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1.
The main focus of this paper is calculation of the diameters of asteroids belonging to five families (Vesta, Eos, Eunomia, Koronis, and Themis). To do that, we used the HCM algorithm applied for a data set containing 292,003 numbered asteroids, and a numerical procedure for choosing the crucial parameter of the HCM, called “the cutting velocity” vcut. It was established with a precision as high as 1 m s?1. Thereafter, we used the WISE (Wide‐field Infrared Survey Explorer) catalog to set a range of albedo for the largest members of each family considered. The albedo data were supported by the data concerning color classification (SDSS MOC4). The asteroids with albedo out of this range were classified as interlopers and were therefore disqualified as family members. Sizes were calculated for the asteroids with albedo within the acceptable range. For the other asteroids (those chosen by means of the HCM, but with albedo not listed in the WISE), the value of albedo of the largest member of the family was adopted. Results are given in a set of figures showing the families on the planes (a, e), (a, i), (e, i). Diameters and volumes of the asteroids that are the individual members of a family were calculated on the basis of their known or assumed albedo and on their absolute magnitude. Volumes of the parent bodies of the families were found on the basis of the cumulative volume distribution of these families. We also studied the secular resonances of the family members. We have shown that the locations of members of the considered asteroid families are related to the lines of secular resonances z1, z2, and z3 with Saturn. 相似文献
2.
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
3.
N. Caranicolas 《Astrophysics and Space Science》1982,87(1-2):237-245
We study the families of periodic orbits in a time-independent two-dimensional potential field symmetric with respect to both axes. By numerical calculations we find characteristic curves of several families of periodic orbits when the ratio of the unperturbed frequencies isA
1/2/B
1/2=2/1. There are two groups of characteristic curves: (a) The basic characteristic and the characteristics which bifurcate from it. (b) The characteristics which start from the boundary line and the axisx=0. 相似文献
4.
The aim of the planar inverse problem of dynamics is: given a monoparametric family of curves f(x, y) = c, find the potential V (x, y) under whose action a material point of unit mass can describe the curves of the family. In this study we look for V in the class of the anisotropic potentials V(x, y) = v(a2x2 + y2), (a=constant). These potentials have been used lately in the search of connections between classical, quantum, and relativistic mechanics. We establish a general condition which must be satisfied by all the families produced by an anisotropic potential. We treat special cases regarding the families (e. g. families traced isoenergetically) and we present certain pertinent examples of compatible pairs of families of curves and anisotropic potentials. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
5.
The three families of three-dimensional periodic oscillations which include the infinitesimal periodic oscillations about the Lagrangian equilibrium pointsL
1,L
2 andL
3 are computed for the value =0.00095 (Sun-Jupiter case) of the mass parameter. From the first two vertically critical (|a
v
|=1) members of the familiesa, b andc, six families of periodic orbits in three dimensions are found to bifurcate. These families are presented here together with their stability characteristics. The orbits of the nine families computed are of all types of symmetryA, B andC. Finally, examples of bifurcations between families of three-dimensional periodic solutions of different type of symmetry are given. 相似文献
6.
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
7.
Alexander Kuznetsov 《Astrophysics and Space Science》2008,314(4):311-318
This paper establishes united classification of gamma-ray bursts and their counterparts on the basis of measured characteristics:
photon energy E and emission duration T. We find that the interrelation between these characteristics is such that as the energy increases, the duration decreases
(and vice versa). The given interrelation reflects the nature of the phenomenon and forms the E–T diagram, which represents a natural classification of all observed events in the energy range from about 109 to 10−6 eV and in the corresponding interval of durations from about 10−2 up to 108 s. The proposed classification results from our findings, which are principal for the theory and practical study of the phenomenon. 相似文献
8.
O. Ragos K. E. Papadakis C. G. Zagouras 《Celestial Mechanics and Dynamical Astronomy》1997,67(4):251-274
The regions of quasi-periodic motion around non-symmetric periodic orbits in the vicinity of the triangular equilibrium points
are studied numerically. First, for a value of the mass parameter less than Routh's critical value, the stability regions
determined by quasi-periodic motion are examined around the existing families of short (Ls
4) and long (Ll
4) period solutions. Then, for two values of μ greater than the Routh value, the unified family Lsl
4, to which, in these cases, Ls
4 and Ll
4 merge, is considered. It is found that such regions surround in general the linearly stable segments of the corresponding
families and become smaller as the mass ratio increases.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
Magnetic monopoles and antimonopoles with masses M=1016 Gev and charges q=68.5e in the early universe are considered. Pair production may occur as a result of their Coulomb interaction. Some conditions for formation of such pairs are discussed. In particular, numerical simulations of three particle collisions are carried out. Probabilities for pair production are found in terms of the N-body problem. 相似文献
10.
Queenie H. S. Chan Ian A. Franchi Xuchao Zhao Alice Stephant Ian P. Wright Conel M. O'D. Alexander 《Meteoritics & planetary science》2020,55(6):1320-1348
The chondritic‐porous subset of interplanetary dust particles (CP‐IDPs) are thought to have a cometary origin. Since the CP‐IDPs are anhydrous and unaltered by aqueous processes that are common to chondritic organic matter (OM), they represent the most pristine material of the solar system. However, the study of IDP OM might be hindered by their further alteration by flash heating during atmospheric entry, and we have limited understanding on how short‐term heating influences their organic content. In order to investigate this problem, five CP‐IDPs were studied for their OM contents, distributions, and isotopic compositions at the submicro‐ to nanoscale levels. The OM contained in the IDPs in this study spans the spectrum from primitive OM to that which has been significantly processed by heat. Similarities in the Raman D bands of the meteoritic and IDP OMs indicate that the overall gain in the sizes of crystalline domains in response to heating is similar. However, the Raman ΓG values of the OM in all of the five IDPs clearly deviate from those of chondritic OM that had been processed during a prolonged episode of parent body heating. Such disparity suggests that the nonaromatic contents of the OM are different. Short duration heating further increases the H/C ratio and reduces the δ13C and δD values of the IDP OM. Our findings suggest that IDP OM contains a significant proportion of disordered C with low H content, such as sp2 olefinic C=C, sp3 C–C, and/or carbonyl contents as bridging material. 相似文献
11.
