Slow and Fast Diffusion in Asteroid-Belt Resonances: A Review

This paper reviews recent advances in several topics of resonant asteroidal dynamics as the role of resonances in the transportation of asteroids and asteroidal debris to the inner and outer solar system; the explanation of the contrast of a depleted 2/1 resonance (Hecuba gap) and a high-populated 3/2 resonance (Hilda group); the overall stochasticity created in the asteroid belt by the short-period perturbations of Jupiter's orbit, with emphasis in the formation of significant three-period resonances, the chaotic behaviour of the outer asteroid belt, and the depletion of the Hecuba gap. This revised version was published online in July 2006 with corrections to the Cover Date.     

CCD-photometry and pole coordinates for eight asteroids

The long time photometric observations were carried out for eight asteroids: (122) Gerda, (153) Hilda, (190) Ismene, (221) Eos, (411) Xanthe, (679) Pax, (700) Auravictrix, (787) Moskva. New rotation periods have been determined for the asteroids (153) Hilda (5.959 h) and (411) Xanthe (11.408 h), and known rotation periods for some of the others have been confirmed. Using our data and others data we have estimated new pole coordinates for the observed asteroids.     

Numerical studies of chaotic Hilda-type orbits

Earlier work indicates a comparatively rapid chaotic evolution of the orbits of some Hilda asteroids that move at the border of the domain occupied by the characteristic parameters of the objects at the 3/2 mean motion resonance. A simple Jupiter–Saturn model of the forces leads to numerical results on some of these cases and allows a search for additional resonances that can contribute to the chaotic evolution. In this context the importance of the secondary resonances that depend on the period of revolution of the argument of perihelion is pointed out. Among the studied additional resonances there are three-body resonances with arguments that depend on the mean longitudes of Jupiter, Saturn, and asteroid, but on slowly circulating angular elements of the asteroid as well, and the frequency of these arguments is close to a rational ratio with respect to the frequency of the libration due to the basic resonance.     

Correction to the mass of Jupiter derived from the motion of (153) Hilda, (279) Thule,and (334) Chicago

An analysis of the observations of the minor planets (153) Hilda, (279) Thule and (334) Chicago yields the following values for the reciprocal mass of Jupiter: (153) Hilda 1047.378±0.019, (279) Thule 1047.347±0.023, (334) Chicago 1047.325±0.010. A possible error in the mass of Saturn that might affect these results is discussed.Presented at IAU Colloquium No. 9, The IAU System of Astronomical Constants, Heidelberg, Germany, August 12–14, 1970.     

Hilda asteroids among Jupiter family comets

Hilda asteroids and comets are similar from the compositional point of view. The D-taxonomic class prevailing among Hildas has all the characteristics found in cometary spectra. Jupiter Family Comets (JFCs) coming from the trans-neptunian region are under the gravitational control of Jupiter, making them a dynamically unstable population with a mean dynamical lifetime of 10⁴ to ¹⁰⁵ years. In contrast, Hilda asteroids residing in the 3:2 mean motion resonance with Jupiter are a very stable population. But once they escape from the resonance, they are dynamically controlled by Jupiter, and in this sense their behavior resembles that of JFC. We performed a numerical simulation to analyze the dynamical evolution that Hildas follow after escaping from the resonance, and their contribution to the JFC population. We found that 8% of the particles leaving the resonance end up impacting Jupiter. 98.7% of the escaped Hildas live at least 1000 years as a JFC, with a mean lifetime of 1.4×¹⁰⁶ years. In particular, escaped Hildas stay mainly in the region of perihelion distances greater than 2.5 AU. On the other hand, the number of escaped Hildas reaching the inner Solar System (q<2.5 AU) is negligible. So, there are almost no Hilda asteroids among the NEO population. We also analyzed the possibility that the Shoemaker-Levy 9 were an escaped Hilda asteroid. In this case, it would be possible to give stronger constraints to its pre-capture orbital elements.     

