Search

Understanding the evolution of asteroid spin states is challenging work, in part because asteroids have a variety of orbits, shapes, spin states, and collisional histories but also because they are strongly influenced by gravitational and non-gravitational (YORP) torques. Using efficient numerical models designed to investigate asteroid orbit and spin dynamics, we study here how several individual asteroids have had their spin states modified over time in response to these torques (i.e., 951 Gaspra, 60 Echo, 32 Pomona, 230 Athamantis, 105 Artemis). These test cases which sample semimajor axis and inclination space in the inner main belt, were chosen as probes into the large parameter space described above. The ultimate goal is to use these data to statistically characterize how all asteroids in the main belt population have reached their present-day spin states. We found that the spin dynamics of prograde-rotating asteroids in the inner main belt is generally less regular than that of the retrograde-rotating ones because of numerous overlapping secular spin-orbit resonances. These resonances strongly affect the spin histories of all bodies, while those of small asteroids ([??]40 km) are additionally influenced by YORP torques. In most cases, gravitational and non-gravitational torques cause asteroid spin axis orientations to vary widely over short ([less than or equal to] 1 My) timescales. Our results show that (951) Gaspra has a highly chaotic rotation state induced by an overlap of the s and [s.sub.6] spin-orbit resonances. This hinders our ability to investigate its past evolution and infer whether thermal torques have acted on Gaspra's spin axis since its origin. Keywords: Rotational dynamics; Asteroids, rotation

The Agnia asteroid family, a cluster of asteroids located near semimajor axis [alpha] = 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 [Z.sub.1]. 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.sup.+30.sub.-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. Keywords: Asteroids, dynamics; Resonances

Asteroid families are the byproducts of catastrophic collisions whose fragments form clusters in proper semimajor axis, eccentricity, and inclination space. Although many families have been observed in the main asteroid belt, only two very young families, Karin and Veritas, have well-determined ages. The ages of other families are needed, however, if we hope to infer information about their ejection velocity fields, space weathering processes, etc. In this paper, we developed a method that allows us to estimate the ages of moderately young asteroid families (approximately in between 0.1 and 1 Gyr). We apply it to four suitable cases--Erigone, Massalia, Merxia, and Astrid--and derive their likely ages and approximate ejection velocity fields. We find that Erigone and Merxia were produced by large catastrophic disruption events (i.e., parent body [greater than or equal to] 100 km) that occurred approximately 280 and 330 Myr ago, respectively. The Massalia family was likely produced by a cratering event on Asteroid (20) Massalia less than 200 Myr ago. Finally, the Astrid family, which was produced by the disruption of a 60-70 km asteroid, is 100-200 Myr old, though there is considerable uncertainty in this result. We estimate that the initial ejection velocities for these families were only a few tens of meters per second, consistent with numerical hydrocode models of asteroid impacts. Our results help to verify that asteroid families are constantly undergoing dynamical orbital evolution from thermal (Yarkovsky) forces and spin vector evolution from thermal (YORP) torques. Keywords: Asteroids, dynamics; Thermal effects

The Eos asteroid family is the third most populous, after Themis and Koronis, and one of the largest non-random groups of asteroids in the main belt. It has been known and studied for decades, but its structure and history still presented difficulties to understand. We first revise the Eos family identification as a statistical cluster in the space of proper elements. Using the most to-date catalogue of proper elements we determine a nominal Eos family, defined by us using the hierarchical-clustering method with the cut-off velocity of 55 m/s, contains some 4400 members. This unforeseen increase in known Eos asteroids allows us to perform a much more detailed study than was possible so far. We show, in particular, that most of the previously thought peculiar features are explained within the following model: (i) collisional disruption of the parent body leads to formation of a compact family in the proper element space (with characteristic escape velocities of the observed asteroids of tens of meters per second, compatible with hydrocode simulations), and (ii) as time goes, the family dynamically evolves due to a combination of the thermal effects and planetary perturbations. This model allows us to explain sharp termination of the family at the J7/3 mean motion resonance with Jupiter, uneven distribution of family members about the J9/4 mean motion resonance with Jupiter, semimajor axis distribution of large vs small members in the family and anomalous residence of Eos members inside the high-order secular resonance [z.sub.1]. Our dynamical method also allows us to estimate Eos family age to [1.3.sup.+0.15.sub.-0.2] Gyr. Several formal members of the Eos family are in conflict with our model and these are suspected interlopers. We use spectroscopic observations, whose results are also reported here, and results of 5-color wide-band Sloan Digital Sky Survey photometry to prove some of them are indeed spectrally incompatible with the family. Keywords: Asteroids, dynamics; Thermal effects

