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1.
We present results from a large suite of simulations of Saturn’s dense A and B rings using a new model of particle sticking in local simulations (Perrine, R.P., Richardson, D.C., Scheeres, D.J. [2011]. Icarus 212, 719–735). In this model, colliding particles can be incorporated into or help fragment rigid aggregations on the basis of certain user-specified parameters that can represent van der Waals forces or interlocking surface frost layers.Our investigation is motivated by laboratory results that show that interpenetration of surface layers can allow impacting frost-covered ice spheres to stick together. In these experiments, cohesion only occurs below specific impact speeds, which happen to be characteristic of impact speeds in Saturn’s rings. Our goal is to determine if weak bonding is consistent with ring observations, to constrain cohesion parameters in light of existing ring observations, to make predictions about particle populations throughout the rings, and to discover other diagnostics that may constrain bonding parameters.We considered the effects of five parameters on the equilibrium characteristics of our ring simulations: speed-based merge and fragmentation limits, bond strength, ring surface density, and patch orbital distance (i.e., the A or B ring), some with both monodisperse and polydisperse comparison cases. In total, we present data from 95 simulations.We find that weak cohesion is consistent with observations of the A and B rings (e.g., French, R.G., Nicholson, P.D. [2000]. Icarus 145, 502–523), and we present a range of simulation parameters that reproduce the observed size distribution and maximum particle size. It turns out that the parameters that match observations differ between the A and B rings, and we discuss the potential implications of this result. We also comment on other observable consequences of cohesion for the rings, such as optical depth and scale height effects, and discuss whether very large objects (e.g., “propeller” source objects) are grown bottom-up from cohesion of smaller ring particles. 相似文献
2.
The sizes, composition, and number of particles comprising the rings of Saturn may be meaningfully constrained by a combination of radar- and radio-astronomical observations. In a previous paper, we have discussed constraints obtained from radar observations. In this paper, we discuss the constraints imposed by complementary “passive” radio observations at similar wavelengths. First, we present theoretical models of the brightness of Saturn's rings at microwave wavelengths (0.34–21.0 cm), including both intrinsic ring emission and diffuse scattering by the rings of the planetary emission. The models are accurate simulations of the behavior of realistic ring particles and are parameterized only by particle composition and size distribution, and ring optical depth. Second, we have reanalyzed several previously existing sets of interferometric observations of the Saturn system at 0.83-, 3.71-, 6.0-, 11.1-, and 21.0-cm wavelengths. These observations all have spatial resolution sufficient to resolve the rings and planetary disk, and most have resolution sufficient to resolve the ring-occulted region of the disk as well. Using our ring models and a realistic model of the planetary brightness distribution, we are able to establish improved constraints on the properties of the rings. In particular, we find that: (a) the maximum optical depth in the rings is ～ 1.5 ± 0.3 referred to visible wavelengths; (b) a significant decrease in ring optical depth from λ3.7 to λ21.0 cm allows us to rule out the possibility that more than ～30% of the cross section of the rings is composed of particles larger than a meter or so; this assertion is essentially independent of uncertainties in particle adsorption coefficient; and (c) the ring particles cannot be primarily of silicate composition, independently of particle size, and the particles cannot be primarily smaller than ～0.1 cm, independently of composition. 相似文献
3.
The Voyager spacecraft discovered that small moons orbit within all four observed ring systems coincident with the discovery of narrow and dusty rings around Jupiter, Saturn, Uranus and Neptune. These moons can provide the source for new rings if they are catastrophically disrupted by a comet or large meteoroid impact. This hypothesis for ring origins provides a natural mechanism for the ongoing creation of planetary rings. While it relieves somewhat the problem of explaining the continued existence of rings with apparently short evolutionary lifetimes, it raises the problem of explaining the continued existence of small moons, and the coexistence of moons and rings at comparable locations within the Roche zones of the giant planets. This problem has been studied in some detail recently, and the present work is a review of our current understanding of the processes in satellite disruption that pertain to the creation of planetary rings and the collisional cascade of circumplanetary bodies. Significant progress has been made. Narrow rings are produced by disruption of small moons in numerical simulations, and a self-consistent model of the collisional cascade can explain present-day moon populations. Absolute timescales and initial moon populations remain uncertain due to our poor knowledge of the impactor population and uncertainties in the strength of planetary satellites. More pressing are the qualitative issues that remain to be resolved including the nature of reaccretion of the debris and the origin of Saturn's rings. 相似文献
4.