On the Asteroidal Population of the First-Order Jovian Resonances

The frequency map analysis was applied to the fairly realistic models of the 2/1, 3/2, and 4/3 jovian resonances and the results were compared with the asteroidal distribution at these commensurabilities. The presence of the Hecuba gap at the 2/1 and of the Hilda group in the 3/2 is explained on the basis of different rates of the chaotic transport (diffusion) in these resonances. The diffusion in the most stable 2/1-resonant region is almost two orders in magnitude faster than the diffusion in the region which accommodates the Hildas. In the 2/1 commensurability there are two possible locations for long-surviving asteroids: the one centered at an eccentricity of 0.3 near the libration stable centers with small libration amplitude and the other at a slightly lower eccentricity with a moderate libration amplitude (∼90°). Surprisingly, all asteroids observed in the 2/1 resonance (8 numbered and multi-opposition objects in Bowell's catalog from 1994) occupy the moderate-libration area and avoid the area in a close vicinity of the libration stable centers. Possible explanations of this fact were discussed. Concerning the 4/3 resonance, the only asteroid in the corresponding stable region is 279 Thule, in spite of the fact that this region is almost as regular (although not as extensive) as the one where the Hilda group in the 3/2, with 79 members, is found.     

Gas-drag-assisted capture of Himalia's family

To elucidate the capture of Jupiter's outer moons, we reverse-evolve satellites from their present orbits to their original heliocentric paths in the presence of Jupiter's primordial circumplanetary disk (Lubow et al., 1999, Astrophys. J. 526, 1001-1012; Canup and Ward, 2003, Astron. J. 124, 3404-3423). Our orbital histories use a symplectic integrator that allows dissipation. We assume that the present satellites Himalia, Elara, Lysithea, Leda, and S/2000 J11 are collisional fragments of a single parent. Our simulations show that this “prograde-cluster progenitor” (PCP) could be derived from objects with heliocentric orbits like those of the Hilda asteroid group. We show analytically that this capture is energetically possible. We also compare the spectroscopic characteristics of the prograde cluster members (Grav et al., 2003, Icarus, submitted for publication) with those of the Hildas, and conclude that the surface color of the prograde-cluster progenitor is consistent with an origin within the Hilda group. Accordingly, gas drag in the primordial jovian nebula is found to offer a plausible explanation for the origin of the prograde cluster. A similar capture mechanism is proposed for Saturn's Phoebe.     

Asteroid identification using BTA images

We report the results of identification of the Main Belt asteroid 2006 HO 153 accidentally found during the observations of transneptunian objects in 1998. We briefly describe the technique of identification, where the use of change rates of spherical coordinates of the observed asteroid plays an important role.     

Trojans’ Odyssey: Unveiling the early history of the Solar System

In our present understanding of the Solar System, small bodies (asteroids, Jupiter Trojans, comets and TNOs) are the most direct remnants of the original building blocks that formed the planets. Jupiter Trojan and Hilda asteroids are small primitive bodies located beyond the ‘snow line’, around respectively the L₄ and L₅ Lagrange points of Jupiter at ～5.2?AU (Trojans) and in the 2:3 mean-motion resonance with Jupiter near 3.9?AU (Hildas). They are at the crux of several outstanding and still conflicting issues regarding the formation and evolution of the Solar System. They hold the potential to unlock the answers to fundamental questions about planetary migration, the late heavy bombardment, the formation of the Jovian system, the origin and evolution of trans-neptunian objects, and the delivery of water and organics to the inner planets. The proposed Trojans’ Odyssey mission is envisioned as a reconnaissance, multiple flyby mission aimed at visiting several objects, typically five Trojans and one Hilda. It will attempt exploring both large and small objects and sampling those with any known differences in photometric properties. The orbital strategy consists in a direct trajectory to one of the Trojan swarms. By carefully choosing the aphelion of the orbit (typically 5.3?AU), the trajectory will offer a long arc in the swarm thus maximizing the number of flybys. Initial gravity assists from Venus and Earth will help reducing the cruise time as well as the ΔV needed for injection thus offering enough capacity to navigate among Trojans. This solution further opens the unique possibility to flyby a Hilda asteroid when leaving the Trojan swarm. During the cruise phase, a Main Belt Asteroid could be targeted if requiring a modest ΔV. The specific science objectives of the mission will be best achieved with a payload that will perform high-resolution panchromatic and multispectral imaging, thermal-infrared imaging/ radiometry, near- and mid-infrared spectroscopy, and radio science/mass determination. The total mass of the payload amounts to 50?kg (including margins). The spacecraft is in the class of Mars-Express or a down-scaled version of Jupiter Ganymede Orbiter. It will have a dry mass of 1200?kg, a total mass at launch of 3070?kg and a ΔV capability of 700?m/s (after having reached the first Trojan) and can be launched by a Soyuz rocket. The mission operations concept (ground segment) and science operations are typical of a planetary mission as successfully implemented by ESA during, for instance, the recent flybys of Main Belt asteroids Steins and Lutetia.     

