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1.
N -body simulations are an important tool in the study of formation of large-scale structures. Much of the progress in understanding the physics of galaxy clustering and comparison with observations would not have been possible without N -body simulations. Given the importance of this tool, it is essential to understand its limitations as ignoring these can easily lead to interesting but unreliable results. In this paper, we study the limitations due to the finite size of the simulation volume. In an earlier work, we proposed a formalism for estimating the effects of a finite box size on physical quantities and applied it to estimate the effect on the amplitude of clustering, mass function. Here, we extend the same analysis and estimate the effect on skewness and kurtosis in the perturbative regime. We also test the analytical predictions from the earlier work as well as those presented in this paper. We find good agreement between the analytical models and simulations for the two-point correlation function and skewness. We also discuss the effect of a finite box size on relative velocity statistics and find the effects for these quantities scale in a manner that retains the dependence on the averaged correlation function . 相似文献
2.
Luis Floría 《Celestial Mechanics and Dynamical Astronomy》1997,68(1):75-85
We study the possibilities and limitations of the application of generalized Delaunay-like transformations (in the 6-dimensional
phase space) and TR-like mappings (in the 8-dimensional, extended phase space) to perturbed two-body problems with a time-varying
Keplerian parameter μ(t), that is, to Gylden-type systems. For the sake of theoretical completeness, both negative- and positive-energy
motion (with nonstationary coupling parameter) are, in principle, considered. Our developments are intended to introduce canonical
variables parallelling the classical ones of Delaunay and the Delaunay-Similar variables of Scheifele.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
3.
A.G.W. Cameron 《Icarus》1973,18(3):407-450
Particle accumulation processes are discussed for a variety of physical environments, ranging from the collapse phase of an interstellar cloud to the different parts of the models of the primitive solar nebula constructed by Cameron and Pine. Because of turbulence in the collapsing interstellar gas, it is concluded that interstellar grains accumulate into bodies with radii of a few tens of centimeters before the outer parts of the solar nebula are formed. These bodies can descend quite rapidly through the gas toward midplane of the nebula, and accumulation to planetary size can occur in a few thousand years. Substantial modifications of these processes take place in the outer convection zone of the solar nebula, but again it is concluded that bodies in that zone can grow to planetary size in a few thousand years.From the discussion of the interstellar collapse phase it is concluded that the angular momentum of the primitive solar nebula was predominantly of random turbulent origin, and that it is plausible that the primitive solar nebula should have possessed satellite nebulae in highly elliptical orbits. It is proposed that the comets were formed in these satellite nebulae.A number of other detailed conclusions are drawn from the analysis. It is shown to be plausible that an iron-rich planet should be formed in the inner part of the outer nebular convection zone. Discussions are given of the processes of planetary gas accretion, the formation of satellites, the T Tauri solar wind, and the dissipation of excess condensed material after the nebular gases have been removed by the T Tauri solar wind. It is shown that the present radial distances of the planets (but not Bode's Law) should be predicted reasonably well by a solar nebula model intermediate between the uniform and linear cases of Cameron and Pine. 相似文献
4.
We analyzed 134 images of Saturn taken by the Hubble Space Telescope between 1991 and 2004. The images cover wavelengths between 231 and 2370 nm in 30 filters. We combined some 10 million calibrated reflectivity measurements into 18,000 center-to-limb curves. We used the method of principal component analysis to find the main latitudinal and temporal variations in Saturn's atmosphere and their spectral characteristics. The first principal variation is a strong latitudinal variation of the aerosol optical depth in the upper troposphere. This structure shifts with Saturn's seasons, but the structure on small scales of latitude stays constant. The second principal variation is a variable optical depth of stratospheric aerosols. The optical depth is large at the poles and small at mid- and low latitudes with a steep gradient in-between. This structure remains essentially constant in time. The third principal variation is a variation in the tropospheric aerosol size, which has only shallow gradients with latitude, but large seasonal variations. Thus, aerosol sizes and their phase functions inferred at a particular season are not representative of Saturn's atmosphere at other seasons. Aerosols are largest in the summer and smallest in the winter. The fourth principal variation is a feature of the tropospheric aerosols with irregular latitudinal structure and fast variability, on the time scale of months. Spherical aerosols do not display the spectral characteristic of that feature. We suspect that variations in the shape of aerosols may play a role. We found a spectral feature of the imaginary index of aerosols, which darkens them near 400 nm wavelength. While we can describe Saturn's variations quite accurately, our presented model of Saturn's average atmosphere is still uncertain due to possible systematic offsets in methane absorption data and limitations of the knowledge about the shape of aerosols. In order to compare our results with those from comparable investigations, which used less than 30 filters, we fit models to spectral subsets of our data. We found very different best-fitting models, depending on the subset of filters, indicating a high sensitivity of results on the spectral sampling. 相似文献
5.
