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1.
Slow and Fast Diffusion in Asteroid-Belt Resonances: A Review 总被引：1，自引：0，他引：1
S. Ferraz-Mello 《Celestial Mechanics and Dynamical Astronomy》1999,73(1-4):25-37
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. 相似文献
2.
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. 相似文献
3.
S. Ferraz-Mello T. A. Michtchenko D. Nesvorný F. Roig A. Simula 《Planetary and Space Science》1998,46(11-12)
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
4.
F. Cachucho P. M. Cincotta S. Ferraz-Mello 《Celestial Mechanics and Dynamical Astronomy》2010,108(1):35-58
The theory of diffusion in many-dimensional Hamiltonian system is applied to asteroidal dynamics. The general formulation
developed by Chirikov is applied to the Nesvorny-Morbidelli analytic model of three-body (three-orbit) mean-motion resonances
(Jupiter-Saturn-asteroid). In particular, we investigate the diffusion along and across the separatrices of the (5, −2, −2) resonance of the (490) Veritas asteroidal family and their relationship to diffusion
in semi-major axis and eccentricity. The estimations of diffusion were obtained using the Melnikov integral, a Hadjidemetriou-type
sympletic map and numerical integrations for times up to 108 years. 相似文献
5.
We review theoretical and numerical results obtained for secular resonant motion in the asteroidal belt. William's theory (1969) yields the locations of the principal secular resonances 5, 6, and 16 in the asteroidal belt. Theories by Nakai and Kinoshita (1985) and by Yoshikawa (1987) allow us to model the basic features of orbital evolution at the secular resonances 16 and 6, respectively. No theory is available for the secular resonance v5. Numerical experiments by Froeschlé and Scholl yield quantitative and new qualitative results for orbital evolutions at the three principal secular resonances 5, 6, and 16. These experiments indicate possible chaotic motion due to overlapping resonances. A secular resonance may overlap with another secular resonance or with a mean motion resonance. The role of the secular resonances as possible sources of meteorites is discussed. 相似文献
6.
Both the Poynting-Robertson drag and resonant orbits appear to be very important for the motion of small grains in the early solar system. While orbital resonances are very often stable and tend to force bodies into noncircular orbits, the Poynting-Robertson drag produces secular variations in the semimajor axis and tends to circularize the orbits. We study numerically the competition between the Poynting-Robertson drag and the gravitational interaction of grains with Jupiter near the 2/1 resonance. Computations are based on the plane-restricted problem. Numerical investigations show that the grains always cross the resonance region without any oscillation, except in the special case where the grains were initially inside the resonance. In both cases the variations of the osculating elements exhibit a drastic step, which can be explained by Greenberg's and Schubart's theories. 相似文献
7.
Yi-Sui Sun Ji-Lin Zhou Tian-Ling Zhang Chong-Qing Cheng 《Celestial Mechanics and Dynamical Astronomy》1994,59(4):313-325
For the 3 : 1 Jovian resonance problem, the time scales of the two degrees of freedom of the resonant Hamiltonian are well-separated [5]. With the adiabatic approximation, the solution for the fast oscillations can be found in terms of the slowly varying variables. Thus the rapidly oscillating terms in the slow oscillation equations can be treated as forced terms. We refer to the resonance between the forcing and intrinsic frequencies as a forced secondary one in this paper. We discuss the forced secondary resonances in asteroidal motion at the 3 : 1 commensurability by using Wisdom's method. The results show that the orbits situated originally near the resonance will leave the neighbourhood of resonance and tend to the separatrices and critical points for different energies, respectively. We have not found any stochastic web as expected in this case. Moreover, we study the problem of validity on the approximation of a system.The Project Supported by the National Natural Science Foundation of China. 相似文献
8.
Jacques Henrard 《Celestial Mechanics and Dynamical Astronomy》1996,64(1-2):107-114
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
9.
