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1.
The dynamical behavior of asteroids inside the 2:1 and 3:2 commensurabilities with Jupiter presents a challenge. Indeed most of the studies, either analytical or numerical, point out that the two resonances have a very similar dynamical behavior. In spite of that, the 3:2 resonance, a little outside the main belt, hosts a family of asteroids, called the Hildas, while the 2:1, inside the main belt, is associated to a gap (the Hecuba gap) in the distribution of asteroids.In his search for a dynamical explanation for the Hecuba gap, Wisdom (1987) pointed out the existence of orbits starting with low eccentricity and inclination inside the 2:1 commensurability and going to high eccentricity, and thus to possible encounters with Mars. It has been shown later (Henrard et al.), that these orbits were following a path from the low eccentric belt of secondary resonances to the high eccentric domain of secular resonances. This path crosses a bridge, at moderate inclination and large amplitude of libration, between the two chaotic domains associated with these resonances.The 3:2 resonance being similar in many respects to the 2:1 resonance, one may wonder whether it contains also such a path. Indeed we have found that it exists and is very similar to the 2:1 one. This is the object of the present paper.  相似文献   

2.
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   

3.
Near-Earth asteroids (10302) 1989 ML and (4660) Nereus have attracted much attention as candidates for the next generation of deep space explorations. In the study, the maximum Lyapunov exponent (MLE) and MEGNO (Mean Exponential Growth factor of Nearby Orbits) index are calculated after considering the effects of major objects in the Solar system, and the stabilities of these two asteroids are discussed. For each asteroid, 1000 clonal particles consistent with the observational uncertainties are generated from a multivariate normal distribution. Statistical results display probably emerging regions of each asteroid within 0.1 million years, and provide distributions of occurrence times in the phase space of semi-major axis versus eccentricity. We estimate the probability of close encounters and collisions between the asteroid and Earth or other planets. Furthermore, secular resonances, Kozai resonance, and mean motion resonances are analyzed for nominal orbits of the two asteroids. We conclude that 1989 ML is in the region dominated by mean motion resonances with terrestrial planets. The probability of close encounters with them is relatively small, therefore its orbit is relatively stable. Nereus is located in a region that can have close-encounters with the Earth, and it has an extremely unstable orbit.  相似文献   

4.
In a previous publication (Tsiganis et al. 2000, Icarus146, 240-252), we argued that the occurrence of stable chaos in the 12/7 mean motion resonance with Jupiter is related to the fact that there do not exist families of periodic orbits in the planar elliptic restricted problem and in the 3-D circular problem corresponding to this resonance. In the present paper we show that nonexistence of resonant periodic orbits, both for the planar and for the 3-D problem, also occurs in other jovian resonances—namely the 11/4, 22/9, 13/6, and 18/7—where cases of real asteroids on stable-chaotic orbits have been identified. This property may provide a “protection mechanism”, leading to semiconfinement of chaotic orbits and extremely slow migration in the space of proper elements, so that diffusion is practically unrelated to the value of the Lyapunov time, TL, of chaotic orbits. However, we show that, in more complicated dynamical models, the long-term evolution of chaotic orbits initiated in the vicinity of these resonances may also be governed by secular resonances. Finally, we find that stable-chaotic orbits have a characteristic spectrum of autocorrelation times: for the action conjugate to the critical argument the autocorrelation time is of the order of the Lyapunov time, while for the eccentricity- and inclination-related actions the autocorrelation time may be longer than 103TL. This behavior is consistent with the trajectory being sticky around a manifold of lower-than-full dimensionality in phase space (e.g., a 4-D submanifold of the 5-D energy manifold in a three-degrees-of-freedom autonomus Hamiltonian system) and reflects the inability of these “flawed” resonances to modify secular motion significantly, at least for times of the order of 200 Myr.  相似文献   

