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1.
The present paper reviews the Nekhoroshev theorem from the point of view of physicists and astronomers. We point out that Nekhoroshev result is strictly connected with the existence of a specific structure of the phase space, the existence of which can be checked with several numerical tools. This is true also for a degenerate system such as the one describing the motion of an asteroid in the so called main belt. The main difference is that in some parts of the belt, the Nekhoroshev result cannot apply a priori. Mean motion resonances of order smaller than the logarithm of the mass of Jupiter and first order secular resonances must be excluded. In the remaining parts, conversely, the Nekhoroshev theorem can be proved, provided someparameters, such as the masses, the eccentricities and the inclinations of the planets are small enough. At the light of this result, a massive campaign of numerical integrations of real and fictitious asteroids should allow to understand which is the real dynamical structure of the asteroid belt.  相似文献   

2.
An analysis of ordered and chaotic regions of motion in the outer asteroid belt has shown that once the eccentricity of Jupiter is introduced the chaotic regions of the circular model are quite easily depleted. This suggests that also objects in neighbouring regions must be strongly perturbed. Therefore it is not surprising that many outer belt asteroids have been reported in the literature as resonant or anyway dynamically protected. By using the planar elliptic restricted 3-body model we have investigated the motion of outer belt asteroids which had not been suspected to librate. We find 3 cases of libration and 11 cases of e, coupling that can be explained within the theory of secular resonances. It is thus established that in the outer belt only resonant and dynamically protected asteroids can have lifetimes of the same order as the age of the Solar System.  相似文献   

3.
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 (?1 My) timescales. Our results show that (951) Gaspra has a highly chaotic rotation state induced by an overlap of the s and s6 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.  相似文献   

4.
We investigate the possibility of obtaining a Nekhoroshev like result for the dynamical system describing the motion of an asteroid in the main belt, From the mathematical point of view this is a new result since the problem is degenerate and we want to control also the motion of degenerate actions, We find that there are regions, such as the resonances of low order among the fast angles (mean motion resonances), where a Nekhoroshev like result cannot be proved a priori, Conversely, we are able to confine the motions in the mean motion resonances of logarithmically large order in the perturbation parameters, as well as in the non-resonant region, We discuss also the connection with the existence of invariant tori.  相似文献   

5.
The study of the stochasticity of the asteroid belt requires the analysis of a large number of orbits. We detect the dynamical character of a set of 5 400 asteroids using the Fast Lyapunov Indicator, a method of analysis closely related to the computation of the Lyapunov Characteristic Exponents, but cheaper in computational time. For both regular and chaotic orbits we try to associate the motion to the underlying resonances network. For it we consider different methods of classification of rational numbers proposed by number theory, and we choose the one which seems to be strictly related to the dynamical behaviour of a system. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

6.
The size distribution of main belt of asteroids is determined primarily by collisional processes. Large asteroids break up and form smaller asteroids in a collisional cascade, with the outcome controlled by the strength-size relationship for asteroids. In addition to collisional processes, the non-collisional removal of asteroids from the main belt (and their insertion into the near-Earth asteroid (NEA) population) is critical, and involves several effects: strong resonances increase the orbital eccentricity of asteroids and cause them to enter the inner planet region; chaotic diffusion by numerous weak resonances causes a slow leak of asteroids into the Mars- and Earth-crossing populations; and the Yarkovsky effect, a radiation force on asteroids, is the primary process that drives asteroids into these resonant escape routes. Yarkovsky drift is size-dependent and can modify the main-belt size distribution. The NEA size distribution is primarily determined by its source, the main-belt population, and by the size-dependent processes that deliver bodies from the main belt. All of these effects are simulated in a numerical collisional evolution model that incorporates removal by non-collisional processes. We test our model against a wide range of observational constraints, such as the observed main-belt and NEA size distributions, the number of asteroid families, the preserved basaltic crust of Vesta and its large south-pole impact basin, the cosmic ray exposure ages of meteorites, and the cratering records on asteroids. We find a strength-size relationship for main-belt asteroids and non-collisional removal rates from the main belt such that our model fits these constraints as best as possible within the parameter space we explore. Our results are consistent with other independent estimates of strength and removal rates.  相似文献   

