共查询到20条相似文献，搜索用时 31 毫秒
1.
Massimiliano Guzzo Zoran Knežević Andrea Milani 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):121-140
We apply the spectral formulation of the Nekhoroshev theorem to investigate the long-term stability of real main belt asteroids. We find numerical indication that some asteroids are in the so-called Nekhoroshev stability regime, that is they are on chaotic orbits but their motion is stable over very long times. We have analyzed the motion of bodies in different regions of the belt, to assess the sensitivity of our method. We found that it allows us to clearly discriminate between different dynamical regimes, such as the one described by the Nekhoroshev stability, the one well described by the KAM theory, and the unstable chaotic regime in which diffusion in phase space can be detected over time spans much shorter than the age of the solar system. 相似文献
2.
《New Astronomy》2022
In this paper, we study the weak deflection angle in the spacetime of improved Schwarzschild black hole using the method derived by Gibbons and Werner. To do so, we derive the optical curvature from the optical metric and calculate deflection angle in weak field limits by using the Gauss–Bonnet theorem. Moreover, we study the effect of the plasma medium on the weak gravitational lensing using the Gauss–Bonnet theorem. Furthermore, we also study the graphical analysis of the deflection angle in both the plasma and non-plasma mediums. Moreover, we obtain the bound on greybody for improved Schwarzschild black hole. 相似文献
3.
Alessandro Morbidelli Massimiliano Guzzo 《Celestial Mechanics and Dynamical Astronomy》1996,65(1-2):107-136
The present paper reviews the Nekhoroshev theorem from the point of view of physicists and astronomers. We point out that Nekhoroshev result is strictly connected with the existence of a specific structure of the phase space, the existence of which can be checked with several numerical tools. This is true also for a degenerate system such as the one describing the motion of an asteroid in the so called main belt. The main difference is that in some parts of the belt, the Nekhoroshev result cannot apply a priori. Mean motion resonances of order smaller than the logarithm of the mass of Jupiter and first order secular resonances must be excluded. In the remaining parts, conversely, the Nekhoroshev theorem can be proved, provided someparameters, such as the masses, the eccentricities and the inclinations of the planets are small enough. At the light of this result, a massive campaign of numerical integrations of real and fictitious asteroids should allow to understand which is the real dynamical structure of the asteroid belt. 相似文献
4.
A. M. Aliaga J. A. Rubiño-Martín E. Martínez-González R. B. Barreiro J. L. Sanz 《Monthly notices of the Royal Astronomical Society》2005,356(4):1559-1570
We adapt the smooth tests of goodness-of-fit developed by Rayner and Best to the study of the non-Gaussianity of interferometric observations of the cosmic microwave background (CMB). The interferometric measurements (visibilities) are transformed into signal-to-noise ratio eigenmodes, and then the method is applied directly in Fourier space. This transformation allows us to perform the analysis in different subsets of eigenmodes according to their signal-to-noise ratio level. The method can also deal with non-uniform or incomplete coverage of the UV plane. We explore here two possibilities: we analyse either the real and imaginary parts of the complex visibilities (Gaussianly distributed under the Gaussianity hypothesis) or their phases (uniformly distributed under the Gaussianity hypothesis). The power of the method in discriminating between Gaussian and non-Gaussian distributions is studied by using several kinds of non-Gaussian simulations. On the one hand, we introduce a certain degree of non-Gaussianity directly into the Fourier space using the Edgeworth expansion, and afterwards the desired correlation is introduced. On the other hand, we consider interferometric observations of a map with topological defects (cosmic strings). To these previous non-Gaussian simulations we add different noise levels and quantify the required signal-to-noise ratio necessary to achieve a detection of these non-Gaussian features. Finally, we have also studied the ability of the method to constrain the so-called non-linear coupling constant f NL using χ2 simulations. The whole method is illustrated here by application to simulated data from the Very Small Array interferometer. 相似文献
5.
Some experimental tests and improvements to the Very Fast Inversion of the Stokes Vector program, which is designed for the inversion calculation used by the Helioseismic and Magnetic Imager instrument on the Solar Dynamics Observatory,are given. On one hand, the interpolation for calculating the Voigt function is not smooth, which may occasionally cause the iteration process to converge to different minima although they are very close to initial values. This problem can be solved by a smoother interpolation. On the other hand, in order to improve the performance of this program, we have tried to abandon the randomly-jump-out strategy and set the initial value properly to avoid non-global minima. The resulting method costs only1/4 of the computational time, and will be very competitive when the users are only interested in the vectorial magnetic fields and the velocities along the line of sight. 相似文献
6.