5.
In the last three years we have carried out numerical and semi-analytical studies on the secular dynamical mechanisms in the region (semimajor axis a < 2 AU) where the NEA orbits evolve. Our numerical integrations (over a time span of a few Myr) have shown that: (i) the linear secular resonances with both the inner and the outer planets may play an important role in the dynamical evolution of NEAs; (ii) the apsidal secular resonance with Mars could provide an important dynamical transport mechanism by which asteroids in the Mars-crossing region eventually achieve Earth-crossing orbits; (iii) in this region, due to the interaction with the terrestrial planets, the Kozai resonance can occur at small inclinations, with the argument of perihelion ω librating around 0° or 180°, providing a temporary protection mechanism against close approaches to the planets. The location of the linear secular resonances in this zone has also been obtained by an automatic procedure using a semi-numerical method valid for all values of the inclinations and eccentricities of the small bodies, and also in the case of libration of the argument of perihelion. A map of the secular resonances in the (a, i) plane shows — in agreement with the numerical integrations — that all the resonances with the terrestrial and giant planets are present, and also that some of them overlap. Thus the way is now open to fully take into account secular resonances in modelling the dynamical evolution of NEAs. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

6.
The twenty most chaotic objects found among first hundred of numbered asteroids are studied. Lyapunov time calculated with and without inner planets indicates that for eleven of those asteroids the strongest chaotic effect results from the resonances with Mars. The filtered semimajor axis displays an abrupt variation only when a close approach to Mars takes place. The study of the behaviour of the critical argument for candidate resonances can reveal which is responsible for the semimajor axis variation. We have determined these resonances for the asteroids in question. For the asteroids chaotic even without the inner planets we have determined the most important resonances with Jupiter, or three-body resonances. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

7.
As follows from dynamical studies, in the course of evolution, most near-Earth objects reach orbits with small perihelion distances. Changes of the asteroids in the vicinity of the Sun should play a key role in forming the physical properties, size distribution, and dynamical features of the near-Earth objects. Only seven of the discovered asteroids are currently moving along orbits with perihelion distances q < 0.1 AU. However, due to the Kozai–Lidov secular perturbations, the asteroids, having recently passed near the Sun, could by now have moved to orbits farther from the Sun. In this study, we found asteroids that have been recently orbiting with perihelion distances q < 0.1 AU. Asteroids may be on such orbits for hundreds to tens of thousands of years. To carry out astrophysical observations of such objects is a high priority.  相似文献   

8.
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   

9.
To try to understand the dynamical and collisional evolution of the Hungaria asteroids we have built a large catalog of accurate synthetic proper elements. Using the distribution of the Hungaria, in the spaces of proper elements and of proper frequencies, we can study the dynamical boundaries and the internal structure of the Hungaria region, both within a purely gravitational model and also showing the signature of the non-gravitational effects. We find a complex interaction between secular resonances, mean motion resonances, chaotic behavior and Yarkovsky-driven drift in semimajor axis. We also find a rare occurrence of large scale instabilities, leading to escape from the region. This allows to explain the complex shape of a grouping which we suggest is a collisional family, including most Hungaria but by no means all; we provide an explicit list of non-members of the family. There are finer structures, of which the most significant is a set of very close asteroid couples, with extremely similar proper elements. Some of these could have had, in a comparatively recent past, very close approaches with low relative velocity. We argue that the Hungaria, because of the favorable observing conditions, may soon become the best known sub-group of the asteroid population.  相似文献   

10.
近地小行星(10302) 1989 ML和(4660) Nereus作为下一代深空探测的候选目标一直备受关注. 在考虑太阳系主要天体的动力学背景下, 通过计算最大Lyapunov指数(MLE)及MEGNO (Mean Exponential Growth factor of Nearby Orbits)指数讨论它们的稳定性. 同时, 对每个小行星, 在其观测误差范围内按多元正态分布各选取1000个克隆粒子, 通过统计分析显示这两个小行星在10万年内可能的运动范围, 给出半长径-偏心率空间中的出现次数分布图, 并统计小行星与地球或其他大行星之间的密近交汇及碰撞的概率. 此外还对这两个小行星的标称轨道进行长期共振、Kozai共振及平运动共振的动力学分析. 综上得出结论, 1989 ML处在平运动共振主导的区域, 发生密近交汇的概率较小, 从而其轨道相对较稳定; 而Nereus处在地球的密近交汇区域, 轨道极不稳定.  相似文献   