7.
The restricted problem of 2+2 bodies is applied to the study of the stability and dynamics of binary asteroids in the solar system. Numerical investigation of the behavior of the orbital elements and the maximal Lyapunov characteristic number of binary asteroids reveal extensive regions where bounded quasiperiodic motion is possible. These regions are compared to the bounded regions which are predicted by the classical restricted problem of three bodies. Regions of bounded chaotic solutions are also found.  相似文献   

8.
A symplectic mapping model for the co-orbital motion (Sándor et al., 2002, Cel. Mech. Dyn. Astr. 84, 355) in the circular restricted three body problem is used to derive Nekhoroshev stability estimates for the Sun–Jupiter Trojans. Following a brief review of the analytical part of Nekhoroshev theory, a direct method is developed to construct formal integrals of motion in symplectic mappings without use of a normal form. Precise estimates are given for the region of effective stability based on the optimization of the size of the remainder of the formal series. The stability region found for t=1010 yrs corresponds to a libration amplitude Dp=10.6°. About 30% of asteroids with accurately known proper elements (Milani, 1993, Cel. Mech. Dyn. Astron. 57, 59), at low eccentricities and inclinations, are included within this region. This represents an improvement with respect to previous estimates given in the literature. The improvement is due partly to the choice of better variables, but also to the use of a mapping model, which is a simplification of the circular restricted three body problem.  相似文献   

9.
For both asteroids and meteor streams, and also for comets, resonances play a major role for their orbital evolutions but on different time scales. For asteroids both mean motion resonances and secular resonances not only structure the phase space of regular orbits but are mainly at the origin for the inherent chaos of planet crosser objects.For comets and their chaotic routes temporary trapping into orbital resonances is a well known phenomenon. In addition for slow diffusion through the Kuiper belt resonances are the only candidates for originating a slow chaos.Like for asteroids, resonances with Jupiter play a major role for the orbital evolution of meteor streams. Crossing of separatrix like zones appears to be crucial for the formation of arcs and for the dissolution of streams. In particular the orbital inclination of a meteor stream appears to be a critical parameter for arc formation. Numerical results obtained in an other context show that the competition between the Poynting-Robertson drag and the gravitational interaction of grains near the 2/1 resonance might be very important in the long run for the structure of meteor streams.  相似文献   

10.
David A. Minton  Renu Malhotra 《Icarus》2010,207(2):744-7225
The cumulative effects of weak resonant and secular perturbations by the major planets produce chaotic behavior of asteroids on long timescales. Dynamical chaos is the dominant loss mechanism for asteroids with diameters in the current asteroid belt. In a numerical analysis of the long-term evolution of test particles in the main asteroid belt region, we find that the dynamical loss history of test particles from this region is well described with a logarithmic decay law. In our simulations the loss rate function that is established at persists with little deviation to at least . Our study indicates that the asteroid belt region has experienced a significant amount of depletion due to this dynamical erosion—having lost as much as ∼50% of the large asteroids—since 1 Myr after the establishment of the current dynamical structure of the asteroid belt. Because the dynamical depletion of asteroids from the main belt is approximately logarithmic, an equal amount of depletion occurred in the time interval 10-200 Myr as in 0.2-4 Gyr, roughly ∼30% of the current number of large asteroids in the main belt over each interval. We find that asteroids escaping from the main belt due to dynamical chaos have an Earth-impact probability of ∼0.3%. Our model suggests that the rate of impacts from large asteroids has declined by a factor of 3 over the last 3 Gyr, and that the present-day impact flux of objects on the terrestrial planets is roughly an order of magnitude less than estimates currently in use in crater chronologies and impact hazard risk assessments.  相似文献   

11.
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 107-108-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 108-year time scale and that its age may be significantly less than 109 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.  相似文献   

