∼5% of the primary size) suggesting that they are fragments captured after a disruptive collision of a parent body or captured ejecta due to an impact. For each asteroid, we have estimated the minimum size of a moonlet that can positively detected within the Hill sphere of the system by estimating and modeling a 2-σ detection profile: in average on the data set, a moonlet located at 2/100×RHill (1/4×RHill) with a diameter larger than 6 km (4 km) would have been unambiguously seen. The apparent size and shape of each asteroid was estimated after deconvolution using a new algorithm called AIDA. The mean diameter for the majority of asteroids is in good agreement with IRAS radiometric measurements, though for asteroids with a D<200 km, it is underestimated on average by 6-8%. Most asteroids had a size ratio that was very close to those determined by lightcurve measurements. One observation of 104 Klymene suggests it has a bifurcated shape. The bi-lobed shape of 121 Hermione described in Marchis et al. [Marchis, F., Hestroffer, D., Descamps, P., Berthier, J., Laver, C., de Pater, I., 2005c. Icarus 178, 450-464] was confirmed after deconvolution. The ratio of contact binaries in our survey, which is limited to asteroids larger than 40 km, is surprisingly high (∼6%), suggesting that a non-single configuration is common in the main-belt. Several asteroids have been analyzed with lightcurve inversions. We compared lightcurve inversion models for plane-of-sky predictions with the observed images (9 Metis, 52 Europa, 87 Sylvia, 130 Elektra, 192 Nausikaa, and 423 Diotima, 511 Davida). The AO images allowed us to determine a unique photometric mirror pole solution, which is normally ambiguous for asteroids moving close to the plane of the ecliptic (e.g., 192 Nausikaa and 52 Europa). The photometric inversion models agree well with the AO images, thus confirming the validity of both the lightcurve inversion method and the AO image reduction technique.     

Secular effects of tidal friction on the planet-satellite systems of the solar system

We separate the tidal evolution of a planet-satellite system with zero eccentricity in two phases:phase 1—from the formation of the system to satellite's corotation (satellite's corotation means that its spin angular velocity equals the orbital angular velocity);phase 2—after satellite's corotation.We study the planet-satellite system during phase 1 with Darwin's graphical method and obtain an upper limit to satellite'sQ which discloses whether or not it is corotating. Moreover we obtain some qualitative information about the future evolution of the corotating satellites.The present work does not give any new result for the Earth-Moon case and for the Neptune-Triton case.     

Volume and mass distribution in selected asteroid families

The main focus of this paper is calculation of the diameters of asteroids belonging to five families (Vesta, Eos, Eunomia, Koronis, and Themis). To do that, we used the HCM algorithm applied for a data set containing 292,003 numbered asteroids, and a numerical procedure for choosing the crucial parameter of the HCM, called “the cutting velocity” v_cut. It was established with a precision as high as 1 m s^?1. Thereafter, we used the WISE (Wide‐field Infrared Survey Explorer) catalog to set a range of albedo for the largest members of each family considered. The albedo data were supported by the data concerning color classification (SDSS MOC4). The asteroids with albedo out of this range were classified as interlopers and were therefore disqualified as family members. Sizes were calculated for the asteroids with albedo within the acceptable range. For the other asteroids (those chosen by means of the HCM, but with albedo not listed in the WISE), the value of albedo of the largest member of the family was adopted. Results are given in a set of figures showing the families on the planes (a, e), (a, i), (e, i). Diameters and volumes of the asteroids that are the individual members of a family were calculated on the basis of their known or assumed albedo and on their absolute magnitude. Volumes of the parent bodies of the families were found on the basis of the cumulative volume distribution of these families. We also studied the secular resonances of the family members. We have shown that the locations of members of the considered asteroid families are related to the lines of secular resonances z₁, z₂, and z₃ with Saturn.     

High-Precision Ephemerides of Planets—EPM and Determination of Some Astronomical Constants

The latest version of the planetary part of the numerical ephemerides EPM (Ephemerides of Planets and the Moon) developed at the Institute of Applied Astronomy of the Russian Academy of Sciences is presented. The ephemerides of planets and the Moon were constructed by numerical integration in the post-Newtonian metric over a 140-year interval (from 1880 to 2020). The dynamical model of EPM2004 ephemerides includes the mutual perturbations from major planets and the Moon computed in terms of General Relativity with allowance for effects due to lunar physical libration, perturbations from 301 big asteroids, and dynamic perturbations due to the solar oblateness and the massive asteroid ring with uniform mass distribution in the plane of the ecliptic. The EPM2004 ephemerides resulted from a least-squares adjustment to more than 317000 position observations (1913–2003) of various types, including radiometric measurements of planets and spacecraft, CCD astrometric observations of the outer planets and their satellites, and meridian and photographic observations. The high-precision ephemerides constructed made it possible to determine, from modern radiometric measurements, a wide range of astrometric constants, including the astronomical unit AU = (149597870.6960 ± 0.0001) km, parameters of the rotation of Mars, the masses of the biggest asteroids, the solar quadrupole moment J ₂ = (1.9 ± 0.3) × 10⁻⁷, and the parameters of the PPN formalism β and γ. Also given is a brief summary of the available state-of-the-art ephemerides with the same precision: various versions of EPM and DE ephemerides from the Jet Propulsion Laboratory (JPL) (USA) and the recent versions of these ephemerides—EPM2004 and DE410—are compared. EPM2004 ephemerides are available via FTP at ftp://qua-sar.ipa.nw.ru/incoming/EPM2004.__________Translated from Astronomicheskii Vestnik, Vol. 39, No. 3, 2005, pp. 202–213.Original Russian Text Copyright © 2005 by Pitjeva.     