11.
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   

12.
H. Scholl  F. Marzari 《Icarus》2005,175(2):397-408
In this paper we explore the dynamical stability of the Mars Trojan region applying mainly Laskar's Frequency Map Analysis. This method yields the chaotic diffusion rate of orbits and allows to determine the most stable regions. It also gives the frequencies which are responsible for the instability of orbits. The most stable regions are found for inclinations between about 15° and 30°. For inclinations smaller than 15°, we confirm, by applying a synthetic secular theory, that the secular resonances ν3, ν4, ν13, ν14 rapidly excite asteroid orbits within a few Myrs, or even faster. The asteroids are removed from the Trojan region after a close encounter with Mars. For large inclinations, the secular resonance ν5 clears a small region around 30° while the Kozai resonance rapidly removes bodies for inclinations larger than 35°. The dynamical lifetimes of the three L5 Trojans, (5261) Eureka, 1998 VF31, 2001 DH47, and the only L4 Trojan 1999 UJ7 are determined by numerically integrating clouds of corresponding clones over the age of the Solar System. All four Trojans reside in the most stable region with smallest diffusion coefficients. Their dynamical half-lifetime is of the order of the age of the Solar System. The Yarkovsky force has little effect on the known Trojans but for bodies smaller than about 1-5 m the drag is strong enough to destabilize Trojans on a timescale shorter than 4.5 Gyr.  相似文献   

13.
The orbits of 12 Trojan asteroids, which have Lyapunov times T L105 years and were previously classified as ASCs(=asteroids in stable chaos), are integrated for 50 Myrs, along with a group of neighbouring initial conditions for each nominal orbit. About 40% of the orbits present strong instabilities in the inclination, which may be attributed primarily to the action of the 16 secular resonance; two escapes are also recorded. Higher-order secular resonances, involving the nodes of the outer planets, are also found to be responsible for chaotic motion. Orbital stability depends critically on the choice of initial conditions and, thus, these objects can be regarded as being on the edge of strong chaos.  相似文献   

14.
Spectroscopic observations of Asteroid (4) Vesta and numerous members of the Vesta family located in the inner asteroid belt have determined that these objects have reflectance properties of basaltic material. A plausible hypothesis is that the surface of Vesta was punctured by large impacts in the past which dispersed fragments of its basaltic crust into space and produced one of the most prominent asteroid families ever created in the belt. Until recently, Vesta was the only known object in the asteroid belt which underwent differentiation and survived to the present epoch. Since 2000, many new small basaltic asteroids have been discovered in the inner and outer parts of the asteroid belt, possibly representing fragments from distinct differentiated bodies. These discoveries may help us to better understand the number and nature of objects in the inner Solar System that underwent geological differentiation. To investigate these issues we performed extensive numerical simulations whose aim was to reproduce, as precisely as possible, the dynamical evolution of Vesta's ejected fragments over timescales comparable to the family's age. Specifically, we numerically integrated the orbital evolution of 6600 test bodies with orbits that started within the Vesta family and dynamically evolved over 2 Gy. Our model included gravitational perturbation of all planets (except Mercury) and the Yarkovsky effect. The results show that a relatively large fraction of the original Vesta family members may have evolved out of the family borders defined by clustering algorithms and are now dispersed over the inner asteroid belt. We compared the orbital distribution of our model fragments with the orbital locations of known basaltic asteroids in various parts of the inner main belt to find that: (i) Most basaltic asteroids with semimajor axis located outside the Vesta family's borders in the inner main belt, including (809) Lundia and (956) Elisa, are most likely fugitives from the Vesta family that have evolved to their current orbits via various identified dynamical pathways. Our results also suggest that the Vesta family is at least ∼1 Gy old. (ii) Interestingly, orbits of many basaltic asteroids with , like those of (4796) Lewis and (5379) Abehiroshi, are displaced from the Vesta family to low inclinations and are not obtained in our simulations with sufficient efficiency. We propose that: (i) these small basaltic asteroids may be fragments of differentiated bodies other than (4) Vesta; or (ii) they were liberated from the Vesta's surface before (or during) the Late Heavy Bombardment epoch ∼3.8 Gy ago and their orbital inclinations separated from that of Vesta when secular resonances swept through the region.  相似文献   