Naomi Murdoch Patrick Michel Derek C. Richardson Kerstin Nordstrom Christian R. Berardi Simon F. Green Wolfgang Losert 《Icarus》2012,219(1):321-335
Surfaces of planets and small bodies of our Solar System are often covered by a layer of granular material that can range from a fine regolith to a gravel-like structure of varying depths. Therefore, the dynamics of granular materials are involved in many events occurring during planetary and small-body evolution thus contributing to their geological properties.We demonstrate that the new adaptation of the parallel N-body hard-sphere code pkdgrav has the capability to model accurately the key features of the collective motion of bidisperse granular materials in a dense regime as a result of shaking. As a stringent test of the numerical code we investigate the complex collective ordering and motion of granular material by direct comparison with laboratory experiments. We demonstrate that, as experimentally observed, the scale of the collective motion increases with increasing small-particle additive concentration.We then extend our investigations to assess how self-gravity and external gravity affect collective motion. In our reduced-gravity simulations both the gravitational conditions and the frequency of the vibrations roughly match the conditions on asteroids subjected to seismic shaking, though real regolith is likely to be much more heterogeneous and less ordered than in our idealised simulations. We also show that collective motion can occur in a granular material under a wide range of inter-particle gravity conditions and in the absence of an external gravitational field. These investigations demonstrate the great interest of being able to simulate conditions that are to relevant planetary science yet unreachable by Earth-based laboratory experiments. 相似文献
5.
Three-dimensional numerical simulations show that large-scale latent heating resulting from condensation of water vapor can produce multiple zonal jets similar to those on the gas giants (Jupiter and Saturn) and ice giants (Uranus and Neptune). For plausible water abundances (3-5 times solar on Jupiter/Saturn and 30 times solar on Uranus/Neptune), our simulations produce ∼20 zonal jets for Jupiter and Saturn and 3 zonal jets on Uranus and Neptune, similar to the number of jets observed on these planets. Moreover, these Jupiter/Saturn cases produce equatorial superrotation whereas the Uranus/Neptune cases produce equatorial subrotation, consistent with the observed equatorial-jet direction on these planets. Sensitivity tests show that water abundance, planetary rotation rate, and planetary radius are all controlling factors, with water playing the most important role; modest water abundances, large planetary radii, and fast rotation rates favor equatorial superrotation, whereas large water abundances favor equatorial subrotation regardless of the planetary radius and rotation rate. Given the larger radii, faster rotation rates, and probable lower water abundances of Jupiter and Saturn relative to Uranus and Neptune, our simulations therefore provide a possible mechanism for the existence of equatorial superrotation on Jupiter and Saturn and the lack of superrotation on Uranus and Neptune. Nevertheless, Saturn poses a possible difficulty, as our simulations were unable to explain the unusually high speed (∼) of that planet’s superrotating jet. The zonal jets in our simulations exhibit modest violations of the barotropic and Charney-Stern stability criteria. Overall, our simulations, while idealized, support the idea that latent heating plays an important role in generating the jets on the giant planets. 相似文献
6.