12.
Abstract— We review the meteoritical and astronomical literature to answer the question: What is the evidence for the importance of ordinary chondritic material to the composition of the asteroid belt? From the meteoritical literature, we find that currently (1) our meteorite collections sample at least 135 different asteroids; (2) out of 25+ chondritic meteorite parent bodies, 3 are (by definition) ordinary chondritic; (3) out of 14 chondritic grouplets and unique chondrites, 11 are affiliated with a carbonaceous group/clan of chondrites; (4) out of 24 differentiated groups of meteorites, only the HE iron meteorites clearly formed from ordinary chondritic precursor material; (5) out of 12 differentiated grouplets and unique differentiated meteorites, 8 seem to have had carbonaceous chondritic precursors; (6) a high frequency of carbonaceous clasts in ordinary chondritic breccias suggests that ordinary chondrites have been embedded in a swarm of carbonaceous material. The rare occurrence (only one example) of ordinary chondritic clasts in carbonaceous chondritic breccias indicates that ordinary chondritic material has not been widespread in the asteroid belt; (7) cosmic spherules, micrometeorites, and stratospheric interplanetary dust particles—believed to represent a less biased sampling of asteroidal material—show that only a very small fraction (less than ～1%) of asteroidal dust has an ordinary chondritic composition. From the astronomical literature, we find that currently (8) spectroscopic surveys of the main asteroid belt are finding more and more nonordinary chondritic primitive material in the inner main belt; (9) the increase in spectroscopic data has increased the inferred mineralogical diversity of main belt asteroids; and (10) no ordinary chondritic asteroids have been directly observed in the main belt. These lines of evidence strongly suggest a scenario in which ordinary chondritic asteroids were never abundant in the main belt. The S-type asteroids may currently be primarily differentiated, but the precursor material is more likely to have been carbonaceous chondritic, not ordinary chondritic. Historically, carbonaceous material could have dominated the entire main belt. This could explain the presence in the inner main belt of asteroids linked to the primitive carbonaceous chondrites, and the absence of asteroids linked to the ordinary chondrites. The implications of this scenario for the asteroid heating mechanism(s) are briefly discussed.  相似文献   

13.
This paper presents a comparative analysis of the 2/1 and 3/2 asteroidal resonances based on several analytical and numerical tools. The frequency map analysis was used to obtain a refined estimation of the chaotic transport. Fourier and wavelet analyses were used to construct the web of inner resonances and showed that they are the seat of the strongly unstable motion observed in the numerical simulations. The most regular regions in both resonances were classified. A fast symplectic mapping allowed a number of direct runs over 108 years of the orbits initially in these regions. The stability of orbits over the age of the solar system was discussed and compared to the distribution of the observed asteroids in both resonances.  相似文献   

14.
We study the global dynamics of the jovian Trojan asteroids by means of the frequency map analysis. We find and classify the main resonant structures that serve as skeleton of the phase space near the Lagrangian points. These resonances organize and control the long-term dynamics of the Trojans. Besides the secondary and secular resonances, that have already been found in other asteroid sets in mean motion resonance (e.g. main belt, Kuiper belt), we identify a new type of resonance that involves secular frequencies and the frequency of the great inequality, but not the libration frequency. Moreover, this new family of resonances plays an important role in the slow transport mechanism that drives Trojans from the inner stable region to eventual ejections. Finally, we relate this global view of the dynamics with the observed Trojans, identify the asteroids that are close to these resonances and study their long-term behaviour.  相似文献   