Cometary particles mainly consist of silicates and carbon compounds; they seem to be fluffy aggregates of tiny grains, as found in some IDPs. The linear polarization of the scattered light is an efficient method to characterize their physical properties. Laboratory simulations of light scattering by cometary analog particles help to disentangle different physical parameters by comparison with observational data. We present here polarization laboratory results with nine samples levitating particles: five samples of vapor-condensed magnesiosilica, one ferrosilica smoke, a mixture of magnesio-ferrosilica smokes, one mixture of ferrosilica with carbon and one mixture of magnesio-ferrosilica with carbon. The phase curves are bell-shaped with a maximum polarization at a phase range of (80°-100°). A shallow negative branch can be present at phase angles smaller than 20°. The different characteristics of the phase curves are discussed considering the size and the structure of the constituent grains and the size of the particles. For the five magnesiosilica samples, the maximum in polarization is in the 40% range (close to cometary values), and no wavelength dependence is detected; the negative branch, whose presence seems to be linked to the presence of large aggregates of fine silica (SiO2) grains, does not always exist. For the ferrosilica smoke, the maximum in polarization is about 30% in red light (632.8 nm) and 40% in green light (543.5 nm); the negative branch occurs for phase angles smaller than 20°. For the two mixtures with carbon black, the polarization spectral gradient is positive, as expected for cometary analog particles. Finally, the phase curves obtained for agglomerates of magnesio-ferrosilica and carbon (expected to be the main components of cometary particles) are comparable to those obtained by remote observations of dust in cometary comae. 相似文献
6.
Mariner 9 ultraviolet spectra of the 1971 dust clouds were analyzed to obtain the phase function times single scattering albedo of the dust particles. The phase functions were matched with Mie scattering calculations for size distributions of spheres of homogeneous and isotropic material. The absorption index of the dust particles was found to increase with decreasing wavelenght from 350 nm down to about 210 nm, and drop off shortward of this wavelength. A structural shoulder occurs in the absorption spectrum between 240 and 250 nm. Titanium dioxide (anatase) has the correct transitions at 210 and 250 nm to match the absorption curve of Martian dust, and is proposed as a candidate constituent in Martian surface material. The spectral neutrality of TiO2 between 0.5 and 4 μm is consistent with visible and infrared observations of Mars. The high refractive index of TiO2 can explain the large refringence of Martian dust. The titanium dioxide content of the dust particles is estimated to be a few percent or less. Uncertainties in the results due to limitations in the model and data are discussed. 相似文献
7.
Christian Wolf 《Monthly notices of the Royal Astronomical Society》2009,397(1):520-533
We combine in a single framework the two complementary benefits of χ2 template fits and empirical training sets used e.g. in neural nets: χ2 is more reliable when its probability density functions (PDFs) are inspected for multiple peaks, while empirical training is more accurate when calibration and priors of query data and training set match. We present a χ2 empirical method that derives PDFs from empirical models as a subclass of kernel regression methods, and apply it to the Sloan Digital Sky Survey Data Release 5 sample of >75 000 quasi-stellar objects, which is full of ambiguities. Objects with single-peak PDFs show <1 per cent outliers, rms redshift errors <0.05 and vanishing redshift bias. At z > 2.5 , these figures are two times better. Outliers result purely from the discrete nature and limited size of the model, and rms errors are dominated by the intrinsic variety of object colours. PDFs classed as ambiguous provide accurate probabilities for alternative solutions and thus weights for using both solutions and avoiding needless outliers. E.g. the PDFs predict 78.0 per cent of the stronger peaks to be correct, which is true for 77.9 per cent of them. Redshift incompleteness is common in faint spectroscopic surveys and turns into a massive undetectable outlier risk above other performance limitations, but we can quantify residual outlier risks stemming from size and completeness of the model. We propose a matched χ2 error scale for noisy data and show that it produces correct error estimates and redshift distributions accurate within Poisson errors. Our method can easily be applied to future large galaxy surveys, which will benefit from the reliability in ambiguity detection and residual risk quantification. 相似文献
8.