We have performed 8 numerical simulations of the final stages of accretion of the terrestrial planets, each starting with over 5× more gravitationally interacting bodies than in any previous simulations. We use a bimodal initial population spanning the region from 0.3 to 4 AU with 25 roughly Mars-mass embryos and an equal mass of material in a population of ∼1000 smaller planetesimals, consistent with models of the oligarchic growth of protoplanetary embryos. Given the large number of small planetesimals in our simulations, we are able to more accurately treat the effects of dynamical friction during the accretion process. We find that dynamical friction can significantly lower the timescales for accretion of the terrestrial planets and leads to systems of terrestrial planets that are much less dynamically excited than in previous simulations with fewer initial bodies. In addition, we study the effects of the orbits of Jupiter and Saturn on the final planetary systems by running 4 of our simulations with the present, eccentric orbits of Jupiter and Saturn (the EJS simulations) and the other 4 using a nearly circular and co-planar Jupiter and Saturn as predicted in the Nice Model of the evolution of the outer Solar System [Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466-469; Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461; Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462-465] (the CJS simulations). Our EJS simulations provide a better match to our Solar System in terms of the number and average mass of the final planets and the mass-weighted mean semi-major axis of the final planetary systems, although increased dynamical friction can potentially improve the fit of the CJS simulations as well. However, we find that in our EJS simulations, essentially no water-bearing material from the outer asteroid belt ends up in the final terrestrial planets, while a large amount is delivered in the CJS simulations. In addition, the terrestrial planets in the EJS simulations receive a late veneer of material after the last giant impact event that is likely too massive to reconcile with the siderophile abundances in the Earth's mantle, while the late veneer in the CJS simulations is much more consistent with geochemical evidence. 相似文献
7.
Saturn’s diffuse E ring consists of many tiny (micron and sub-micron) grains of water ice distributed between the orbits of Mimas and Titan. Various gravitational and non-gravitational forces perturb these particles’ orbits, causing the ring’s local particle density to vary noticeably with distance from the planet, height above the ring-plane, hour angle and time. Using remote-sensing data obtained by the Cassini spacecraft in 2005 and 2006, we investigate the E-ring’s three-dimensional structure during a time when the Sun illuminated the rings from the south at high elevation angles (>15°). These observations show that the ring’s vertical thickness grows with distance from Enceladus’ orbit and its peak brightness density shifts from south to north of Saturn’s equator plane with increasing distance from the planet. These data also reveal a localized depletion in particle density near Saturn’s equatorial plane around Enceladus’ semi-major axis. Finally, variations are detected in the radial brightness profile and the vertical thickness of the ring as a function of longitude relative to the Sun. Possible physical mechanisms and processes that may be responsible for some of these structures include solar radiation pressure, variations in the ambient plasma, and electromagnetic perturbations associated with Saturn’s shadow. 相似文献
8.
We constructed new models of Saturn with an allowance made for a helium mass fraction of ～0.18–0.25 in its atmosphere. Our modeling shows that the composition of Saturn differs markedly from the solar composition; more specifically, during its formation, the planet was ～11–15 planetary masses short of the hydrogen-helium component. Saturn, as well as the other giant planets, must have been formed according to Schmidt’s scenario, through the formation of embryonic nuclei, rather than according to Laplace’s scenario. The masses of the embryonic nuclei themselves lie within the range (3.5–8) M⊕. We calculated a theoretical free-oscillation spectrum for our models of Saturn, each of which fits all of the available observational data. The results of our calculations are presented graphically and in tables. Of particular interest are the diagnostic potentialities of the discontinuity gravitational modes related to density jumps in the molecular envelope of Saturn and at the interface between its molecular and metallic envelopes. When observational data appear, our results can be used both to identify the observed modes and to improve the models themselves. We discuss some of the cosmogonical aspects associated with the formation of the giant planets. 相似文献
9.