In this paper, we show that Asteroid (433) Eros is currently residing in a spin--orbit resonance, with its spin axis undergoing a small-amplitude libration about the Cassini state 2 of the proper mode in the nonsingular orbital element sin 1/2 exp(1[ohm]), where I the orbital inclination and [ohm] the longitude of the node. The period of this libration is [??] 53.4 kyr. By excluding these libration wiggles, we find that Eros' pole precesses with the proper orbital plane in inertial space with a period of [??] 61.4 kyr. Eros' resonant state forces its obliquity to oscillate with a period of [??] 53.4 kyr between 276[degrees] and 289.5[degrees]. The observed value of [??] 89[degrees] places it near the latter extreme of this cycle. We have used these results to probe Eros' past orbit and spin evolution. Our computations suggest that Eros is unlikely to have achieved its current spin state by solar and planetary gravitational perturbations alone. We hypothesize that some dissipative process such as thermal torques (e.g., the so-called YORP effect) may be needed in our model to obtain a more satisfactory match with data. A detailed study of this problem is left for future work. Keywords: Asteroids, dynamics; Asteroids, rotation; Eros

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. Keywords: Asteroids, Asteroid, Dynamics, Orbits, Resonances

It is well known that asteroid families have steeper absolute magnitude (H) distributions for H < 12-13 values than the background population. Beyond this threshold, the shapes of the absolute magnitude distributions in the family/background populations are difficult to determine, primarily because both populations are not yet observationally complete. Using a recently generated catalog containing the proper elements of 106,284 main belt asteroids and an innovative approach, we debiased the absolute magnitude distribution of the major asteroid families relative to the local background populations. Our results indicate that the magnitude distributions of asteroid families are generally not steeper than those of the local background populations for H > 13 (i.e., roughly for diameters smaller than 10 km). In particular, most families have shallower magnitude distributions than the background in the range 15-17 mag. Thus, we conclude that, contrary to previous speculations, the population of kilometer-size asteroids in the main belt is dominated by background bodies rather than by members of the most prominent asteroid families. We believe this result explains why the Spacewatch, Sloan Digital Sky Survey, and Subaru asteroid surveys all derived a shallow magnitude distribution for the dimmer members of the main belt population. We speculate on a few dynamical and collisional scenarios that can explain this shallow distribution. One possibility is that the original magnitude distributions of the families (i.e., at the moment of the formation event) were very shallow for H larger than ~ 13, and that most families have not yet had the time to collisionally evolve to the equilibrium magnitude distribution that presumably characterizes the background population. A second possibility is that family members smaller than about 10 km, eroded over time by collisional and dynamical processes, have not yet been repopulated by the break-up of larger family members. For this same reason, the older (and possibly characterized by a weaker impact strength) background population shows a shallow distribution in the range 15-60 km. Keywords: Asteroids; Collisional physics

We investigate the possibility that fractions of the primordial populations at the triangular Lagrangian points of Saturn, Uranus, and Neptune have survived to the present and form (as yet unobserved) clusters of bodies coorbiting with these planets. Such leftovers would be analogs of the numerous objects (Trojans) leading and trailing the revolutions of Jupiter around the Sun. We focus on the dynamical stability of such populations over the age of the Solar System, assuming the current configuration of planets, and also discuss effects of the early radial migration of the outer planets. Our results suggest that, while Saturn's and Uranus' primordial Trojan populations should have been depleted by a factor of 100, Neptune may retain 50% of its original population of Trojans. A population of neptunian Trojans comparable to, or even larger than, Jupiter's Trojan population cannot be ruled out by existing observations. We compute the present-day sky densities of the hypothetical Trojans of the outer planets which can be used to guide observational surveys. Finally, we propose that the long-term instabilities that cause some jovian Trojans to escape the region of the Lagrange points at the present are due to three-body resonances. Key Words: Trojans; dynamics; resonances.

Numerous studies in the past few years have analyzed possible effects of planetary migration on the small bodies of the Solar System (mainly asteroids and KBOs), with the double aim of explaining certain dynamical structures in these systems, as well as placing limits on the magnitude of the radial migration of the planets. Here we undertake a similar aim, only this time concentrating on the dynamical stability of planetary satellites in a migration scenario. However, different from previous works, the strongest perturbations on satellite systems are not due to the secular variation of the semimajor axes of the planets, but from the planetesimals themselves. These perturbations result from close approaches between the planetesimals and satellites. We present results of several numerical simulations of the dynamical evolution of real and fictitious satellite systems around the outer planets, under the effects of multiple passages of a population of planetesimals representing the large-body component of a residual rocky disk. Assuming that this component dominated the total mass of the disk, our results show that the present systems of satellites of Uranus and Neptune do not seem to be compatible with a planetary migration larger than even one quarter that suggested by previous studies, unless these bodies were originated during the late stage of evaporation of the planetesimal disk. For larger variations of the semimajor axes of the planets, most of the satellites would either be ejected from the system or suffer mutual collisions due to excitation in their eccentricities. For the systems of Jupiter and Saturn, these perturbations are not so severe, and even large migrations do not introduce large instabilities. Nevertheless, even a small number of 1000-km planetesimals in the region may introduce significant excitation in the eccentricities and inclinations of satellites. Adequate values of this component may help explain the present dynamical distribution of distant satellites, including the highly peculiar orbit of Nereid. Key Words: celestial mechanics; jovian planets; satellites--General; planetesimals; Solar System--Origin.

