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1.
Axford and McKenzie [1992] suggested that the energy released in impulsive reconnection events generates high frequency Alfvén waves. The kinetic equation for spectral energy density of waves is derived in the random phase approximation. Solving this equation we find the wave spectrum with the power law "−1" in the low frequency range which is matched to the spectrum above the spectral brake with the power low "−1.6." The heating rate of solar wind protons due to the dissipation of Alfvén waves is obtained. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

2.
This paper aims at studying the long-term orbital consequences of the perturbations related to De Haerdtl inequality, a current quasi-commensurability between the Galilean satellites of Jupiter Ganymede and Callisto. We used the method of Frequency Map Analysis to detect a chaotic behavior in a 5-bodies system where every inequality has been dropped, except of De Haerdtl one. We also used Frequency Analysis to draw the behavior of the arguments likely to become resonant, in several numerical integrations. We show that De Haerdtl inequality might have induced chaos in the past if Ganymede's and Callisto's eccentricities have been higher than 4×10−3. Moreover, we enlight the influence of Jupiter's obliquity on this chaos. We also enlight some aspects of this chaotic behavior, showing for instance stable chaos and single resonances. The main result of this study is that De Haerdtl inequality should be taken into account in every study of the long term orbital evolution of the Galilean satellites.  相似文献   

3.
Data obtained by the Explorer 34 satellite regarding the degree of anisotropy of ≳ 70 keV electrons of solar origin are reported. It is shown that the anisotropies are initially field aligned, and that they decay to ≲ 10% in a time of the order of 1 hr. The decays of the concurrent ionic and electronic anisotropies for one well observed event are in good agreement with the diffusive propagation model of Fisk and Axford. The data suggest parallel diffusion coefficients for both ions and electrons that are rigidity independent. From considerations of a long lived electron event, it is shown that the electronic fluxes exhibit ‘equilibrium’ anositropies at late times. These are interpreted as indicating that convective removal at the solar wind velocity is the dominant mechanism whereby solar cosmic ray electrons (∼- 70 keV) leave the solar system. They also indicate that there is a positive density gradient at late times in a solar electron event. The data suggest that this was established prior to the establishment of a similar gradient for the cosmic ray ions. This research was supported by the National Aeronautics and Space Administration under contracts NASr-198 and NAS5-9075. The research in India was supported by funds from the Department of Atomic Energy, Government of India and funds from the grant NAS-1492 from the National Academy of Sciences, U.S.A. Support in data analysis was also provided by Air Force Cambridge Research Laboratories, and by the Australian Research Grants Committee.  相似文献   

4.
From IPS and spacecraft measurements of the solar wind combined with geomagnetic observations, we identify the passage of three main disturbances through the solar wind from solar flares on August 2, 4 and 7. From a detailed study of the IPS data covering the third event, we conclude that the extent of the disturbance front at 1 AU covered about ±60° in longitude and more than 30° in latitude from the flare normal. If interpreted as a blast wave according to the model of De Young and Hundhausen (1971), the disturbance was ejected from the Sun into a cone of half-angle 45°±15°.  相似文献   

5.
A complex exponential solution has been derived which unifies the elliptic and hyperbolic trajectories into a single set of equations and provides an exact, analytical solution to the unperturbed, Keplerian two-body problem. The formulation eliminates singularities associated with the elliptic and hyperbolic trajectories that arise from these orbits. Using this complex exponential solution formulation, a variation of parameters formulation for the perturbed two-body problem has been derived. In this paper, we present the analytical formulation of the complex exponential solution, numerical simulations, a comparison with classical solution methods, and highlight the benefits of this approach compared with the classical developments. Previously presented as AAS 07-136 at the 17th AAS/AIAA Spaceflight Mechanics Meeting Sedona, Arizona, AAS 08-206 and AAS 08-230 at the 18th AAS/AIAA Spaceflight Mechanics Meeting Galveston, Texas.  相似文献   

6.
The way is discussed by which microinstabilities of an exact charge neutral magnetopause could lead to a trapped particle flow, the absence of which causes the non-existence of an equilibrium magnetospheric boundary layer in the Parker-Lerche model. Furthermore, it is argued that instead of the non-equilibrium effect of Parker and Lerche, microinstabilities of an exact charge neutral magnetopause might be the underlying physical process of an Axford and Hines' type viscous interaction.  相似文献   

7.
We briefly review the status of the “graceful exit” problem in superstring cosmology and present a possible resolution. It is shown that there exists a solution to this problem in two-dimensional dilaton gravity provided quantum corrections are incorporated. This is similar to the recently proposed solution of Rey. However, unlike in his case, in our one-loop corrected model the graceful exit problem is solved for any finite number of massless scalar matter fields present in the theory.  相似文献   