Wudalianchi volcanic field, located in northeast China, consists of 14 Quaternary volcanoes with each volcano as a steep-sided scoria cone surrounded by gently sloping lava flows. Each cone is topped with a bowl-shaped or funnel-shaped crater. The volcanic cones are constructed by the accumulation of tephra and other ejecta. In this paper, their geologic features have been investigated and compared with some Martian volcanic features at Ascraeus Mons volcanoes observed on images obtained from High-Resolution Imaging Science Experiments (HiRISE), Mars Orbiter Camera (MOC), Context Imager (CTX) and Thermal Emission Imaging System (THEMIS). The results show that both Wudalianchi and Ascraeus Mons volcanoes are basaltic, share similar eruptive and geomorphologic features and eruptive styles, and have experienced multiple eruptive phases, in spite of the significant differences in their dimension and size. Both also show a variety of eruptive styles, such as fissure and central venting, tube-fed and channel-fed lava flows, and probably pyroclastic deposits. Three volcanic events are recognized at Ascraeus Mons, including an early phase of shield construction, a middle eruptive phase forming a low lava shield, and the last stage with aprons mantling both NE and SW flanks. We suggest that magma generation at both Wudalianchi and Ascraeus Mons might have been facilitated by an upwelling mantle plume or upwelling of asthenospheric mantle, and a deep-seated fault zone might have controlled magma emplacement and subsequent eruptions in Ascraeus Mons as observed in the Wudalianchi field, where the volcanoes are constructed along the northeast-striking faults. Fumarolic cones produced by water/magma interaction at the Wudalianchi volcanic field may also serve as an analogue for the pseudocraters identified at Isidis and Cerberus Planitia on Mars, suggesting existence of frozen water in the ground on Mars during Martian volcanic eruptions. 相似文献
9.
Sanaz Vahidinia Jeffrey N. Cuzzi Matt Hedman Bruce Draine Roger N. Clark Ted Roush Gianrico Filacchione Philip D. Nicholson Robert H. Brown Bonnie Buratti Christophe Sotin 《Icarus》2011,215(2):682-694
We present models of the near-infrared (1-5 μm) spectra of Saturn’s F ring obtained by Cassini’s Visual and Infrared Mapping Spectrometer (VIMS) at ultra-high phase angles (177.4-178.5°). Modeling this spectrum constrains the size distribution, composition, and structure of F ring particles in the 0.1-100 μm size range. These spectra are very different from those obtained at lower phase angles; they lack the familiar 1.5 and 2 μm absorption bands, and the expected 3 μm water ice primary absorption appears as an unusually narrow dip at 2.87 μm. We have modeled these data using multiple approaches. First, we use a simple Mie scattering model to constrain the size distribution and composition of the particles. The Mie model allows us to understand the overall shapes of the spectra in terms of dominance by diffraction at these ultra-high phase angles, and also to demonstrate that the 2.87 μm dip is associated with the Christiansen frequency of water ice (where the real refractive index passes unity). Second, we use a combination of Mie scattering with Effective Medium Theory to probe the effect of porous (but structureless) particles on the overall shape of the spectrum and depth of the 2.87 μm band. Such simple models are not able to capture the shape of this absorption feature well. Finally, we model each particle as an aggregate of discrete monomers, using the Discrete Dipole Approximation (DDA) model, and find a better fit for the depth of the 2.87 μm feature. The DDA models imply a slightly different overall size distribution. We present a simple heuristic model which explains the differences between the Mie and DDA model results. We conclude that the F ring contains aggregate particles with a size distribution that is distinctly narrower than a typical power law, and that the particles are predominantly crystalline water ice. 相似文献
10.