The giant planetary magnetospheres surrounding Jupiter and Saturn respond in quite different ways, compared to Earth, to changes in upstream solar wind conditions. Spacecraft have visited Jupiter and Saturn during both solar cycle minima and maxima. In this paper we explore the large-scale structure of the interplanetary magnetic field (IMF) upstream of Saturn and Jupiter as a function of solar cycle, deduced from solar wind observations by spacecraft and from models. We show the distributions of solar wind dynamic pressure and IMF azimuthal and meridional angles over the changing solar cycle conditions, detailing how they compare to Parker predictions and to our general understanding of expected heliospheric structure at 5 and 9 AU. We explore how Jupiter’s and Saturn’s magnetospheric dynamics respond to varying solar wind driving over a solar cycle under varying Mach number regimes, and consider how changing dayside coupling can have a direct effect on the nightside magnetospheric response. We also address how solar UV flux variability over a solar cycle influences the plasma and neutral tori in the inner magnetospheres of Jupiter and Saturn, and estimate the solar cycle effects on internally driven magnetospheric dynamics. We conclude by commenting on the effects of the solar cycle in the release of heavy ion plasma into the heliosphere, ultimately derived from the moons of Jupiter and Saturn. 相似文献
10.
11.
《Planetary and Space Science》1999,47(10-11):1201-1210
New models of Jupiter are based on observational data provided by the Galileo spaceprobe, which considerably improved previously existing estimates of the helium abundance in the atmosphere of Jupiter. These data yield for Jupiter’s atmosphere 20% of the solar oxygen abundance and do not agree with the results of the analysis of the collision of comet Shoemaker-Levy 9 with Jupiter (10 times the solar value). Therefore, both the models of Jupiter with water-depleted and water-enriched atmosphere are considered. By analogy with Jupiter, trial models of Saturn with a water-depleted external envelope are also developed. The molecular-metallic phase transition pressure of hydrogen Pm was taken to be 1.5, 2 and 3 Mbar. Since Saturn’s internal molecular envelope is noticeably enriched in the IR-component (its weight concentration, 0.25–0.30, being by a factor of 3–4 higher than in Jupiter), the phase transition pressure in Saturn can be lower than in Jupiter. In the constructed models, the IR-core masses are 3–3.5 M⊕ for Jupiter and 3–5.5 M⊕ for Saturn. Jupiter’s and Saturn’s IR-cores can be considered embryos onto which the accretion of the gas occurred during the formation of the planets. The mass of the hydrogen–helium component dispersed in the zone of planetary formation constitutes ≈2–5 planetary masses for Jupiter and ≈11–14 planetary masses for Saturn. 相似文献
12.
《Icarus》1998,132(1):113-124
We present results of two-dimensional gravitationalN-body simulations of the late stage of planetary formation. This stage is characterized by the direct accretion of hundreds of lunar-sized planetesimals into planetary bodies. Our simulation code is based on the Hermite Individual Timestep integration algorithm, and gravitational interactions among all bodies are included throughout the simulations. We compare our simulation with earlier works that do not include all interactions, and we find very good agreement. A previously published collisional fragmentation model is included in our simulation to study the effects of the production of fragments on the subsequent evolution of the larger planetary bodies. It is found that for realistic two-body collisions that, according to this model, both bodies will suffer fragmentation, and that the outcome of the collision will be a relatively large core containing most of the mass and a few small fragments. We present the results of simulations that include this simple fragmentation model. They indicate that the presence of small fragments have only a small effect on the growth or orbital evolution of the large planet-sized bodies. 相似文献
13.
《Icarus》1987,71(1):115-136
The Jovian and Uranian rings exist within severe energetic particle and plasma environments where magnetosphere-related losses of small ring particles and surface reflectance alteration by sputtering are likely to be important. In contrast, the main Saturnian rings exist within a zone where magnetospheric losses and surface alteration effects are negligible, primarily because of solid-body absorption of inwardly diffusing magnetospheric particles. It is shown here that solid-body absorption of radially diffusing ions is a much more efficient process in the inner Saturnian magnetosphere than in the inner Jovian and Uranian magnetospheres because of the near axial symmetry of the planetary magnetic field with respect to the rotational equatorial plane. This is especially true for continuous rings (as opposed to satellites) for which the approximate time scale against absorption is the particle bounce period in an axially symmetric field, whereas it is the particle drift period in an asymmetric field. Assuming comparable diffusion rates, inward transport of magnetospheric particles is much more strongly inhibited in the inner Saturnian magnetosphere than in the inner magnetospheres of Jupiter and Uranus. This remains true when only rings of comparable widths and optical depths are considered (e.g., the F ring at Saturn and the ϵ ring at Uranus). The most extreme possible consequence of this difference in solid-body absorption efficiency may have been the preferential development of a radially extensive, optically thick ring system at Saturn where magnetospheric losses are minimized in comparison to those at Jupiter and Uranus. A more definite consequence is that the Uranian rings are most probably directly exposed to nearly the same proton fluxes measured at Voyager 2's closest approach. Exposure of ring particle surfaces to radiation belt ion fluxes therefore remains as a viable explanation for the low albedos of the Uranian rings. 相似文献
14.