On the Origin of the Last Meteorite Parent Bodies

The existence of gaps in the perihelion distribution of the orbits of multikilometer-sized asteroids that approach the orbits of terrestrial-group planets is confirmed. This property of the orbits of large asteroids suggests the existence among them of a family of last meteorite parent bodies. Astrophysical data were considered for S-asteroids of the Main Belt and those that approach terrestrial planets. The u–x color index, which is related to the position of the absorption band at 950 nm in the asteroid spectra, was chosen for a qualitative comparison of the surface composition of these asteroids (identical or differing composition). The u – x color-index distributions were analyzed statistically according to the perihelion (q) and mean heliocentric distances (a) of the S-asteroids. It is shown that these distributions are -shaped, peaking at q 1.8 AU and a 2.2 AU. The wings of the distributions can be approximated by linear regressions. A comparison of the u – x color-index mean values for S-asteroids in the regions of the Earth and Mars and of the Main Belt prompts the conclusion that the last meteorite parent bodies in the vicinity of the orbits of the Earth and Mars come primarily from various regions of the asteroid Main Belt.     

The new period of the intermediate polar V709 Cas

We present the results of 10 years of photometric CCD observations of the intermediate polar V709 Cas obtained by using different instruments during 2003–2013. We detected a new variability with a period of P_new = 0.^d016449979(5) which seems to be real. The spin variability is not clearly seen in all our data, so we are unable to study any evolution of the white dwarf rotation. From the best night (in 2010) we obtained a spin period of P_spin = 311.^s8(5). We analyzed the orbital variability using (O – C) analysis. We found no variations of the orbital period on a timescale of 10 years, but the linear fit to the (O – C) diagram shows that the value of the orbital period is P_orb = 0.^d2222123(6), which is close to the earlier published values. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Particle stirring in turbulent gas disks: Including orbital oscillations

We describe the diffusion and random velocities of solid particles due to stochastic forcing by turbulent gas. We include the orbital dynamics of Keplerian disks, both in-plane epicycles and vertical oscillations. We obtain a new result for the diffusion of solids. The Schmidt number (ratio of gas to particle diffusivity) is Sc≈1+(Ωt_stop)², in terms of the particle stopping time t_stop and the orbital frequency Ω. The standard result, Sc=1+t_stop/t_eddy, in terms of the eddy turnover time, t_eddy, is shown to be incorrect. The main difference is that Sc rises quadratically, not linearly, with stopping time. Consequently, particles larger than 10 cm in protoplanetary disks will suffer less radial diffusion and will settle closer to the midplane. Such a layer of boulders would be more prone to gravitational collapse. Our predictions of RMS speeds, vertical scale height and diffusion coefficients will help interpret numerical simulations. We confirm previous results for the vertical stirring of particles (scale heights and random velocities), and add a correction for arbitrary ratios of eddy to orbital times. The particle layer becomes thinner for t_eddy>1/Ω with the strength of turbulent diffusion held fixed. We use two analytic techniques—the Hinze–Tchen formalism and the Fokker–Planck equation with velocity diffusion—with identical results when the regimes of validity overlap. We include simple physical arguments for the scaling of our results.     

Analytical solutions to the four post-Newtonian effects in a near-Earth satellite orbit

On the basis of the results by Huang et al. (1990), this paper further discusses and analyses the four post-Newtonian effects in a near-Earth satellite orbit: the Schwarzschild solution, the post-Newtonian effects of the geodesic precession, the Lense-Thirring precession and the oblateness of the Earth. A full analytical solution to the effects including their direct perturbations and mixed perturbations due to the Newtonian oblateness (J ₂) perturbation and the Schwarzschild solution is obtained using the quasi-mean orbital element method analogous to the Kozai's mean orbital element one. Some perturbation properties of the post-Newtonian effects are revealed. The results obtained not only can provide a sound scientific basis for the precise determination of a man-made satellite orbit but also is suitable for similar mechanics systems, such as the motions of planets, asteroids and natural satellites.     

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 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.