Matthew J. Genge Matthias van Ginneken Martin D. Suttle Ralph P. Harvey 《Meteoritics & planetary science》2018,53(10):2051-2066
We report the discovery of a large accumulation of micrometeorites (MMs) in a supraglacial moraine at Larkman Nunatak in the Grosvenor Mountains of the Transantarctic Range in Antarctica. The MMs are present in abundances of ~600 particles kg−1 of moraine sediment and include a near-complete collection of MM types similar to those observed in Antarctic blue ice and within bare-rock traps in the Antarctic. The size distribution of the observed particles is consistent with those collected from snow collections suggesting the moraine has captured a representative collection of cosmic spherules with significant loss of only the smallest particles (<100 μm) by wind. The presence of microtektites with compositions similar to those of the Australasian strewn field suggests the moraine has been accumulating for 780 ka with dust-sized debris. On the basis of this age estimate, it is suggested that accumulation occurs principally through ice sublimation. Direct infall of fines is suggested to be limited by snow layers that act as barriers to accumulation and can be removed by wind erosion. MM accumulation in many areas in Antarctica, therefore, may not be continuous over long periods and can be subject to climatic controls. On the basis of the interpretation of microtektites as Australasian, Larkman Nunatak deposit is the oldest known supraglacial moraine and its survival through several glacial maxima and interglacial periods is surprising. We suggest that stationary ice produced by the specific ice flow conditions at Larkman Nunatak explains its longevity and provides a new type of record of the East Antarctic ice sheet. 相似文献
11.
We study the collimation of radio jets in the high-luminosity Fanaroff–Riley class II sources by examining the dependence of the sizes of hotspots and knots in the radio jets on the overall size of the objects for a sample of compact steep-spectrum (CSS) and larger-sized objects. The objects span a wide range in overall size from about 50 pc to nearly 1 Mpc. The mean size of the hotspots increases with the source size during the CSS phase, which is typically taken to be about 20 kpc, and the relationship flattens for the larger sources. The sizes of the knots in the compact as well as the larger sources are consistent with this trend. We discuss possible implications of these trends. We find that the hotspot closer to the nucleus or core component tends to be more compact for the most asymmetric objects where the ratio of separations of the hotspots from the nucleus r d >2. These highly asymmetric sources are invariably CSS objects, and their location in the hotspot size ratio–separation ratio diagram is possibly the result of their evolution in an asymmetric environment. We also suggest that some sources, especially of lower luminosity, exhibit an asymmetry in the collimation of the oppositely directed radio jets. 相似文献
12.
In this paper, we characterize the morphology of the disk-integrated phase functions of satellites and rings around the giant planets of our solar system. We find that the shape of the phase function is accurately represented by a logarithmic model [Bobrov, M.S., 1970. Physical properties of Saturn's rings. In: Dollfus, A. (Ed.), Surfaces and Interiors of Planets and Satellites. Academic, New York, pp. 376-461]. For practical purposes, we also parametrize the phase curves by a linear-exponential model [Kaasalainen, S., Muinonen, K., Piironen, J., 2001. Comparative study on opposition effect of icy solar system objects. Journal of Quantitative Spectroscopy and Radiative Transfer 70, 529-543] and a simple linear-by-parts model [Lumme, K., Irvine, W.M., 1976. Photometry of Saturn's rings. Astronomical Journal 81, 865-893], which provides three morphological parameters: the amplitude A and the half-width at half-maximum (HWHM) of the opposition surge, and the slope S of the linear part of the phase function at larger phase angles.Our analysis demonstrates that all of these morphological parameters are correlated with the single-scattering albedos of the surfaces.By taking more accurately into consideration the finite angular size of the Sun, we find that the Galilean, Saturnian, Uranian and Neptunian satellites have similar HWHMs (?0.5°), whereas they have a wide range of amplitudes A. The Moon has the largest HWHM (∼2°). We interpret that as a consequence of the “solar size bias”, via the finite angular size of the Sun which varies dramatically from the Earth to Neptune. By applying a new method that attempts to morphologically deconvolve the phase function to the solar angular size, we find that icy and young surfaces, with active resurfacing, have the smallest values of A and HWHM, whereas dark objects (and perhaps older surfaces) such as the Moon, Nereid and Saturn's C ring have the largest A and HWHM.Comparison between multiple objects also shows that solar system objects belonging to the same planet have comparable opposition surges. This can be interpreted as a “planetary environmental effect” that acts to locally modify the regolith and the surface properties of objects which are in the same environment. 相似文献
13.