《Icarus》1987,70(3):506-516
We present 2.7-mm interferometric observations of Saturn made near opposition in June 1984 and June 1985, when the ring opening angle was 19° and 23°, respectively. By combining the data sets we produce brightness maps of Saturn and its rings with a resolution of 6″. The maps show flux from the ring ansae, and are the first direct evidence of ring flux in the 3-mm wavelength region. Modelfits to the visibility data yield a disk brightness temperature of 156 ± 5°K, a combined A, B, and C ring brightness temperature of 19 ± 3°K, and a combined a ring cusp (region of the rings which block the planet's disk) brightness temperature of 85 ± 5°K. These results imply a normal-to-the-ring optical depth for the combined ABC ringof 0.31 ± 0.04, which is nearly the same value found for wavelenghts from the UV to 6 cm. About 6°K of the ring flux is attributed to scattered planetary emission, leaving an intrinsic thermal component of ∼13°K. These results, together with the ring particle size distributions found by the Voyager radio occultation experiments, are consistent with the idea that the ring particles are composed chiefly of water ice. 相似文献
15.
Hypothesis of possible superconductivity of the iced matter of the rings of Saturn (based on the data of Voyager and Pioneer
space missions) allow us to explain many phenomena which have not been adequately understood earlier. Introducing into planetary
physics force of magnetic levitation of the superconducting iced particle of the rings, which interact with magnetosphere
of the planet, becomes to be possible to explain origin, evolution, and dynamics of the rings; to show how the consequent
precipitation of the rings’ matter upon the planet was concluded; how the rings began their rotation; how they were compressed
by the magnetic field into the thin disc, and how this disc was fractured into hundreds of thousands of separated rings; why
in the ring B do exist “spokes”; why magnetic field lines have distortion near by ring F; why there is a variable azimuth brightness of the ring A; why the rings reflected radio waves so efficiently; why exists strong electromagnetic radiation of the rings in the 20.4
kHz–40.2 MHz range and Saturnian kilometric radiation; why there is anomalous reflection of circularly polarized microwaves;
why there are spectral anomalies of the thermal radiation of the rings; why the matter of the various rings does not mix but
preserves its small-scale color differences; why there is an atmosphere of unknown origin nearby the rings of Saturn; why
there are waves of density and bending waves within Saturn’s rings; why planetary rings in the solar system appear only after
the Belt of Asteroids (and may be the Belt of Asteroids itself is a ring for the Sun); why our planet Earth has no rings of
its own. 相似文献
16.