Our Sun and planetary system were born about 4.5 billion years ago. How did this happen, and what is the nature of our heritage from these early times? This review tries to address these questions from an astrochemical point of view. On the one hand, we have some crucial information from meteorites, comets and other small bodies of the Solar System. On the other hand, we have the results of studies on the formation process of Sun-like stars in our Galaxy. These results tell us that Sun-like stars form in dense regions of molecular clouds and that three major steps are involved before the planet-formation period. They are represented by the prestellar core, protostellar envelope and protoplanetary disk phases. Simultaneously with the evolution from one phase to the other, the chemical composition gains increasing complexity. In this review, we first present the information on the chemical composition of meteorites, comets and other small bodies of the Solar System, which is potentially linked to the first phases of the Solar System??s formation. Then we describe the observed chemical composition in the prestellar core, protostellar envelope and protoplanetary-disk phases, including the processes that lead to them. Finally, we draw together pieces from the different objects and phases to understand whether and how much we inherited chemically from the time of the Sun??s birth. 相似文献
7.
基于目前流行的冷暗物质等级成团理论的星系形成的半解析模型取得了很大进展．在引入一系列合理的关于重子物质物理过程的假设，如气体冷却、恒星形成率、超新星能量反馈以后，结合N体数值模拟，星系形成的半解析模型一方面能较成功地预言许多与观测符合的近邻星系的性质，如光度函数、星系的两点相关函数、Thlly-Fisher关系、星系团中椭圆星系的颜色一星等关系等；另一方面还能较成功地预言宇宙的恒星形成历史，以及一部分高红移星系的性质，如Lyman-Break星系的数目随红移的分布．但是最近一些观测表明，半解析模型在高红移预言的大质量星系较少，且红星系数目也较观测少．重点讨论半解析模型成功与不足之处，并指出解决这些问题可能的途径。 相似文献
8.
We discuss contradictions existing in the literature in the problem on the stability of collisionless spherical stellar systems,
which are the simplest anisotropic generalization of the well-known polytropic models. On the one hand, calculations of the
growth rates within the framework of a linear stability theory and N-body simulations suggest that these systems should become stable when the parameter s characterizing the degree of anisotropy of the stellar velocity distribution becomes lower than some critical value s
crit > 0. On the other hand, according to Palmer and Papaloizou, the growth rate should be nonzero up to the isotropic limit s = 0. Using our method of determining the eigenmodes of stellar systems, we show that even though the mode growth rates in
weakly radially anisotropic systems of this type are nonzero, they are exponentially small, i.e., decrease as γ ∝ exp(−a/s) when s → 0. For slightly radially anisotropic systems with a finite lifetime, this actually implies stability. 相似文献
9.
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
10.
J. E. Howard 《Celestial Mechanics and Dynamical Astronomy》2005,92(1-3):219-241
We reexamine the classical virial theorem for bounded orbits of arbitrary autonomous Hamiltonian systems possessing both regular and chaotic orbits. New and useful forms of the virial theorem are obtained for natural Hamiltonian flows of arbitrary dimension. A discrete virial theorem is derived for invariant circles and periodic orbits of natural symplectic maps. A weak and a strong form of the virial theorem are proven for both flows and maps. While the Birkhoff Ergodic Theorem guarantees the existence of the relevant time averages for both regular and chaotic orbits, the convergence is very rapid for the former and extremely slow for the latter. This circumstance leads to a simple and efficient measure of chaoticity. The results are applied to several problems of current physical interest, including the Hénon–Heiles system, weak chaos in the standard map, and a 4D Froeschlé map. 相似文献
11.
12.
E. A. Mikhailov 《Astronomy Letters》2014,40(7):398-405
We propose a possible scenario of large-scale magnetic field evolution for galaxies with star formation. An important point affecting the results of our calculations is a parametrization of dynamo-governing quantities. In comparison with previous works, we have reconsidered the views of how star formation affects the stationary magnetic field strength, viscosity, and other parameters important for galactic dynamos. The calculations have been performed by taking into account the magnetic helicity fluxes, which introduce an additional nonlinearity into the model and change the regime of galactic dynamo action. We have confirmed the previously suggested idea that for weak star formation its influence on the magnetic field strength is minor and the relationship between them clearly manifests itself only when the star formation rate reaches a certain threshold value. In this case, on the one hand, the threshold lowers-this effect manifests itself at a star formation surface density greater than that in the Milky Way by a factor of 5. On the other hand, intense star formation can cause both a monotonic decay of the large-scale magnetic field and its oscillations near some value. 相似文献
13.
The non-linear stability of the triangular libration points of the restricted three-body problem is studied under the presence
of third and fourth order resonance's, when the more massive primary is an oblate spheroid. In this study Markeev's theorem
are utilised with the help of KAM theorem. It is found that the stability of the triangular libration points are unstable
in the third order resonance case and stable in the fourth order resonance case, for all the values of oblateness factor A1.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
14.
Francesco Fassò 《Celestial Mechanics and Dynamical Astronomy》1995,62(1):43-69
This paper deals with Hamiltonian perturbation theory for systems which, like Euler-Poinsot (the rigid body with a fixed point and no torques), are degenerate and do not possess a global system of action-angle coordinates. It turns out that the usual methods of perturbation theory, which are essentially local being based on the construction of normal forms within the domain of a local coordinate system, are not immediately usable to study perturbations of these systems, since degeneracy makes impossible to control that the system does not fall into a singularity of the coordinates. To overcome this difficulty, we develop a global formulation of Hamiltonian perturbation theory, in which the normal forms are globally defined on the phase space manifold. The key for this study lies in the geometry of the fibration by the invariant tori of an integrable degenerate Hamiltonian system, which is described by some generalizations of the Liouville-Arnol'd theorem and is reviewed in the paper. As an application, we provide a global formulation of Nekhoroshev's theorem on the stability for exponentially long times. 相似文献
15.
