共查询到20条相似文献，搜索用时 15 毫秒
1.
S. J. Aarseth 《Astrophysics and Space Science》1971,14(1):118-132
A fourth-order polynomial method for the integration ofN-body systems is described in detail together with the computational algorithm. Most particles are treated efficiently by an individual time-step scheme but the calculation of close encounters and persistent binary orbits is rather time-consuming and is best performed by special techniques. A discussion is given of the Kustaanheimo-Stiefel regularization procedure which is used to integrate dominant two-body encounters as well as close binaries. Suitable decision-making parameters are introduced and a simple method is developed for regularizing an arbitrary number of simultaneous two-body encounters. 相似文献
2.
We deal with the problem of a zero mass body oscillating perpendicular to a plane in which two heavy bodies of equal mass orbit each other on Keplerian ellipses. The zero mass body intersects the primaries plane at the systems barycenter. This problem is commonly known as theSitnikov Problem. In this work we are looking for a first integral related to the oscillatory motion of the zero mass body. This is done by first expressing the equation of motion by a second order polynomial differential equation using a Chebyshev approximation techniques. Next we search for an autonomous mapping of the canonical variables over one period of the primaries. For that we discretize the time dependent coefficient functions in a certain number of Dirac Delta Functions and we concatenate the elementary mappings related to the single Delta Function Pulses. Finally for the so obtained polynomial mapping we look for an integral also in polynomial form. The invariant curves in the two dimensional phase space of the canonical variables are investigated as function of the primaries eccentricity and their initial phase. In addition we present a detailed analysis of the linearized Sitnikov Problem which is valid for infinitesimally small oscillation amplitudes of the zero mass body. All computations are performed automatically by the FORTRAN program SALOME which has been designed for stability considerations in high energy particle accelerators. 相似文献
3.
Zdeněk Kopal 《Astrophysics and Space Science》1983,93(1):149-175
The aim of the present paper will be to establish the explicit form of the equations which govern the internal structure of stars rotating with constant angular velocity formulated in terms of Clairaut coordinates (cf. Kopal, 1980) in which the radial coordinate is replaced by the total potential, which for equilibrium configurations remains constant over distorted level surfaces. The introductory Section 1 contains an account of previous work on rotating stars, commencing with Milne (1923), von Zeipel (1924) and Chandrasekhar (1933), who all employed orthogonal coordinates for their analysis. In Section 2 we shall apply to this end the curvilinear Clairaut coordinates introduced already in our previous work (cf. Kopal, 1980, 1981); and although these are not orthogonal, this disadvantage is more than offset by the fact that, in their terms, the fundamental equation of our problem will assume the form of ordinary differential equations, subject to very simple boundary conditions. The explicit form of these equations — exact to terms of fourth order in surficial distortion caused by centrifugal force—will be obtained in Section 3; while in the concluding Section 4 these will be particularized (for the sake of comparison with work of previous investigators) to stars of initially polytropic structure. These will prove to be much simpler in Clairaut coordinates than they were in any previously used frame of reference. Lastly, in Appendix A we shall present the explicit forms, in Clairaut coordinates, of the differential operators which were needed to establish the results given in Sections 3–4; while Appendix B will summarize other auxiliary algebraic relations of which use was made to formulate our fourth-order theory developed in Section 3. 相似文献
4.
Massimo Giovannozzi 《Celestial Mechanics and Dynamical Astronomy》1997,68(2):177-192
We study the stability domain of generic 2D area-preserving polynomialdiffeomorphisms. The starting point of our analysis is the study of thedistribution of stable and unstable fixed points. We show that the locationof fixed points and their stability type are linked to the degree of thepolynomial map. These results are based on a classification Theorem forplane automorphisms by Friedland and Milnor. Then we discuss the problem ofdetermining the domain in phase space where stable motion occurs. We showthat the boundary of the stability domain is given by the invariantmanifolds emanating from the outermost unstable fixed point of low period(one or two). This fact extends previous results obtained for reversiblearea-preserving polynomial maps of the plane. This analysis is based onanalytical arguments and is supported by the results of numericalsimulations. 相似文献
5.
We present sixth- and eighth-order Hermite integrators for astrophysical N-body simulations, which use the derivatives of accelerations up to second-order (snap) and third-order (crackle). These schemes do not require previous values for the corrector, and require only one previous value to construct the predictor. Thus, they are fairly easy to implement. The additional cost of the calculation of the higher-order derivatives is not very high. Even for the eighth-order scheme, the number of floating-point operations for force calculation is only about two times larger than that for traditional fourth-order Hermite scheme. The sixth-order scheme is better than the traditional fourth-order scheme for most cases. When the required accuracy is very high, the eighth-order one is the best. These high-order schemes have several practical advantages. For example, they allow a larger number of particles to be integrated in parallel than the fourth-order scheme does, resulting in higher execution efficiency in both general-purpose parallel computers and GRAPE systems. 相似文献
6.