15.
F. Roig  D. Nesvorný  R. Gil-Hutton 《Icarus》2008,194(1):125-136
V-type asteroids are bodies whose surfaces are constituted of basalt. In the Main Asteroid Belt, most of these asteroids are assumed to come from the basaltic crust of Asteroid (4) Vesta. This idea is mainly supported by (i) the fact that almost all the known V-type asteroids are in the same region of the belt as (4) Vesta, i.e., the inner belt (semi-major axis 2.1<a<2.5 AU), (ii) the existence of a dynamical asteroid family associated to (4) Vesta, and (iii) the observational evidence of at least one large craterization event on Vesta's surface. One V-type asteroid that is difficult to fit in this scenario is (1459) Magnya, located in the outer asteroid belt, i.e., too far away from (4) Vesta as to have a real possibility of coming from it. The recent discovery of the first V-type asteroid in the middle belt (2.5<a<2.8 AU), (21238) 1995WV7 [Binzel, R.P., Masi, G., Foglia, S., 2006. Bull. Am. Astron. Soc. 38, 627; Hammergren, M., Gyuk, G., Puckett, A., 2006. ArXiv e-print, astro-ph/0609420], located at ∼2.54 AU, raises the question of whether it came from (4) Vesta or not. In this paper, we present spectroscopic observations indicating the existence of another V-type asteroid at ∼2.53 AU, (40521) 1999RL95, and we investigate the possibility that these two asteroids evolved from the Vesta family to their present orbits by a semi-major axis drift due to the Yarkovsky effect. The main problem with this scenario is that the asteroids need to cross the 3/1 mean motion resonance with Jupiter, which is highly unstable. Combining N-body numerical simulations of the orbital evolution, that include the Yarkovsky effect, with Monte Carlo models, we compute the probability that an asteroid of a given diameter D evolves from the Vesta family and crosses over the 3/1 resonance, reaching a stable orbit in the middle belt. Our results indicate that an asteroid like (21238) 1995WV7 has a low probability (∼1%) of having evolved through this mechanism due to its large size (D∼5 km), because the Yarkovsky effect is not sufficiently efficient for such large asteroids. However, the mechanism might explain the orbits of smaller bodies like (40521) 1999RL95 (D∼3 km) with ∼70-100% probability, provided that we assume that the Vesta family formed ?3.5 Gy ago. We estimate the debiased population of V-type asteroids that might exist in the same region as (21238) and (40521) (2.5<a?2.62 AU) and conclude that about 10 to 30% of the V-type bodies with D>1 km may come from the Vesta family by crossing over the 3/1 resonance. The remaining 70-90% must have a different origin.  相似文献   

16.
Gao  Jian  Zhu  Jin 《Earth, Moon, and Planets》2002,91(2):95-105
The astrometric observations of asteroids are often performednear their opposition, where they have faster apparent motions andbrighter visual magnitudes. However, the physical observations ofasteroids (photometric and spectral) often require longer exposuretimes as well as brighter magnitudes for better signal-to-noiseratio, which are combined effects of both apparent moving speedsand visual magnitudes. We derive the equations of the apparentmotion of asteroid in geocentric ecliptic coordinates. Comparisonof the apparent magnitudes of asteroid at opposition and atstationary shows that the magnitude differences in the two casesare around 1 magnitude in average for most main belt asteroids,but are much larger for Near Earth Asteroids. Combining withcomparison of asteroid apparent motion, the proper time forasteroid physical observation in different cases are discussed.  相似文献   

17.
We have shown, in previous publications, that stable chaos is associated with medium/high-order mean motion resonances with Jupiter, for which there exist no resonant periodic orbits in the framework of the elliptic restricted three-body problem. This topological “defect” results in the absence of the most efficient mechanism of eccentricity transport (i.e., large-amplitude modulation on a short time scale) in three-body models. Thus, chaotic diffusion of the orbital elements can be quite slow, while there can also exist a nonnegligible set of chaotic orbits which are semiconfined (stable chaos) by “quasi-barriers” in the phase space. In the present paper we extend our study to all mean motion resonances of order q≤9 in the inner main belt (1.9-3.3 AU) and q≤7 in the outer belt (3.3-3.9 AU). We find that, out of the 34 resonances studied, only 8 possess resonant periodic orbits that are continued from the circular to the elliptic three-body problem (regular families), namely, the 2/1, 3/1, 4/1, and 5/2 in the inner belt and the 7/4, 5/3, 11/7, and 3/2 in the outer belt. Numerical results indicate that the 7/3 resonance also carries periodic orbits but, unlike the aforementioned resonances, 7/3-periodic orbits belong to an irregular family. Note that the five inner-belt resonances that carry periodic orbits correspond to the location of the main Kirkwood gaps, while the three outer-belt resonances correspond to gaps in the distribution of outer-belt asteroids noted by Holman and Murray (1996, Astron. J.112, 1278-1293), except for the 3/2 case where the Hildas reside. Fast, intermittent eccentricity increase is found in resonances possessing periodic orbits. In the remaining resonances the time-averaged elements of chaotic orbits are, in general, quite stable, at least for times t∼250 Myr. This slow diffusion picture does not change qualitatively, even if more perturbing planets are included in the model.  相似文献   