Bálint érdi Renáta Rajnai Zsolt Sándor Emese Forgács-Dajka 《Celestial Mechanics and Dynamical Astronomy》2012,113(1):95-112
Third and fourth order mean motion resonances are studied in the model of the restricted three-body problem by numerical methods for mass parameters corresponding approximately to the Sun?CJupiter and Sun?CNeptune systems. In the case of inner resonances, it is shown that there are two regions of libration in the 8:5 and 7:4 resonances, one at low, the other at high eccentricities. In the 9:5 and 7:3 resonances libration can exist only in one region at high eccentricities. The 5:2 and 4:1 resonances are very regular, with one librational zone existing for all eccentricities. There is no visible region of libration at any eccentricities in the 5:1 resonance, the transition between the regions of direct and retrograde circulation is very sharp. In the case of outer resonances, the 8:5 and 7:4 resonances have also two regions of libration, but the 9:5 resonance has three, the 7:3 resonance two librational zones. The 5:2 resonance is again very regular, but it is parted for two regions of libration at high eccentricities. Libration is possible in the 4:1 resonance only at high eccentricities. The 5:1 resonance is very symmetric. In the case of outer resonances, a comparison is made with trans-Neptunian objects (TNO) in higher order mean motion resonances. Several new librating TNOs are identified. 相似文献
10.
T.A. Heppenheimer 《Icarus》1975,26(3):367-376
This paper examines two proposed mechanisms whereby asteroidal collisions and close approaches may have given rise to the Kirkwood Gaps. The first hypothesis is that asteroids in near-resonant orbits have markedly increased collision probabilities and so are preferentially destroyed, or suffer decay in population density, within the resonance zones. A simple order-of-magnitude analysis shows that this hypothesis is untenable since it leads to conclusions which are either unrealistic or not in accord with present understanding of asteroidal physics.The second hypothesis is the Brouwer-Jefferys theory that collisions would smooth an asteroidal distribution function, as a function of Jacobi constant, thus forming resonance gaps. This hypothesis is examined by direct numerical integration of 50 asteroid orbits near the 2:1 resonance, with collisions simulated by random variables. No tendency to form a gap was observed. 相似文献
11.
George W. Wetherill 《Meteoritics & planetary science》1985,20(1):1-22
The orbital evolution of asteroidal fragments with diameters ranging from 10 cm to 20 km, injected into the 3:1 Kirkwood gap at 2.50 A.U., has been investigated using Monte Carlo techniques. It is assumed that this material can become Earth-crossing on a time scale of 106 years, as a result of a chaotic zone discovered by Wisdom, associated with the 3:1 resonance. This phenomenon, as well as close encounter planetary perturbations, the v6 secular resonance, and the ablative effects of the Earth's atmosphere are included in the determination of the orbital characteristics of meteorites impacting the Earth derived by fragmentation of this asteroidal material. It is found that the predicted meteorite orbits closely match those found for observed ordinary chondrites, and the total flux is in approximate agreement with the observed fall rate of ordinary chondrites. About 10% of the predicted impacting bodies are meteorite-size bodies originating directly from the asteroid belt. The remainder are obtained by subsequent fragmentation of larger (～1 m to 20 km diameter) Earth-crossing asteroidal fragments. The largest of these fragments are observable as Apollo-Amor objects. Thus the apparent paradox between the orbital characteristics of observed ordinary chondrites and those predicted from Apollo object sources is reconciled. Both appear to be complementary aspects of the same phenomena. No other asteroidal resonance is found to be satisfactory as a source of ordinary chondrites. These meteorites are therefore most likely to be derived from S asteroids in this limited region of the asteroidal belt, the largest of which are 11 Parthenope, 17 Thetis, and 29 Amphitrite. 相似文献
12.