E. Pilat-Lohinger P. Robutel Á. Süli F. Freistetter 《Celestial Mechanics and Dynamical Astronomy》2008,102(1-3):83-95
We present a continuation of our numerical study on planetary systems with similar characteristics to the Solar System. This time we examine the influence of three giant planets on the motion of terrestrial-like planets in the habitable zone (HZ). Using the Jupiter–Saturn–Uranus configuration we create similar fictitious systems by varying Saturn’s semi-major axis from 8 to 11 AU and increasing its mass by factors of 2–30. The analysis of the different systems shows the following interesting results: (i) Using the masses of the Solar System for the three giant planets, our study indicates a maximum eccentricity (max-e) of nearly 0.3 for a test-planet placed at the position of Venus. Such a high eccentricity was already found in our previous study of Jupiter–Saturn systems. Perturbations associated with the secular frequency g 5 are again responsible for this high eccentricity. (ii) An increase of the Saturn-mass causes stronger perturbations around the position of the Earth and in the outer HZ. The latter is certainly due to gravitational interaction between Saturn and Uranus. (iii) The Saturn-mass increased by a factor 5 or higher indicates high eccentricities for a test-planet placed at the position of Mars. So that a crossing of the Earth’ orbit might occur in some cases. Furthermore, we present the maximum eccentricity of a test-planet placed in the Earth’ orbit for all positions (from 8 to 11 AU) and masses (increased up to a factor of 30) of Saturn. It can be seen that already a double-mass Saturn moving in its actual orbit causes an increase of the eccentricity up to 0.2 of a test-planet placed at Earth’s position. A more massive Saturn orbiting the Sun outside the 5:2 mean motion resonance (a S ≥9.7 AU) increases the eccentricity of a test-planet up to 0.4. 相似文献
17.
Eugene E. Epstein Michael A. Janssen Jeffrey N. Cuzzi William G. Fogarty John Mottmann 《Icarus》1980,41(1):103-118
We have used 3-mm Saturn observations, obtained from 1965 through 1977 and with Jupiter as a reference, to derive a ring brightness temperature of 18 ± 8°K. Thebrightness temperature of the disk of Saturn is 156 ± 9° K. Part of the ring brightness (≈62K) may be accounted for as disk emission which is scattered from the rings; the remainder (12 ± 8° K we attributed to ring particle thermal emission. Because this thermal component brightness temperatures is so much less than the particle physical temperature, limits are placed on the mean size and composition of the ring particles. In particular, as found by others, the particles cannot be rocky, but must be either metallic or composed of extremely low-loss dielectric material such as water ice. If the particles are pure water ice, for example, then a simple slab model and a multiple-scattering model both give upper limits to the particle sizes of ≈ 1 m, a value three times smaller than previously available. The multiple-scattering model gives a particle single-scattering albedo at 3 mm of 0.83±0.13. 相似文献
18.
This paper deals with Oort cloud formation while the Sun was in an embedded cluster and surrounded by its primordial nebula. This work is a continuation of Brasser et al. [Brasser, R., Duncan, M., Levison, H., 2006. Icarus 184, 59-82], building on the model presented therein, and adding the aerodynamic drag and gravitational potential of the primordial solar nebula. Results are presented of numerical simulations of comets subject to the gravitational influence of the Sun, Jupiter, Saturn, star cluster and primordial solar nebula; some of the simulations included the gravitational influence of Uranus and Neptune as well. The primordial solar nebula was approximated by the minimum-mass Hayashi model [Hayashi, C., Nakozawa, K., Nakagawa, Y., 1985. In: Black, D.C., Matthews, M.S. (Eds.). Protostars and Planets II. Univ. of Arizona Press, Tucson, AZ] whose inner and outer radii have been truncated at various distances from the Sun. A comet size of 1.7 km was used for most of our simulations. In all of our simulations, the density of the primordial solar nebula decayed exponentially with an e-folding time of 2 Myr. It turns out that when the primordial solar nebula extends much beyond Saturn or Neptune, virtually no material will end up in the Oort cloud (OC) during this phase. Instead, the majority of the material will be on circular orbits inside of Jupiter if the inner edge of the disk is well inside Jupiter's orbit. If the disk's inner edge is beyond Jupiter's orbit, most comets end up on orbits in exterior mean-motion resonances with Saturn when Uranus and Neptune are not present. In those cases where the outer edge of the disk is close to Saturn or Neptune, the fraction of material that ends up in the subsequently formed OC is much less than that found in Brasser et al. [Brasser, R., Duncan, M., Levison, H., 2006. Icarus 184, 59-82] for the same cluster densities. This implies that for comets of roughly 2 km in size, the presence of the primordial solar nebula hinders OC formation. A byproduct of some of our simulations are endresults with a substantial fraction of the comets in the Uranus-Neptune scattered disk. A subsequent followup of this material is planned for the near future. In order to determine the effect of the size of the comets on OC formation efficiency, a set of runs with the same initial conditions but different cometary radii have been performed as well, from which it is determined that the threshold comet size to begin producing significant Oort clouds is roughly 20 km. This implies that the presence of the primordial solar nebula acts as a size-sorting mechanism, with large bodies unaffected by the gas drag and ending up in the OC while small bodies remain trapped in the planetary region, in the models studied. 相似文献
19.