We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of
the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where often
the information contained in the observations allows only to compute, by interpolation, two angular positions of the observed
body and their time derivatives at a given epoch; we call this set of data attributable. Given two attributables of the same body at two different epochs we can use the energy and angular momentum integrals of
the two-body problem to write a system of polynomial equations for the topocentric distance and the radial velocity at the
two epochs. We define two different algorithms for the computation of the solutions, based on different ways to perform elimination
of variables and obtain a univariate polynomial. Moreover we use the redundancy of the data to test the hypothesis that two
attributables belong to the same body (linkage problem). It is also possible to compute a covariance matrix, describing the uncertainty of the preliminary orbits which results
from the observation error statistics. The performance of this method has been investigated by using a large set of simulated
observations of the Pan-STARRS project. 相似文献
7.
Having formulated the Clairaut second-order differential equations up to the fourth order in superficial distortion due to Hensen's coefficients in the previous article (El-Sharawyet al., 1989 III, hereafter denotes by SM3), we are now in a position to solve them. In this paper we shall discuss the methods of solving the Clairaut theory, to give an explicit form about the distortion of the surfaces of Jupiter and Saturn, numerically up to the fourth-order. 相似文献
8.
We calculate the rate at which dark matter haloes merge to form higher mass systems. Two complementary derivations using Press–Schechter theory are given, both of which result in the same equation for the formation rate. First, a derivation using the properties of the Brownian random walks within the framework of Press–Schechter theory is presented. We then use Bayes' theorem to obtain the same result from the standard Press–Schechter mass function. The rate obtained is shown to be in good agreement with results from Monte Carlo and N -body simulations. We illustrate the usefulness of this formula by calculating the expected cosmological evolution in the rate of star formation that is due to short-lived, merger-induced starbursts. The calculated evolution is well-matched to the observed evolution in ultraviolet luminosity density, in contrast to the lower rates of evolution that are derived from semi-analytic models that do not include a dominant contribution from starbursts. Hence we suggest that the bulk of the observed ultraviolet starlight at z >1 arises from merger-induced starbursts. Finally, we show that a simple merging-halo model can also account for the bulk of the observed evolution in the comoving quasar space density. 相似文献
9.
Size distributions of chondrules and dispersed droplets caused by liquid breakup: An application to shock wave conditions in the solar nebula 总被引：1，自引：0，他引：1
We present the results of an aerodynamic liquid dispersion experiment using initially molten silicate samples. We investigate the threshold of breakup and the size distribution of dispersed droplets. The breakup threshold is consistent with the previous experiments using water and a mixture of water and glycerol. Also, we confirm the previous results that the size distributions of dispersed droplets are represented by an exponential form and that the characteristic size of dispersed droplets is related to the dynamic pressure of high-velocity gas flow. The size distribution has a similar form to that of chondrules, though the experiment is not exactly corresponding to the shock heating models for chondrule formation that consider solid precursors which are molten by the shocks. The experimental results indicate that, if liquid chondrule-precursors were dispersed by high-velocity flow, the dynamic pressure of the flow is ∼10 kPa. A chondrule formation condition in a shock-wave heating model suggests that this pressure can be realized at the regions within ∼1 AU in the minimum solar-nebula mass models. However, if the nebula had a larger mass and gravitational instabilities occurred, this pressure may be realized in the spiral arms at 2-3 AU and chondrules may be formed in asteroid belt. 相似文献
10.
Rolando Dünner Pablo A. Araya rés Meza † Andreas Reisenegger 《Monthly notices of the Royal Astronomical Society》2006,366(3):803-811
According to the latest evidence, the Universe is entering an era of exponential expansion, where gravitationally bound structures will get disconnected from each other, forming isolated 'island universes'. In this scenario, we present a theoretical criterion to determine the boundaries of gravitationally bound structures and a physically motivated definition of superclusters as the largest bound structures in the Universe. We use the spherical collapse model self-consistently to obtain an analytical condition for the mean density enclosed by the last bound shell of the structure (2.36 times the critical density in the present Universe, assumed to be flat, with 30 per cent matter and 70 per cent cosmological constant, in agreement with the previous, numerical result of Chiueh & He). N -body simulations extended to the future show that this criterion, applied at the present cosmological epoch, defines a sphere that encloses ≈99.7 per cent of the particles that will remain bound to the structure at least until the scale parameter of the Universe is 100 times its present value. On the other hand, (28 ± 13) per cent of the enclosed particles are in fact not bound, so the enclosed mass overestimates the bound mass, in contrast with the previous, less rigorous criterion of, e.g. Busha and collaborators, which gave a more precise mass estimate. We also verify that the spherical collapse model estimate for the radial infall velocity of a shell enclosing a given mean density gives an accurate prediction for the velocity profile of infalling particles, down to very near the centre of the virialized core. 相似文献
11.