William K. Hartmann Paolo Farinella David Vokrouhlický Stuart J. Weidenschilling Alessandro Morbidelli Francesco Marzari Donald R. Davis Eileen Ryan 《Meteoritics & planetary science》1999,34(Z4):A161-A167
Abstract— We give a nonmathematical review of recent work regarding the Yarkovsky effect on asteroidal fragments. This effect may play a critical, but underappreciated, role in delivering meteorites to Earth. Two variants of the effect cause drifts in orbital elements, notably semimajor axes. The “classic” or “diurnal” Yarkovsky effect is associated with diurnal rotation at low obliquity. More recently, a “seasonal” effect has also been described, associated with high obliquity. Studies of these Yarkovsky effects are combined with studies of resonance effects to clarify meteorite delivery. If there were no Yarkovsky drift, asteroid fragments could reach a resonance only if produced very near that resonance. However, objects in resonances typically reach Earth-crossing orbits within a few million years, which is inconsistent with stone meteorites' cosmic-ray exposure (CRE) ages (5–50 Ma) and iron meteorites' CRE ages (100–1000 Ma). In the new view, on the other hand, large objects in the asteroid belt are “fixed” in semimajor axis, but bodies up to 100 m in diameter are in a constant state of mixing and flow, especially if the thermal conductivity of their surface layers is low. Thus, small asteroid fragments may reach the resonances after long periods of drift in the main belt. Yarkovsky drift effects, combined with resonance effects, appear to explain many meteorite properties, including: (1) the long CRE ages of iron meteorites (due to extensive drift lifetimes in the belt); (2) iron meteorites' sampling of numerous parent bodies; (3) the shorter CRE ages of most stone meteorites (due to faster drift, coupled with weaker strength and more rapid collisional erosion); and (4) the abundance of falls from discrete impact events near resonances, such as the 8 Ma CRE age of H chondrites. Other consequences include: the delivery of meteorite parent bodies to resonances is enhanced; proportions of stone and iron meteorites delivered to Earth may be different from the proportions at the same sizes left in the belt, which in turn may differ from the ratio produced in asteroidal collisions; Rabinowitz's 10–100 m objects may be preferentially delivered to near-Earth space; and the delivery of C-class fragments from the outer belt may be inhibited, compared to classes in other parts of the belt. Thus, Yarkovsky effects may have important consequences in meteoritics and asteroid science. 相似文献
13.
We present results from a suite of N-body simulations that follow the formation and accretion history of the terrestrial planets using a new parallel treecode that we have developed. We initially place 2000 equal size planetesimals between 0.5 and 4.0 AU and the collisional growth is followed until the completion of planetary accretion (>100 Myr). A total of 64 simulations were carried out to explore sensitivity to the key parameters and initial conditions. All the important effect of gas in laminar disks are taken into account: the aerodynamic gas drag, the disk-planet interaction including Type I migration, and the global disk potential which causes inward migration of secular resonances as the gas dissipates. We vary the initial total mass and spatial distribution of the planetesimals, the time scale of dissipation of nebular gas (which dissipates uniformly in space and exponentially in time), and orbits of Jupiter and Saturn. We end up with 1-5 planets in the terrestrial region. In order to maintain sufficient mass in this region in the presence of Type I migration, the time scale of gas dissipation needs to be 1-2 Myr. The final configurations and collisional histories strongly depend on the orbital eccentricity of Jupiter. If today’s eccentricity of Jupiter is used, then most of bodies in the asteroidal region are swept up within the terrestrial region owing to the inward migration of the secular resonance, and giant impacts between protoplanets occur most commonly around 10 Myr. If the orbital eccentricity of Jupiter is close to zero, as suggested in the Nice model, the effect of the secular resonance is negligible and a large amount of mass stays for a long period of time in the asteroidal region. With a circular orbit for Jupiter, giant impacts usually occur around 100 Myr, consistent with the accretion time scale indicated from isotope records. However, we inevitably have an Earth size planet at around 2 AU in this case. It is very difficult to obtain spatially concentrated terrestrial planets together with very late giant impacts, as long as we include all the above effects of gas and assume initial disks similar to the minimum mass solar nebular. 相似文献
14.