Asteroid families are believed to originate by catastrophic disruptions of large asteroids. They are nowadays identified as clusters in the proper orbital elements space. The proper elements are analytically defined as constants of motion of a suitably simplified dynamical system. Indeed, they are generally nearly constant on a [10.sup.7]-[10.sup.8]-year time scale. Over longer time intervals, however, they may significantly change, reflecting the accumulation of the tiny nonperiodic evolutions provided by chaos and nonconservative forces. The most important effects leading to a change of the proper orbital elements are (i) the chaotic diffusion in narrow mean motion resonances, (ii) the Yarkovsky nongravitational force, and (iii) the gravitational impulses received at close approaches with large asteroids. A natural question then arises: How are the size and shape of an asteroid family modified due to evolution of the proper orbital elements of its members over the family age? In this paper, we concentrate on the dynamical dispersion of the proper eccentricity and inclination, which occurs due to (i), but with the help of (ii) and (iii). We choose the Flora family as a model case because it is unusually dispersed in eccentricity and inclination and, being located in the inner main belt, is intersected by a large number of effective mean motion resonances with Mars and Jupiter. Our results suggest that the Flora family dynamically disperses on a few [10.sup.8]-year time scale and that its age may be significantly less than [10.sup.9] years. We discuss the possibility that the parent bodies of the Flora family and of the ordinary L chondrite meteorites are the same object. In a broader sense, this work suggests that the common belief that the present asteroid families are simple images of their primordial dynamical structure should be revised. Key Words: asteroids; dynamics; meteorites; 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 asteroidaldistribution at these commensurabilities. The presence of the Hecuba gap at the2/1 and of the Hilda group in the 3/2 is explained on the basis of different ratesof the chaotic transport (diffusion) in these resonances. The diffusion in the moststable 2/1-resonant region is almost two orders in magnitude faster than thediffusion in the region which accommodates the Hildas. In the 2/1 commensurabilitythere are two possible locations for long-surviving asteroids: the one centeredat an eccentricity of 0.3 near the libration stable centers with small librationamplitude and the other at a slightly lower eccentricity with a moderate librationamplitude ([approximately]90 [degrees]). Surprisingly, all asteroids observed inthe 2/1 resonance (8 numbered and multi-opposition objects in Bowell's catalog from1994) occupy the moderate.libration area and avoid the area in a close vicinityof the libration stable centers. Possible explanations of this fact were discussed.Concerning the 4/3 resonance, the only asteroid in the corresponding stable regionis 279 Thule, in spite of the fact that this region is almost as regular (althoughnot as extensive) as the one where the Hilda group in the 3/2, with 79 members,is found. Key Words: asteroids; resonances; frequency map analysis.

The stability of orbits in the transneptunian region is numerically computed. It is found that, in analogy to the asteroid belt, there exist many chaotic layers associated with thin mean-motion resonances. These are either moderate- and high-order resonances with Neptune or three-body resonances with Neptune and Uranus. The orbital eccentricity chaotically increases at the thin resonances, allowing some Kuiper Belt objects to be slowly transferred to Neptune-crossing orbits. The stability of two large mean-motion resonances with Neptune, the 1:2 and 3:4, is systematically explored. It is shown that orbits in both resonances, with small resonant amplitudes are stable over the age of the Solar System. The possible role of collisions and dynamical scattering in clearing the resonances is discussed. It is inferred from orbital angles of 1997 SZ10 and 1996 TR66 that these bodies are most probably on stable tadpole orbits in the 1:2 Neptune resonance. Key Words: Kuiper Belt; Oort Cloud, celestial mechanics; stellar dynamics.

The Cybele region, located between the 2J:-1A and 5J:-3A mean-motion resonances, is adjacent and exterior to the asteroid main belt. An increasing density of three-body resonances makes the region between the Cybele and Hilda populations dynamically unstable, so that the Cybele zone could be considered the last outpost of an extended main belt. The presence of binary asteroids with large primaries and small secondaries suggested that asteroid families should be found in this region, but only relatively recently the first dynamical groups were identified in this area. Among these, the Sylvia group has been proposed to be one of the oldest families in the extended main belt. In this work we identify families in the Cybele region in the context of the local dynamics and non-gravitational forces such as the Yarkovsky and stochastic Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effects. We confirm the detection of the new Helga group at ≅ 3.65 au, which could extend the outer boundary of the Cybele region up to the 5J:-3A mean-motion resonance. We obtain age estimates for the four families, Sylvia, Huberta, Ulla, and Helga, currently detectable in the Cybele region, using Monte Carlo methods that include the effects of stochastic YORP and variability of the solar luminosity. The Sylvia family should be T= 1220 ± 40 Myr old, with a possible older secondary solution. Any collisional Cybele group formed prior to the Late Heavy Bombardment would have been most likely completely dispersed in the jumping Jupiter scenario of planetary migration. [ABSTRACT FROM AUTHOR]