D. Utz A. Hanslmeier A. Veronig O. Kühner R. Muller J. Jurčák B. Lemmerer 《Solar physics》2013,284(2):363-378
Small-scale magnetic fields can be observed on the Sun in high-resolution G-band filtergrams as magnetic bright points (MBPs). We study Hinode/Solar Optical Telescope (SOT) longitude and latitude scans of the quiet solar surface taken in the G-band in order to characterise the centre-to-limb dependence of MBP properties (size and intensity). We find that the MBP’s sizes increase and their intensities decrease from the solar centre towards the limb. The size distribution can be fitted using a log–normal function. The natural logarithm of the mean (μ parameter) of this function follows a second-order polynomial and the generalised standard deviation (σ parameter) follows a fourth-order polynomial or equally well (within statistical errors) a sine function. The brightness decrease of the features is smaller than one would expect from the normal solar centre-to-limb variation; that is to say, the ratio of a MBP’s brightness to the mean intensity of the image increases towards the limb. The centre-to-limb variations of the intensities of the MBPs and the quiet-Sun field can be fitted by a second-order polynomial. The detailed physical process that results in an increase of a MBP’s brightness and size from Sun centre to the limb is not yet understood and has to be studied in more detail in the future. 相似文献
12.
M. Bahgat El-Shaarawy 《Earth, Moon, and Planets》1991,52(1):1-13
An explicit form of the radial part of the exterior gravitational potential of a planet or star, in hydrostatic equilibrium is expanded in terms of fourth-order sectorial harmonics. In developing the theory of figure one seeks to express the Clairaut equation for an equipotential spheroid (level surface) in an explicit form which is an integral form to quantities of fourth-order sectorial harmonics. 相似文献
13.
K. Indulekha 《Journal of Astrophysics and Astronomy》2013,34(3):207-221
Two puzzles associated with open clusters have attracted a lot of attention – their formation, with densities and velocity dispersions that are not too different from those of the star forming regions in the galaxy, given that the observed Star Formation Efficiencies (SFE) are low and, the mass segregation observed/inferred in some of them, at ages significantly less than the dynamical relaxation times in them. Gas dynamical friction has been considered before as a mechanism for contracting embedded stellar clusters, by dissipating their energy. This would locally raise the SFE which might then allow bound clusters to form. Noticing that dynamical friction is inherently capable of producing mass segregation, since here, the dissipation rate is proportional to the mass of the body experiencing the force, we explore further, some of the details and implications of such a scenario, vis-à-vis observations. Making analytical approximations, we obtain a boundary value for the density of a star forming clump of a given mass, such that, stellar clusters born in clumps which have densities higher than this, could emerge bound after gas loss. For a clump of given mass and density, we find a critical mass such that, sub-condensations with larger masses than this could suffer significant segregation within the clump. 相似文献
14.
We propose a new method based on Lie transformations for simplifying perturbed Hamiltonians in one degree of freedom. The method is most useful when the unperturbed part has solutions in non-elementary functions. A non-canonical Lie transformation is used to eliminate terms from the perturbation that are not of the same form as those in the main part. The system is thus transformed into a modified version of the principal part. In conjunction with a time transformation, the procedure synchronizes the motions of the perturbed system onto those of the unperturbed part.A specific algorithm is given for systems whose principal part consists of a kinetic energy plus an arbitrary potential which is polynomial in the coordinate; the perturbation applied to the principal part is a polynomial in the coordinate and possibly the momentum.We demonstrate the strategy by applying it in detail to a perturbed Duffing system. Our procedure allow us to avoid treating the system as a perturbed harmonic oscillator. In contrast to a canonical simplification, our method involves only polynomial manipulations in two variables. Only after the change of time do we start manipulating elliptic functions in an exhaustive discussion of the flows. 相似文献
15.