F. MarzariH. Scholl 《Icarus》2002,159(2):328-338
We have numerically explored the mechanisms that destabilize Jupiter's Trojan orbits outside the stability region defined by Levison et al. (1997, Nature385, 42-44). Different models have been exploited to test various possible sources of instability on timescales on the order of ∼108 years.In the restricted three-body model, only a few Trojan orbits become unstable within 108 years. This intrinsic instability contributes only marginally to the overall instability found by Levison et al.In a model where the orbital parameters of both Jupiter and Saturn are fixed, we have investigated the role of Saturn and its gravitational influence. We find that a large fraction of Trojan orbits become unstable because of the direct nonresonant perturbations by Saturn. By shifting its semimajor axis at constant intervals around its present value we find that the near 5:2 mean motion resonance between the two giant planets (the Great Inequality) is not responsible for the gross instability of Jupiter's Trojans since short-term perturbations by Saturn destabilize Trojans, even when the two planets are far out of the resonance.Secular resonances are an additional source of instability. In the full six-body model with the four major planets included in the numerical integration, we have analyzed the effects of secular resonances with the node of the planets. Trojan asteroids have relevant inclinations, and nodal secular resonances play an important role. When a Trojan orbit becomes unstable, in most cases the libration amplitude of the critical argument of the 1:1 mean motion resonance grows until the asteroid encounters the planet. Libration amplitude, eccentricity, and nodal rate are linked for Trojan orbits by an algebraic relation so that when one of the three parameters is perturbed, the other two are affected as well. There are numerous secular resonances with the nodal rate of Jupiter that fall inside the region of instability and contribute to destabilize Trojans, in particular the ν16. Indeed, in the full model the escape rate over 50 Myr is higher compared to the fixed model.Some secular resonances even cross the stability region delimited by Levison et al. and cause instability. This is the case of the 3:2 and 1:2 nodal resonances with Jupiter. In particular the 1:2 is responsible for the instability of some clones of the L4 Trojan (3540) Protesilaos. 相似文献
15.
Three resonances, the 3:2 exterior mean motion resonance with Neptune, Kozai resonance and 1:1 super resonance, are known to govern concurrently the stability of the motion of Pluto. We explore numerically the resonance zones in which the three resonance coexist. There might exist plutinos with relatively large masses in these zones. Considering that Pluto's perturbation is important to the long-term evolution of plutinos, the resonance zone is mainly explored in the mirror region of Pluto, which is a mirror image of the region around Pluto with respect to the invariant plane of the solar system. We find six resonance zones in the mirror region. The orbit elements at the centers of the six zones and the corresponding heliocentric distances, longitudes and latitudes on July 1, 2003 have been computed and listed for the reference of observation. 相似文献
16.
Miquel Grau Guillermo González-Casado 《Celestial Mechanics and Dynamical Astronomy》1998,72(3):169-186
A comparative study of the evolution of the Sun–Jupiter–Asteroid system near the 4:1 and 7:2 resonances is performed by means
of two techniques that proceed differently from the Hamiltonian corresponding to the planar restricted elliptic three-body
problem. One technique is based on the classical Schubart averaging while the other is based on a mapping method in which
the perturbing part of the Hamiltonian is expanded and the resulting terms are ordered according to a weight function that
depends on the powers of eccentricities and the coefficients of the terms. For the mapping method the effect of Saturn on
the asteroidal evolution is introduced and the degree of chaos is estimated by means of the Lyapunov time. Both methods are
shown to lead to similar results and can be considered a suitable tool for describing the evolution of asteroids in the Kirkwood
gap and the group corresponding to the 4:1 and 7:2 Jovian resonances, respectively.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
17.
- Introduction and Survey. The method for studying the structure and evolution of the solar system is discussed. It is pointed out that theories that account for the origin of planets alone are basically insufficient. Instead one ought to aim for a general theory for the formation of secondary bodies around a central body, applicable both to planet and satellite formation. A satisfactory theory should not start from assumed properties of the primitive Sun, which is a very speculative subject, but should be based on an analysis of present conditions and a successive reconstruction of the past states.