15.
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   

16.
In this paper we present a comprehensive analysis of the dynamics in the region of the (3556) Lixiaohua asteroid family. The family lies in a particularly interesting region of the phase space, crossed by several two-body and three-body mean motion resonances. Also, members of this family can have close encounters with large asteroids, such as Ceres. We have identified the mean motion resonances which contribute to the long-term dynamical evolution of the family and our results confirm that the members of this family can be classified into a number of groups, exhibiting different dynamical behavior. We show for the first time that in the Lixiaohua region, apart from the chaotic diffusion in proper eccentricity and inclination (e p and I p ), there is at least one extended chaotic zone where several resonances overlap, thus giving rise to chaotic diffusion in proper semi-major axis (a p ) as well. Using a code of Monte Carlo type, we simulate the evolution of the family, according to the model which combines the chaotic diffusion (in a p , e p and I p ), Yarkovsky/YORP thermal effect and random walk in a p due to the close encounters with massive asteroids. These simulations show that all these effects should be taken into account in order to accurately explain the observed distribution of family members in the space of proper elements, although a “minimal” model that accounts for chaotic diffusion in (e p , I p ), Yarkovsky-induced drift in a p and random walk in a p due to the close encounters with the most massive asteroids is enough to grossly characterize the shape of the family.  相似文献   

17.
The 2/1 mean motion resonance with Jupiter, intersecting the main asteroid belt at ≈3.27  au, contains a small population of objects. Numerical investigations have classified three groups within this population: asteroids residing on stable orbits (i.e. Zhongguos), those on marginally stable orbits with dynamical lifetimes of the order of 100 Myr (i.e. Griquas), and those on unstable orbits. In this paper, we reexamine the origin, evolution and survivability of objects in the 2/1 population. Using recent asteroid survey data, we have identified 100 new members since the last search, which increases the resonant population to 153. The most interesting new asteroids are those located in the theoretically predicted stable island A, which until now had been thought to be empty. We also investigate whether the population of objects residing on the unstable orbits could be resupplied by material from the edges of the 2/1 resonance by the thermal drag force known as the Yarkovsky effect (and by the YORP effect, which is related to the rotational dynamics). Using N -body simulations, we show that test particles pushed into the 2/1 resonance by the Yarkovsky effect visit the regions occupied by the unstable asteroids. We also find that our test bodies have dynamical lifetimes consistent with the integrated orbits of the unstable population. Using a semi-analytical Monte Carlo model, we compute the steady-state size distribution of magnitude   H < 14  asteroids on unstable orbits within the resonance. Our results provide a good match with the available observational data. Finally, we discuss whether some 2/1 objects may be temporarily captured Jupiter-family comets or near-Earth asteroids.  相似文献   

18.
Rodney S Gomes 《Icarus》2003,161(2):404-418
I simulate the orbital evolution of the four major planets and a massive primordial planetesimal disk composed of 104 objects, which perturb the planets but not themselves. As Neptune migrates by energy and angular momentum exchange with the planetesimals, a large number of primordial Neptune-scattered objects are formed. These objects may experience secular, Kozai, and mean motion resonances that induce temporary decrease of their eccentricities. Because planets are migrating, some planetesimals can escape those resonances while in a low-eccentricity incursion, thus avoiding the return path to Neptune close encounter dynamics. In the end, this mechanism produces stable orbits with high inclination and moderate eccentricities. The population so formed together with the objects coming from the classical resonance sweeping process, originates a bimodal distribution for the Kuiper Belt orbits. The inclinations obtained by the simulations can attain values above 30° and their distribution resembles a debiased distribution for the high-inclination population coming from the real classical Kuiper Belt.  相似文献   

19.
The paper presents the results of a study of the dynamic structure of the orbital space of the navigation systems GLONASS and GPS. It is shown that the dynamic structure of the GLONASS region is determined by the action of one stable Lidov–Kozai secular resonance. The motion of almost all the retired objects of the GLONASS system is stable throughout the 100-year study period. In the GPS region, there is an orbital resonance and a large number of secular resonances. Their combined influence leads to a rapid increase in the eccentricity of the orbits of the retired objects of the system. Features of the dynamic structure of the orbital space are used to find the graveyard (parking) orbits of the retired objects of navigation systems.  相似文献   

20.
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.  相似文献   

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