J. S. Bagla Nishikanta Khandai 《Monthly notices of the Royal Astronomical Society》2009,396(4):2211-2227
Cosmological N -body simulations are used for a variety of applications. Indeed progress in the study of large-scale structures and galaxy formation would have been very limited without this tool. For nearly 20 yr the limitations imposed by computing power forced simulators to ignore some of the basic requirements for modelling gravitational instability. One of the limitations of most cosmological codes has been the use of a force softening length that is much smaller than the typical interparticle separation. This leads to departures from collisionless evolution that is desired in these simulations. We propose a particle-based method with an adaptive resolution where the force softening length is reduced in high-density regions while ensuring that it remains well above the local interparticle separation. The method, called the Adaptive TreePM (ATreePM), is based on the TreePM code. We present the mathematical model and an implementation of this code, and demonstrate that the results converge over a range of options for parameters introduced in generalizing the code from the TreePM code. We explicitly demonstrate collisionless evolution in collapse of an oblique plane wave. We compare the code with the fixed resolution TreePM code and also an implementation that mimics adaptive mesh refinement methods and comment on the agreement and disagreements in the results. We find that in most respects the ATreePM code performs at least as well as the fixed resolution TreePM in highly overdense regions, from clustering and number density of haloes to internal dynamics of haloes. We also show that the adaptive code is faster than the corresponding high-resolution TreePM code. 相似文献
14.
We have made numerical experiments of the collisional and gravitational interaction of a planetesimal swarm in the early Solar System. In particular we study the dynamical evolution of an initial population of kilometer-size planetesimals subject to collisions (accretion, rebound, cratering, and catastrophic fragmentation). This study is based on a Monte-Carlo statistical method and provides the mass and velocity distributions of the planetesimal swarm as a function of time as well as their distribution in heliocentric distance. Several experiments have been performed and three of them are presented here. They simulate the accretional growth of numerous planetesimals in the absence (or presence) of gaseous drag, with (or without) one larger embryo among them, and with (or without) a size gradient. The results show that (i) for a population of planetesimals submitted to a negative gradient in size as the heliocentric distance increases, the outer planetesimals spiral toward the Sun faster than inner ones, leading after some time to an accumulation of bodies inside the cloud which allows the formation of an embryo; (ii) the growth of one embryo among a population of planetesimals is accelerated by the presence of gas and is warranted as long as its feeding zone is fed by the inward flow of planetesimals due to gas drag. These results offer some complementary new insights in the understanding of the accretional formation of 4–5 terrestrial planets instead of the numerous Moon-size planets generally found in numerical experiments. 相似文献
15.
Tropospheric limitations in phase and frequency coordinate measurements in astronomy 总被引：1，自引：0，他引：1
In the framework of power-model of the structure function, the tropospheric limitations of accuracy of coordinate measurements, using phase and fringe frequency are shown. The general formulae, numerical estimates and a comparison between absolute and differential methods are given. It is shown that the tropospheric limitations are especially considerable for coordinate measurements, using fringe frequency. 相似文献
16.
Internal layers in ice masses can be detected with ice-penetrating radar. In a flowing ice mass, each horizon represents a past surface that has been subsequently buried by accumulation, and strained by ice flow. These layers retain information about relative spatial patterns of accumulation and ablation (mass balance). Internal layers are necessary to accurately infer mass-balance patterns because the ice-surface shape only weakly reflects spatial variations in mass balance. Additional rate-controlling information, such as the layer age, the ice temperature, or the ice-grain sizes and ice-crystal fabric, can be used to infer the absolute rate of mass balance. To infer mass balance from the shapes of internal layers, we solve an inverse problem. The solution to the inverse problem is the best set or sets of unknown boundary conditions or initial conditions that, when used in our calculation of ice-surface elevation and internal-layer shape, generate appropriate predictions of observations that are available. We also show that internal layers can be used to infer martian paleo-surface topography from a past era of ice flow, even though the topography may have been largely altered by subsequent erosion. We have successfully inferred accumulation rates and surface topography from internal layers in Antarctica. Using synthetic data, we demonstrate the ability of this method to solve the corresponding inverse problem to infer accumulation and ablation rates, as well as the surface topography, for martian ice. If past ice flow has affected the shapes of martian internal layers, this method is necessary to infer the spatial pattern and rate of mass balance. 相似文献
17.