- Orbits of Planets and Satellites. As a foundation for the subsequent analysis, the relevant properties of planets and satellites are presented.
- The Small Bodies. The motion of small bodies is influenced by non-gravitational forces. Collisions (viscosity) are of special importance for the evolution of the orbits. It is pointed out that the focusing property of a gravitational field (which has usually been neglected) leads to the formation of jet streams. The importance of this concept for the understanding of the comet-meteoroid relations and the structure of the asteroidal belt is shown.
- Resonance Structure. A survey is given of the resonances in the solar system and their possible explanation. It is concluded that in many cases the resonances must already be produced at the times when the bodies formed. It is shown that resonance effects put narrow limits on the post-accretional changes of orbits.
- Spin and Tides. Tidal effects on planetary spins and satellite orbits are discussed. It is very doubtful if any satellite except the Moon and possibly Triton has had its orbit changed appreciably by tidal effects. The isochronism of planetary and asteroidal spins is discussed, as well as its bearing on the accretional process.
- Post-accretional Changes in the Solar System. The stability of the solar system and upper limits for changes in orbital and spin data are examined. It is concluded that much of the present dynamic structure has direct relevance to the primordial processes.
18.
W. -H. IP 《Astrophysics and Space Science》1976,42(1):L1-L3
From a comparison of the 2:1 and 3:2 resonances (in the asteroidal belt) two possible explanations to the absence of 3:2 apocentric librators are suggested. The first one is that such 3:2 resonant motion is dynamically unstable. The second interpretation requires the absence of nearcircular orbits originally at 4 AU. The latter view, if correct, is inconsistent with cosmogonic models which predict the original orbits of the asteroids to be nearly circular. 相似文献
19.
R. de la Fuente Marcos C. de la Fuente Marcos 《Monthly notices of the Royal Astronomical Society》2008,388(1):293-306
Jiang & Yeh proposed gas-drag-induced resonant capture as a mechanism able to explain the dominant 3:2 resonance observed in the trans-Neptunian belt. Using a model of a disc–star–planet system they concluded that gaseous drag in a protoplanetary disc can trap trans-Neptunian object (TNO) embryos into the 3:2 resonance rather easily although it could not trap objects into the 2:1 resonance. Here we further investigate this scenario using numerical simulations within the context of the planar restricted four-body problem by including both present-day Uranus and Neptune. Our results show that mean motion and corotation resonances are possible and trapping into both the 3:2 and 2:1 resonances as well as other resonances is observed. The associated corotation centres may easily form larger planetesimals from smaller ones. Corotation resonances evolve into pure Lindblad resonances in a time-scale of 0.5 Myr. The non-linear corotation and mean motion resonances produced are very size selective. The 3:2 resonance is dominant for submetric particles but for larger particles the 2:1 resonance is stronger. In summary, our calculations show that confined chaotic motion around the resonances not only increases trapping efficiency but also the orbital eccentricities of the trapped material, modifying the relative abundance of trapped particles in different resonances. If we assume a more compact planetary system, instead of using the present-day values of the orbital elements of Uranus and Neptune, our results remain largely unchanged. 相似文献
20.
John Hadjidemetriou George Voyatzis 《Celestial Mechanics and Dynamical Astronomy》2000,78(1-4):137-150
A comparative study is made between the 2/1 and the 3/2 resonant asteroid motion, with the aim to understand their different behaviour (gap in the 2/1 resonance, group in the 3/2 resonance). A symplectic mapping model is used, for each of these two resonances, assuming the asteroid is moving in the three-dimensional space under the gravitational perturbation of Jupiter. It is found that these resonances differ in several points, and although there is, in general, more chaos in the phase space close to the 3/2 resonance, even in the model of circular orbit of Jupiter, there are regions, close to the secondary resonances, which are less chaotic in the 3/2 resonance compared to the 2/1 resonance, and consequently trapping can take place. 相似文献