《Chinese Astronomy and Astrophysics》2022,46(4):346-390
The 1:1 mean motion resonance may be referred to as the lowest order mean motion resonance in restricted or planetary three-body problems. The five well-known libration points of the circular restricted three-body problem are five equilibriums of the 1:1 resonance. Coorbital motion may take different shapes of trajectory. In case of small orbital eccentricities and inclinations, tadpole-shape and horseshoe-shape orbits are well-known. Other 1:1 libration modes different from the elementary ones can exist at moderate or large eccentricities and inclinations. Coorbital objects are not rare in our solar system, for example the Trojans asteroids and the coorbital satellite systems of Saturn. Recently, dozens of coorbital bodies have been identified among the near-Earth asteroids. These coorbital asteroids are believed to transit recurrently between different 1:1 libration modes mainly due to orbital precessions, planetary perturbations, and other possible effects. The Hamiltonian system and the Hill’s three-body problem are two effective approaches to study coorbital motions. To apply the perturbation theory to the Hamiltonian system, standard procedures involve the development of the disturbing function, averaging and normalization, theory of ideal resonance model, secular perturbation theory, etc. Global dynamics of coorbital motion can be revealed by the Hamiltonian approach with a suitable expansion. The Hill’s problem is particularly suitable for the studies on the relative motion of two coorbital bodies during their close encounter. The Hill’s equation derived from the circular restricted three-body problem is well known. However, the general Hill’s problem whose equation of motion takes exactly the same form applies to the non-restricted case where the mass of each body is non-negligible, namely the planetary case. The Hill’s problem can be transformed into a “canonical shape” so that the averaging principle can be applied to construct a secular perturbation theory. Besides the two analytical theories, numerical methods may be consulted, for example the approach of periodic orbit, the surface of section, and the computation of invariant manifolds carried by equilibriums or periodic orbits. 相似文献
20.
Long-period (LP) comets, Halley-type (HT) comets, and even some comets of the Jupiter family, probably come from the Oort cloud, a huge reservoir of icy bodies that surrounds the solar system. Therefore, these comets become important probes to learn about the distant Oort cloud population. We review the fundamental dynamical properties of LP comets, and what is our current understanding of the dynamical mechanisms that bring these bodies from the distant Oort cloud region to the inner planetary region. Most new comets have original reciprocal semimajor axes in the range2 × 10-5 < 1/aorig < 5 × 10-5AU-1. Yet, this cannot be taken to represent the actual space distribution of Oort cloud comets, but only the region in the energy space in which external perturbers have the greatest efficiency in bringing comets to the inner planetary region. The flux of Oort cloud comets in the outer planetary region is found to be at least several tens times greater than the flux in the inner planetary region. The sharp decrease closer to the Sun is due to the powerful gravitational fields of Jupiter and Saturn that prevent most Oort cloud comets from reaching the Earth’s neighborhood (they act as a dynamical barrier). A small fraction of ～10-2 Oort cloud comets become Halley type (orbital periods P < 200 yr), and some of them can reach short-period orbits with P < 20 yr. We analyze whether we can distinguish the latter, very ‘old” LP comets, from comets of the Jupier family coming from the Edgeworth-Kuiper belt. 相似文献