A study was made to see how much information could be extracted from the Mariner 9 Mars isophotes taken at a phase angle of ～60°. We found that the Minneart functions and both isotropic and Rayleigh scattering could easily be ruled out, and that it was essential to use forward-peaked phase functions, which were computed from Mie theory. We could achieve isophotes similar to those observed assuming a semi-infinite dust cloud with a considerable variation in particle properties and size distribution, so long as the ratio of the multiply to singly scattered light was held within certain limits. These conditions are met by micron-sized, moderately absorbing mineral grains whose mean size should not be much larger than a micron. It was also found that a dust cloud of finite optical thickness bounded from below by a Lambert ground would fit the isophote data. 相似文献
18.
We present a method for retrieving the wavefront phase and estimating the point spread function using data from a single imaging
channel. The method involves a set of short exposures and its speckle reconstruction of the observed object, and a parameterized
point spread function model which is used in order to estimate the wavefront phase and the point spread function from the
data. Estimates of the wavefront phase and the point spread function are computed by minimizing an error function with the
method of simulated annealing. Results of tests with simulated data and with real data are shown. We conclude that the proposed
technique provides reliable estimates of the instantaneous point spread function and is robust against noise. 相似文献
19.
We present results from pulsar observations using the Giant Metrewave Radio Telescope (GMRT) as a phased array with infield phasing. The antennas were kept in phase throughout the observation by applying antenna based phase corrections derived from visibilities that were obtained in parallel with the phased array beam data, and which were flagged and calibrated in real time using a model for the continuum emission in the target field. We find that, as expected, the signal to noise ratio (SNR) does not degrade with time. In contrast observations in which the phasing is done only at the start of the observation show a clear degradation of the SNR with time. We find that this degradation is well fit by a function of the form SNR\((\tau ) = \alpha + \beta e^{-(\tau /\tau _{0})^{5/3}}\), which corresponds to the case where the phase drifts are caused by Kolmogorov type turbulence in the ionosphere. We also present general formulae (i.e. including the effects of correlated sky noise, imperfect phasing and self noise) for the SNR and synthesized beam size for phased arrays (as well as corresponding formulae for incoherent arrays). These would be useful in planning observations with large array telescopes. 相似文献
20.
We present a kinetic model of a disk of solid particles, orbiting a primary and experiencing inelastic collisions. In distinction to other collisional models that use a 2D (mass-semimajor axis) binning and perform a separate analysis of the velocity (eccentricity, inclination) evolution, we choose mass and orbital elements as independent variables of a phase space. The distribution function in this space contains full information on the combined mass, spatial, and velocity distributions of particles. A general kinetic equation for the distribution function is derived, valid for any set of orbital elements and for any collisional outcome, specified by a single kernel function. The first implementation of the model utilizes a 3D phase space (mass-semimajor axis-eccentricity) and involves averages over the inclination and all angular elements. We assume collisions to be destructive, simulate them with available material- and size-dependent scaling laws, and include collisional damping. A closed set of kinetic equations for a mass-semimajor axis-eccentricity distribution is written and transformation rules to usual mass and spatial distributions of the disk material are obtained. The kinetic “core” of our approach is generic. It is possible to add inclination as an additional phase space variable, to include cratering collisions and agglomeration, dynamical friction and viscous stirring, gravity of large perturbers, drag forces, and other effects into the model. As a specific application, we address the collisional evolution of the classical population in the Edgeworth-Kuiper belt (EKB). We run the model for different initial disk's masses and radial profiles and different impact strengths of objects. Our results for the size distribution, collisional timescales, and mass loss are in agreement with previous studies. In particular, collisional evolution is found to be most substantial in the inner part of the EKB, where the separation size between the survivors over EKB's age and fragments of earlier collisions lies between a few and several tens of km. The size distribution in the EKB is not a single Dohnanyi-type power law, reflecting the size dependence of the critical specific energy in both strength and gravity regimes. The net mass loss rate of an evolved disk is nearly constant and is dominated by disruption of larger objects. Finally, assuming an initially uniform distribution of orbital eccentricities, we show that an evolved disk contains more objects in orbits with intermediate eccentricities than in nearly circular or more eccentric orbits. This property holds for objects of any size and is explained in terms of collisional probabilities. The effect should modulate the eccentricity distribution shaped by dynamical mechanisms, such as resonances and truncation of perihelia by Neptune. 相似文献