The stability of a self‐gravitating infinitesimally thin gaseous disk rotating around a central mass is studied. Our global linear analysis concerns marginal stability, i.e. it yields the critical temperature for the onset of instability for any given ratio of the disk mass to the central mass. Both axisymmetric and low‐m nonaxisymmetric excitations are analysed. When the fractional disk mass increases, the symmetry character of the instability changes from rings (m = 0) to one‐armed trailing spirals (m = 1). The distribution of the surface density along the spiral arms is not uniform, but describes a sequence of maxima that might be identified with forming planets. The number of the mass concentrations decreases with increasing fractional disk mass. We also obtain solutions in the form of global nonaxisymmetric vortices, which are, however, never excited. 相似文献
16.
Elizabeth Bass Meers Oppenheim Jorge Chau Alice Olmstead 《Earth, Moon, and Planets》2008,102(1-4):379-382
This paper examines current techniques used to determine meteoroid mass from high-power, large aperture (HPLA) radar observations.
We demonstrate why the standard approach of fitting a polynomial to velocity measurements gives inaccurate results by applying
this technique to artificial datasets. We then suggest an alternate approach, fitting velocity data to an ablation model.
Using data taken at the Jicamarca Radio Observatory in July 2005, we compare the results of both methods and demonstrate that
fitting velocity data to an ablation model yields a reasonable result in some instances where alternate methods produce physically
unrealistic mass estimates. 相似文献
17.
We studied the stability of the restricted circular three-body problem. We introduced a model Hamiltonian in action-angle Delaunay variables. which is nearly-integrable with the perturbing parameter representing the mass ratio of the primaries. We performed a normal form reduction to remove the perturbation in the initial Hamiltonian to higher orders in the perturbing parameter. Next we applied a result on the Nekhoroshev theorem proved by Pöschel [13] to obtain the confinement in phase space of the action variables (related to the elliptic elements of the minor body) for an exponentially long time. As a concrete application. we selected the Sun-Ceres-Jupiter case, obtaining (after the proper normal form reduction) a stability result for a time comparable to the age of the solar system (i.e., 4.9 · 109 years) and for a mass ratio of the primaries less or equal than 10–6. 相似文献
18.
M. Bahgat El-Shaarawy 《Earth, Moon, and Planets》1989,45(2):115-126
The aim of this paper is to investigate numerical solutions of third-order Clairaut theory, under the boundary conditions given in our previous work (El-Shaarawy, 1974). This solution gives an explicit form of the shape and rotational distortion, due to third-order sectorial harmonic terms, of the equipotential surfaces of the two rapidly rotating planets, Jupiter and Saturn at the different levels inside these planets owing to a certain internal density distribution model (Zharkov, 1975). We considered each of them as a heterogeneous self-gravitating fluid mass in hydrostatic equilibrium. 相似文献
19.
We study the evolution of globular clusters with mass spectra under the influence of the steady Galactic tidal field, including the effects of velocity anisotropy. Similarly to single-mass models, velocity anisotropy develops as the cluster evolves, but the degree of anisotropy is much smaller than in isolated clusters. Except for very early epochs of the cluster evolution, the velocity distributions of nearly all mass components become tangentially anisotropic at the outer parts. We examine how the mass function (MF) changes in time. Specifically, we find that the power-law index of the MF decreases monotonically with the total mass of the cluster, in agreement with previous findings based on isotropic models or N -body studies. This is also consistent with the behaviour of the observed slopes of MFs for a limited number of clusters. We attempt to compare our results with multimass King models, although it is almost impossible to fit the entire density profiles for all mass components. When the MF is fixed, the central densities of individual components show significant differences between Fokker–Planck and King models. We obtain 'best-fitting' multimass King models, for which the central density of individual components as well as the total density distribution agrees with the Fokker–Planck models by adjusting the MF. The MFs obtained in this way closely resemble the MF within the half-mass radius of the Fokker–Planck result. Also, we find that the local MFs predicted by Fokker–Planck calculations vary more rapidly with radius than best-fitting multimass King models. The projected velocity profiles for anisotropic models show significant flattening toward the tidal radius compared with the isotropic model. This is caused by the fact that the tangential velocity dispersion becomes dominant at the outer parts. Such a behaviour of velocity profile appears to be consistent with the observed profiles of the collapsed cluster M15. 相似文献
20.
We have computed a set of multiphase chemical evolution models in which the radial mass distributions of each theoretical
galaxy is calculated using the universal rotation curve from Persic, Salucci and Steel (1996). We obtain the chemical evolution
for galaxies of different masses and morphological types by changing the efficiencies to form molecular clouds and stars according
with these types. We obtain the radial distributions of diffuse and molecular gas densities, the star formation rate and abundances
for 15 elements for each galaxy.
This revised version was published online in September 2006 with corrections to the Cover Date. 相似文献