8.
In the 19th century De la Rue, Stewart, and Loewy carried out a compilation of drawings and photographs of the solar sunspots in the period 1832–1868. From these drawings and photographs, they determined fortnightly values of the sunspot areas. In this work, monthly values of the sunspot areas for the period 1832–1868 are calculated and the reliability of these data in terms of the solar activity indices is discussed.  相似文献   

9.
A root-finding method due to Laguerre (1834–1886) is applied to the solution of the Kepler problem. The speed of convergence of this method is compared with that of Newton's method and several higher-order Newton methods for the problem formulated in both conventional and universal variables and for both elliptic and hyperbolic orbits. In many thousands of trials the Laguerre method never failed to converge to the correct solution, even from exceptionally poor starting approximations. The non-local robustness and speed of convergence of the Laguerre method should make it the preferred method for the solution of Kepler's equation.  相似文献   

10.
Dans un système d'axes fixes le problème gravitationnel des n. corps possède quatre groupes d'invariance (rectifications). Aucun de ces groupes ne peut échanger une solution non bornée et une solution bornée.Dans le cas du problème non circulaire et non rectilinéaire des deux corps, une transformation paramétrique peut-être définie, changeant seulement l'exentricité et l'horaire. Cette transformation est de type homographique et son expression anlytique dépend des valeurs de l'exentricité par rapport à l'unité. Par conséquent, une solution hyperbolique ou parabolique peut-être changée en une solution elliptique. Les applications et l'utilité d'une telle transformation concerne les captures des comètes. Finalement, une hypothétique extension est indiquée pour le problème des n. corps.
Invariant transformation of the two-body problem associated with eccentricity
In an absolute reference frame the gravitational n-body problem possesses four groups of invariant transformations (rectifications). But no one can change an unbounded solution into a bounded solution.For the non-circular two-body problem, having non-zero angular momentum a parametric transformation may be defined changing only the eccentricity and the time. This transformation is of homographic type, and it is an analytical expression depends on the value of the eccentricity with respect to unity. Therefore an hyperbolic or parabolic solution may be changed into an elliptic solution. The application and usefulness of this transformation is concerned with the capture of comets [5].Finally, an hypothetic extension is indicated to the n-body problem.
  相似文献   

11.
The work presented in paper I (Papadakis, K.E., Goudas, C.L.: Astrophys. Space Sci. (2006)) is expanded here to cover the evolution of the approximate general solution of the restricted problem covering symmetric and escape solutions for values of μ in the interval [0, 0.5]. The work is purely numerical, although the available rich theoretical background permits the assertions that most of the theoretical issues related to the numerical treatment of the problem are known. The prime objective of this work is to apply the ‘Last Geometric Theorem of Poincaré’ (Birkhoff, G.D.: Trans. Amer. Math. Soc. 14, 14 (1913); Poincaré, H.: Rend. Cir. Mat. Palermo 33, 375 (1912)) and compute dense sets of axisymmetric periodic family curves covering the initial conditions space of bounded motions for a discrete set of values of the basic parameter μ spread along the entire interval of permissible values. The results obtained for each value of μ, tested for completeness, constitute an approximation of the general solution of the problem related to symmetric motions. The approximate general solution of the same problem related to asymmetric solutions, also computable by application of the same theorem (Poincaré-Birkhoff) is left for a future paper. A secondary objective is identification-computation of the compact space of escape motions of the problem also for selected values of the mass parameter μ. We first present the approximate general solution for the integrable case μ = 0 and then the approximate solution for the nonintegrable case μ = 10−3. We then proceed to presenting the approximate general solutions for the cases μ = 0.1, 0.2, 0.3, 0.4, and 0.5, in all cases building them in four phases, namely, presenting for each value of μ, first all family curves of symmetric periodic solutions that re-enter after 1 oscillation, then adding to it successively, the family curves that re-enter after 2 to 10 oscillations, after 11 to 30 oscillations, after 31 to 50 oscillations and, finally, after 51 to 100 oscillations. We identify in these solutions, considered as functions of the mass parameter μ, and at μ = 0 two failures of continuity, namely: 1. Integrals of motion, exempting the energy one, cease to exist for any infinitesimal positive value of μ. 2. Appearance of a split into two separate sub-domains in the originally (for μ = 0) unique space of bounded motions. The computed approximations of the general solution for all values of μ appear to fulfill the ‘completeness’ criterion inside properly selected sub-domains of the domain of bounded motions in the (x, C) plane, which means that these sub-domains are filled countably densely by periodic family curves, which form a laminar flow-line pattern. The family curves in this pattern may, or may not, be intersected by a ‘basic’ family curve segment of order from 1 up to 3. The isolated points generating asymptotic solutions resemble ‘sink’ points toward which dense sets of periodic family curves spiral. The points in the compact domain in the (x, C) plane resting outside the domain of bounded motions (μ = 0), including the gap between the two large sub-domains (μ > 0) created by the aforementioned split, generate escape motions. The gap between the two large sub-domains of bounded motions grows wider for growing μ. Also, a number of compact gaps that generate escape motions exist within the body of the two sub-domains of bounded motions. The approximate general solutions computed include symmetric, heteroclinic, asymptotic, collision and escape solutions, thus constituting one component of the full approximate general solution of the problem, the second and final component being that of asymmetric solutions.  相似文献   