On the original distribution of the asteriods. I.

The depletion of an initially uniform distribution of asteroids extending form Mars to Saturn, caused by the gravitational perturbations of Jupiter and Saturn, is calculated by numerical integration of the asteroid orbits. Almost all (about 85%) the asteroids between Jupiter and Saturn are ejected in the first 6000 years Most of the asteroids between the $\text{2}\text{3}$ Jupiter resonance (4.0 A.U.) and Jupiter are ejected in the first 2400 years with the exception of the stable librators (e.g., the Hilda group). Interior to the $\text{2}\text{3}$ resonance the depletion was small, and interior to the $\text{1}\text{2}$ resonance (3.3 A.U.) no asteroids were ejected in the first 2400 years.     

Radar observations of the asteroid 2011 UW158

In July 2015 intercontinental bistatic radar observations of the potentially dangerous asteroid 2011 UW158 during its close approach to the Earth were carried out. The asteroid was illuminated at a frequency of 8.4 GHz with the 70-m DSS-14 antenna of the Goldstone Deep Space Communications Complex, while the signal reflected from the asteroid was received with the 32-m radio telescopes of the Quasar VLBI network at the Zelenchukskaya and Badary Observatories. The spectra of the reflected radio signals were obtained. The sizes and rotation period of the asteroid consistent with photometric observations and the ratio of the powers of the reflected signals with left- and right-hand circular polarizations were determined. The derived values suggest that the asteroid has an inhomogeneous surface and a prolate shape. The observations of the Doppler shift of the reflected signal frequency were obtained, which allowed the orbital parameters of the asteroid to be improved.     

Cratering rate on the jovian system: the contribution from Hilda asteroids

We study the dynamical evolution of the Hilda group of asteroids trough numerical methods, performing also a collisional pseudo-evolution of the present population, in order to calculate the rate of evaporation and its contribution to the cratering history of the Galilean satellites. If the present population of small asteroids in the Hilda's region follows the same size distribution observed at larger radii, we find that this family is the main contributor to the production of small craters (i.e., crater with diameters d∼4 km) on the Galilean system, overcoming the production by Jupiter Family Comets and by Trojan asteroids. The results of this investigation encourage further observational campaigns, in order to determine the size distribution function of small Hilda asteroids.     

Astrometry and photometry of asteroid (308635) 2005 YU55

Astrometric and photometric observations of asteroid (308635) 2005 YU55 were carried out at the computer-aided ZA-320M and MTM-500M telescopes of the Pulkovo observatory in the period of its closest approach to the Earth, from November 9 to 20, 2011. The new orbit of the asteroid changed after its close approach to the Earth was determined. From this orbit, a close approach to Venus on January 19, 2029, was precalculated, and the distance at the closest approach—359000 km—was estimated. From the analysis of the acquired photometric data, the axial rotation period of the asteroid was more accurately determined, and it amounted to 16.3 ± 0.4 h. The color indexes of the asteroid, B-V, V-R, and R-I, were estimated, which allowed the taxonomic class of the asteroid, B, to be determined from them. In addition, from our photometric observations of the asteroid, the earlier unknown change in its brightness with a period of 0.9–1.2 h was detected; the cause of this change has not been completely studied yet.     

Observations of asteroid occultations by the trailed-image method

The method of trailed CCD images for observations of asteroid occultations is described. This method was used to observe 9 asteroid occupations at the Lisnyky observational station in 2006 with the telescope AZT-8 (D= 0.7m and F= 2.8m) equipped by the CCD ST-8 XME. In the case of occultation of the star TYC 0587-00209-1U by the asteroid 76 Freia in November 4, 2006, the distance between the asteroid center and the star, as well as the time of asteroid occultation were determined. The size of asteroid 76 Freia is determined assuming that its shape is spherically symmetric. In other cases, the minimal distances between the asteroid center and the star are determined. The method makes it possible to observe asteroid occultations with high time resolution.     