Scott C. Chapman † Douglas Scott Charles C. Steidel Colin Borys Mark Halpern Simon L. Morris Kurt L. Adelberger Mark Dickinson Mauro Giavalisco Max Pettini 《Monthly notices of the Royal Astronomical Society》2000,319(1):318-330
We have carried out targeted submillimetre observations as part of a programme to explore the connection between the rest-frame ultraviolet and far-infrared properties of star-forming galaxies at high redshift, which is currently poorly understood. On the one hand, the Lyman break technique is very effective at selecting galaxies. On the other, 'blank-field' imaging in the submillimetre seems to turn up sources routinely, amongst which some are star-forming galaxies at similar redshifts. Already much work has been done searching for optical identifications of objects detected using the SCUBA instrument. Here we have taken the opposite approach, performing submillimetre photometry for a sample of Lyman break galaxies, the ultraviolet properties of which imply high star formation rates. The total signal from our Lyman break sample is undetected in the submillimetre, at an rms level of ∼0.5 mJy, which implies that the population of Lyman break galaxies does not constitute a large part of the recently detected blank-field submillimetre sources. However, our one detection suggests that with reasonable SCUBA integrations we might expect to detect those few Lyman break galaxies that are far-infrared brightest. 相似文献
16.
Lobate scarps, thought to be the surface expression of large thrust faults, are the most spectacular contractional tectonic features visible on Mercury. Most lobate scarps follow a general and relatively simple pattern, with a roughly arcuate or linear form in plan view, and an asymmetric cross section characterized by a steeply rising scarp face and a gently declining back scarp. In this work, we study two peculiar and complex scarps in the Rembrandt region of Mercury through MESSENGER imagery. On the one hand, the formation of these scarps resulted in the deformation of features such as impact craters, fractures, extensional faults, and volcanic plains, while on the other hand, the deformed features partly influenced the formation of the scarps. Evidence for structural control on the formation of the scarps includes their orientation, segmentation, bifurcation, change in structural trend and dip orientation, and transition into high-relief ridges or wrinkle ridge morphologies in some cases. Thus, these two lobate scarps provide examples of complex geological relations among other features, expanding the recognized richness of mercurian geology. Also, the southern scarp records a complex history of contraction, suggesting that the development of some mercurian lobate scarps may be more complex than usually thought. 相似文献
17.
Massimiliano Guzzo 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):303-323
We describe a numerical application of the Nekhoroshev theorem to investigate the long-term stability of quasi-integrable systems. We extend the results of a previous paper to a class of degenerate systems, which are typical in celestial mechanics. 相似文献
18.
《天文和天体物理学研究(英文版)》2017,(12)
We consider the geometric Titius-Bode rule for the semimajor axes of planetary orbits. We derive an equivalent rule for the midpoints of the segments between consecutive orbits along the radial direction and we interpret it physically in terms of the work done in the gravitational field of the Sun by particles whose orbits are perturbed around each planetary orbit. On such energetic grounds, it is not surprising that some exoplanets in multiple-planet extrasolar systems obey the same relation. However,it is surprising that this simple interpretation of the Titius-Bode rule also reveals new properties of the bound closed orbits predicted by Bertrand's theorem, which has been known since 1873. 相似文献
19.
The Lie transform method used in Perturbation Theory is based upon an intrinsic algorithm for transforming functions or vector fields by a transformation close to the identity. It can thus be viewed as a specialization of methods and results of differential geometry as is shown in the first part of this paper. In a second part we answer some of the questions left open in connection with the equivalence of the algorithms proposed by Hori and Deprit. From a formal point of view, the methods are shown to be equivalent for non-canonical as well as canonical transformations and a formula relating directly the two generating functions (or vector fields) is presented (formula (5.17)). On the other hand, the equivalence is shown to hold also in the ring ofp-differentiable functions. 相似文献
20.
The stability of 12 small dark globules has been analyzed by using the full scalar virial theorem without magnetic field. We have applied the virial theorem to 18 sub-condensations identified from the column density maps of 12 globules. The sub-condensations are approximated by a uniform sphere of equivalent mass for simplicity. Based on the conventional simplified version of virial theorem, where the viral mass is compared with the LTE mass, we can only say that almost all the sub-condensations are approximately in a virial equilibrium. When we apply the full scalar virial theorem, where the sum of all the energy terms does not vanish and the time variation of the moment of inertia should be kept, one third of our sample cores are likely to collapse, one sixth of them are expected to expand, and the rest half of them are in a dense phase of an oscillatory equilibrium. The globules in the diffuse phase of the oscillatory equilibrium may not be detected by conventional means, because they are too rarefied to get CO molecules excited or to shield molecules from UV photons, or because they may not withstand the tidal disruption by neighboring clouds. 相似文献