12.
The problem of finding a global solution for systems in celestial mechanics was proposed by Weierstrass during the last century. More precisely, the goal is to find a solution of the n-body problem in series expansion which is valid for all time. Sundman solved this problem for the case of n = 3 with non-zero angular momentum a long time ago. Unfortunately, it is impossible to directly generalize this beautiful theory to the case of n > 3 or to n = 3 with zero-angular momentum.A new blowing up transformation, which is a modification of McGehee's transformation, is introduced in this paper. By means of this transformation, a complete answer is given for the global solution problem in the case of n > 3 and n = 3 with zero angular momentum.The main result in this paper has appeared in Chinese in Acta Astro. Sinica. 26 (4), 313–322. In this version some mistakes have been rectified and the problems we solved are now expressed in a much clearer fashion.  相似文献   

13.
This paper gives the results of a programme attempting to exploit ‘la seule bréche’ (Poincaré, 1892, p. 82) of non-integrable systems, namely to develop an approximate general solution for the three out of its four component-solutions of the planar restricted three-body problem. This is accomplished by computing a large number of families of ‘solutions précieuses’ (periodic solutions) covering densely the space of initial conditions of this problem. More specifically, we calculated numerically and only for μ = 0.4, all families of symmetric periodic solutions (1st component of the general solution) existing in the domain D:(x 0 ∊ [−2,2],C ∊ [−2,5]) of the (x 0, C) space and consisting of symmetric solutions re-entering after 1 up to 50 revolutions (see graph in Fig. 4). Then we tested the parts of the domain D that is void of such families and established that they belong to the category of escape motions (2nd component of the general solution). The approximation of the 3rd component (asymmetric solutions) we shall present in a future publication. The 4th component of the general solution of the problem, namely the one consisting of the bounded non-periodic solutions, is considered as approximated by those of the 1st or the 2nd component on account of the `Last Geometric Theorem of Poincaré' (Birkhoff, 1913). The results obtained provoked interest to repeat the same work inside the larger closed domain D:(x 0 ∊ [−6,2], C ∊ [−5,5]) and the results are presented in Fig. 15. A test run of the programme developed led to reproduction of the results presented by Hénon (1965) with better accuracy and many additional families not included in the sited paper. Pointer directions construed from the main body of results led to the definition of useful concepts of the basic family of order n, n = 1, 2,… and the completeness criterion of the solution inside a compact sub-domain of the (x 0, C) space. The same results inspired the ‘partition theorem’, which conjectures the possibility of partitioning an initial conditions domain D into a finite set of sub-domains D i that fulfill the completeness criterion and allow complete approximation of the general solution of this problem by computing a relatively small number of family curves. The numerical results of this project include a large number of families that were computed in detail covering their natural termination, the morphology, and stability of their member solutions. Zooming into sub-domains of D permitted clear presentation of the families of symmetric solutions contained in them. Such zooming was made for various values of the parameter N, which defines the re-entrance revolutions number, which was selected to be from 50 to 500. The areas generating escape solutions have being investigated. In Appendix A we present families of symmetric solutions terminating at asymptotic solutions, and in Appendix B the morphology of large period symmetric solutions though examples of orbits that re-enter after from 8 to 500 revolutions. The paper concludes that approximations of the general solution of the planar restricted problem is possible and presents such approximations, only for some sub-domains that fulfill the completeness criterion, on the basis of sufficiently large number of families.  相似文献   

14.
The decay of a plasmon into two neutrinos in the presence of an intense magnetic field has been studied by Canutoet al. (1970). They suggest that one of the principal longitudinal plasmon modes, which occurs only in magnetized plasmas, would cause certain magnetic stars to cool more rapidly than their unmagnetized counterparts. We show here that this mechanism is inoperative since the plasmon mode involved cannot be excited in the direction parallel to the magnetic field as considered by Canutoet al. Moreover, for ωc/ωp?1, we show that the other principal longitudinal plasmon mode considered earlier by Adamset al. (1963) (which is largely independent of the magnetic field) dominates the plasmon-neutrino decay cooling of magnetic stars.  相似文献   