Characterization of the near-Earth Asteroid 2002 NY40

In August 2002, the near-Earth Asteroid 2002 NY₄₀, made its closest approach to the Earth. This provided an opportunity to study a near-Earth asteroid with a variety of instruments. Several of the telescopes at the Maui Space Surveillance System were trained at the asteroid and collected adaptive optics images, photometry and spectroscopy. Analysis of the imagery reveals the asteroid is triangular shaped with significant self-shadowing. The photometry reveals a 20-h period and the spectroscopy shows that the asteroid is a Q-type.     

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.     

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

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

Application of the theory of jet stream to the asteroidal belt

The possibility of incorporating the resonant effect and jet stream formation process into the problems of the Hilda asteroids and Kirkwood gaps is discussed qualitatively. It appears that formation of the precursor jet streams of the resonant asteroids in the main belt would be suppressed due to the collisional perturbation effect of the ambient matter in this region. Together with the biased distribution of near-resonant asteroids, the depletion across the Kirkwood gaps could be understood. Within the context of jet stream theory the existence of Hilda asteroids outside the main belt requires the original limit of the main belt to be not much more extensive than the present value of 3.5 AU. This is suggestive of a cosmogonic origin of the observed outer limit.     

The light curve of asteroid 2867 Steins measured by VIRTIS-M during the Rosetta fly-by

On 5 September 2008, the Rosetta spacecraft encountered the asteroid 2867 Steins on its way to the comet 67P/Churyumov-Gerasimenko. This was the first of two planned asteroid fly-bys performed by the probe, the second fly-by being with the much larger asteroid 21 Lutetia in July 2010. The VIRTIS imaging spectrometer (IFOV 0.250 mrad, overall spectral range 0.25-5.1 μm) onboard Rosetta acquired data of Steins already before the closest approach phase, when the target was spatially unresolved, in order to obtain a light curve of the asteroid in the infrared spectral range extending up to 5 μm, that was never explored before. The VIRTIS light curve campaign started at 11:30 UTC onboard time, when the spacecraft was about 221,377 km away from the target, and ended at 17:58 UTC, at a distance of 20,741 km away from Steins. During this timeframe, the solar phase angle of the asteroid was roughly constant, ranging from 38.2° to 36.3°.Assuming the most recent value derived for the rotational period of Steins (Lamy et al., 2008), the VIRTIS observations covered slightly more than one rotation of the asteroid. In this interval, VIRTIS collected 8 hyperspectral cubes where Steins was captured 119 times, both in the visual and in the infrared range. Given the low signal and the unresolved appearance of the source, for which the instrument was not designed, only a small subset of wavelengths turned out to be suitable to sample the light curve. Nevertheless, in both the VIS and NIR ranges we find a similar trend, with two different maxima and minima during one rotational period, and amplitudes consistent with the results in the visual range obtained in previous works, including the data set acquired by the OSIRIS camera onboard Rosetta. We also report the presence of a new broad feature centered at approximately 0.81-0.82 μm, which is seen in the visual data throughout the rotation of the asteroid.     

Effect of the finite size of an asteroid on its deflection using a tether–ballast system

Potentially hazardous near-Earth objects which can impose a significant threat on life on the planet have generated a lot of interest in the study of various asteroid deflection strategies. There are numerous asteroid deflection techniques suggested and discussed in the literature. This paper is focused on one of the non-destructive asteroid deflection strategies by attaching a long tether–ballast system to the asteroid. In the existing literature on this technique, very simplified models of the asteroid-tether–ballast system including a point mass model of the asteroid have been used. In this paper, the dynamical effect of using a finite size asteroid model on the asteroid deflection achieved is analyzed in detail. It has been shown that considering the finite size of the asteroid, instead of the point mass approximation, can have significant influence on the deflection predicted. Furthermore the effect of the tether-deployment stage, which is an essential part of any realistic asteroid deflection mission, on the predicted deflection is studied in this paper. Finally the effect of cutting the tether on the deflection achieved is analyzed and it has been shown that depending on the orbital properties of the asteroid as well as its size and rotational rate, cutting the tether at an appropriate time can increase the deflection achieved. Several numerical examples have been used in this paper to elaborate on the proposed technique and to quantitatively analyze the effect of different parameters on the asteroid deflection.