18.
We investigate the flux of main-belt asteroid fragments into resonant orbits converting them into near-Earth asteroids (NEAs), and the variability of this flux due to chance interasteroidal collisions. A numerical model is used, based on collisional physics consistent with the results of laboratory impact experiments. The assumed main-belt asteroid size distribution is derived from that of known asteroids extrapolated down to sizes of ≈ 40 cm, modified in such a way to yield a quasi-stationary fragment production rate over times ≈ 100 Myr. The results show that the asteroid belt can supply a few hundred km-sized NEAs per year, well enough to sustain the current population of such bodies. On the other hand, if our collisional physics is correct, the number of existing 10-km objects implies that these objects either have very long-lived orbits, or must come from a different source (i.e., comets). Our model predicts that the fragments supplied from the asteroid belt have initially a power-law size distribution somewhat steeper than the observed one, suggesting preferential removal of small objects. The component of the NEA population with dynamical lifetimes shorter than or of the order of 1 Myr can vary by a factor reaching up to a few tens, due to single large-scale collisions in the main belt; these fluctuations are enhanced for smaller bodies and faster evolutionary time scales. As a consequence, the Earth's cratering rate can also change by about an order of magnitude over the 0.1 to 1 Myr time scales. Despite these sporadic spikes, when averaged over times of 10 Myr or longer the fluctuations are unlikely to exceed a factor two.  相似文献   

19.
The utilization of chaotic dynamics approaches allowed the identification of many modes of motion in resonant asteroidal dynamics. As these dynamical systems are not integrable, the motion modes are not separated and one orbit may transit from one mode to another. In some cases, as in the \31 resonance, these transitions may lead, in a relatively short time scale, to eccentricities so high that the asteroid may approach the Sun and be destroyed. In the \21 and \32 resonances these transitions are much slower and only indirect estimations of the time which is needed for a generic asteroid to leave the resonance are possible. It may reach hundreds of million years in the more robust regions of the \21 resonance and a time of the order of billions of years in those of the \32 resonance. These values are consistent with the observed depletion of the \21 resonance (only a few asteroids known while almost 60 asteroids are known in the \32 resonance).  相似文献   

20.
The orbits of the asteroids crossing the orbit of the Earth and other planets are chaotic and cannot be computed in a deterministic way for a time span long enough to study the probability of collisions. It is possible to study the statistical behaviour of a large number of such orbits over a long span of time, provided enough computing resources and intelligent post processing software are available. The former, problem can be handled by exploiting the enormous power of parallel computing systems. The orbit of the asteroids can be studied as a restricted (N+M)-body problem which is suitable for the use of parallel processing, by using one processor to compute the orbits of the planets and the others to compute the orbits the asteroids. This scheme has been implemented on LCAP-2, an array of IBM and FPS processors with shared memory designed by E. Clementi (IBM). The parallelisation efficiency has been over 80%, and the overall speed over 90 MegaFLOPS; the orbits of all the asteroids with perihelia lower than the aphelion of Mars (410 objects) have been computed for 200,000, years (Project SPACEGUARD). The most difficult step of the project is the post processing of the very large amount of output data and to gather qualitative information on the behaviour of so many orbits without resorting to the traditional technique, i.e. human examination of output in graphical form. Within Project SPACEGUARD we have developed a qualitative classification of the orbits of the planet crossers. To develop an entirely automated classification of the qualitative orbital behaviour-including crossing behaviour, resonances (mean motion and secular), and protection mechanisms avoiding collisions-is a challenge to be met.  相似文献   

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