15.
In this note extending the technique developed for static fields by De (1964) to the static plane-symmetric solution of Taub (1951) and the conformastat gravitational universe of Das (1971) solutions for coupled gravitational and zero-rest-mass scalar fields have been obtained. Furthermore, it is found that the singularities of these empty spaces cannot be removed by the introduction of zero-rest-mass scalar fields.  相似文献   

16.
We consider a model that describes the evolution of distant satellite orbits and that refines the solution of the doubly averaged Hill problem. Generally speaking, such a refinement was performed previously by J. Kovalevsky and A.A. Orlov in terms of Zeipel’s method by constructing a solution of the third order with respect to the small parameter m, the ratio of the mean motions of the planet and the satellite. The analytical solution suggested here differs from the solutions obtained by these authors and is closest in form to the general solution of the doubly averaged problem (∼m 2). We have performed a qualitative analysis of the evolutionary equations and conditions for the intersection of satellite orbits with the surface of a spherical planet with a finite radius. Using the suggested solution, we have obtained improved analytical time dependences of the elements of evolving orbits for a number of distant satellites of giant planets compared to the solution of the doubly averaged Hill problem and, thus, achieved their better agreement with the results of our numerical integration of the rigorous equations of perturbed motion for satellites.  相似文献   

17.
The integral equation relating to the brightness distribution in a galaxy and in its image formed by an optical system characterized by a Gaussian (or a sum of Gaussians) point-spread function (PSF) is derived. Since the solution of this equation, attainable by any classical method, is numerically unstable, according to the ill-posed nature of the problem, an approximate and stable solution is obtainable by a first-order regularization in Tikhonov's sense. For the bright spike the application to M32 gives a radius of 2.1 arc sec a central surface brightness of 13.10 V mag arc sec–2 and a 12 V integrated magnitude.  相似文献   

18.
A three-body problem is considered in which two masses, forming a close binary, orbit a comparatively distant mass. An asymptotic solution of this problem is presented, where the small parameter is related to the distance separating the binary and the remaining mass. Accepting certain model constraints, this solution is accurate within a constant errorO(11) and uniformly valid for time intervalsO(–3). Two specific examples are chosen to verify the literal solution: one relating to the Sun-Earth-Moon configuration of the solar system, the other to an idealized stellar system where the three masses are in the ratio 20:1:1. In both cases close agreement is found when the analytical solution is compared with an equivalent numerically-generated orbit.  相似文献   

19.
The general solution of the Henon–Heiles system is approximated inside a domain of the (x, C) of initial conditions (C is the energy constant). The method applied is that described by Poincaré as ‘the only “crack” permitting penetration into the non-integrable problems’ and involves calculation of a dense set of families of periodic solutions that covers the solution space of the problem. In the case of the Henon–Heiles potential we calculated the families of periodic solutions that re-enter after 1–108 oscillations. The density of the set of such families is defined by a pre-assigned parameter ε (Poincaré parameter), which ascertains that at least one periodic solution is computed and available within a distance ε from any point of the domain (x, C) for which the approximate general solution computed. The approximate general solution presented here corresponds to ε = 0.07. The same solution is further improved by “zooming” into four square sub-domain of (x, C), i.e. by computing sufficient number of families that reduce the density parameter to ε = 0.003. Further zooming to reduce the density parameter, say to ε = 10−6, or even smaller, although easily performable in both areas occupied by stable as well as unstable solutions, was found unnecessary. The stability of all members of each and all families computed was calculated and presented in this paper for both the large solution domain and for the sub-domains. The correspondence between areas of the approximate general solution occupied by stable periodic solutions and Poincaré sections with well-aligned section points and also correspondence between areas occupied by unstable solutions and Poincaré sections with randomly scattered section points is shown by calculating such sections. All calculations were performed using the Runge-Kutta (R-K) 8th order direct integration method and the large output received, consisting of many thousands of families is saved as “Atlas of the General Solution of the Henon–Heiles Problem,” including their stability and is available at request. It is concluded that approximation of the general solution of this system is straightforward and that the chaotic character of its Poincaré sections imposes no limitations or difficulties.  相似文献   

20.
The problem of magnetic field generation under screw motion in a toroidal channel is studied numerically. The screw dynamo in the cylinder with periodical boundary conditions was found to be a suitable approximation for generation of the magnetic field by a screw flow in a thin torus. For the thick torus, a principally new solution of the screw dynamo problem was obtained. In this case the growing global magnetic field mode has the scale of a maximal geometrical size of the torus and does not vanish on the axis of the torus (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

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