From an analysis of the distribution of sunspot groups with respect to their maximum areas we find that this distribution
consists of two distinct components. One component contributes to spot groups of all possible values of A* with a distribution density varying as ∼ exp (b1 á
*
1/2
) with b1 nearly constant from cycleto cycle and having a mean value ∼10-4 km-1. The other component is predominantly responsible for spot groups withA* ≲, 30 *10-6 hemisphere but may provide a few spot groups even above 50 * l0-6 hemisphere. This component may follow a distribution density ∼ exp (-b2 A*). We also determine the widths of the latitude zones over which spot groups in various intervals of A* appear and study their variation with time. These widths and their variations indicate that the two statistical samples of
spot groups may be produced by two families of flux-tube clusters as suggested earlier in a phenomenological model. Very thin
flux-tube clusters in the statistical samples seem to be related to the ephemeral active regions and X-ray bright points. 相似文献
12.
We describe global bifurcations from the libration points of non-stationary periodic solutions of the restricted three body problem. We show that the only admissible continua of non-stationary periodic solutions of the planar restricted three body problem, bifurcating from the libration points, can be the short-period families bifurcating from the Lagrange equilibria L
4, L
5. We classify admissible continua and show that there are possible exactly six admissible continua of non-stationary periodic solutions of the planar restricted three body problem. We also characterize admissible continua of non-stationary periodic solutions of the spatial restricted three body problem. Moreover, we combine our results with the Déprit and Henrard conjectures (see [8]), concerning families of periodic solutions of the planar restricted three body problem, and show that they can be formulated in a stronger way. As the main tool we use degree theory for SO(2)-equivariant gradient maps defined by the second author in [25].This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
13.
We study the simple periodic orbits of a particle that is subject to the gravitational action of the much bigger primary bodies
which form a regular polygonal configuration of (ν+1) bodies when ν=8. We investigate the distribution of the characteristic curves of the families and their evolution in the phase space of
the initial conditions, we describe various types of simple periodic orbits and we study their linear stability. Plots and
tables illustrate the obtained material and reveal many interesting aspects regarding particle dynamics in such a multi-body
system. 相似文献
14.
We have calculated the desorption rates of both physisorbed and chemisorbed ions from grain surfaces, due to the temperature increase at densities higher than 10–13 g cm–3. It has been found that physisorbed ions desorb from grain surfaces at neutral densities ofn>1.3×1011 cm–3, assuming that the desorption energyD is equal to 0.1 eV, while the desorption of chemisorbed ions from grain surface can only occur at neutral densities ofn>1015 cm–3, at which point thermal ionization becomes more dominant.The electrons are assumed to be emitted from grain surfaces in a manner similar to the thermonic emission from heated solid surfaces. It was found that the temperature at which electrons are emitted from negatively charged grains depends on the value of the work function of the material of the grain.The charge state has been calculated for two limiting cases. Neglecting the grain surface reactions in case 1, the resulting relative charge density represents an upper limit, such that the electrical conductivity remains high. In this situation the magnetic flux dissipation is mainly contributed by ambipolar diffusion. In the second case, it has been assumed that the charged particles are chemically adsorbed on grain surfaces such that their desorption is negligible. In this case the charge density decreases sharply with increase of neutral density. Therefore, the electrical conductivity decreases sufficiently and Ohmic dissipation becomes effective. 相似文献
15.
V. V. Shimansky S. A. Pozdnyakova N. V. Borisov I. F. Bikmaev V. V. Vlasyuk O. I. Spiridonova A. I. Galeev S. S. Mel’nikov 《Astrophysical Bulletin》2009,64(4):349-364
We analyze the physical state and the properties of the close binary systems HS 1857+5144 and Abell 65. We took the spectra
of both systems over a wide range of orbital phases with the 6-m telescope of the Special Astrophysical Observatory of the
Russian Academy of Sciences (SAO RAS) and obtained their multicolor light curves with the RTT150 and Zeiss-1000 telescopes
of the SAO RAS. We demonstrate that both Abell 65 and HS 1857+5144 are young precataclysmic variables (PV) with orbital periods
of P
orb
= 1.
d
003729 and P
orb
= 0.
d
26633331, respectively. The observed brightness and spectral variations during the orbital period are due to the radiation
of the cold component, which absorbs the short-wave radiation of the hot component and reemits it in the visual part of the
spectrum. A joint analysis of the brightness and radial velocity curves allowed us to find the possible and optimum sets of
their fundamental parameters. We found the luminosity excesses of the secondary components of HS 1857+5144 and Abell 65 with
respect to the corresponding Main Sequence stars to be typical for such objects. The excess luminosities of the secondary
components of all young PVs are indicative of their faster relaxation rate towards the quiescent state compared to the rates
estimated in earlier studies. 相似文献
16.
For the equation describing plane oscillations and rotations of a satellite, we consider families of symmetric generalized
periodic solutions with integral rotation number p. We give new confirmations of the hypothesis: there are only four classes of these families with topologically different
structures, namely, the classes of families of periodic solutions with p≥ 1, p= 0, p=−1, and p≤−2. Besides, we demonstrate that the vertices of cusps of these families are placed on some analytical curves, and the same
is true for the multiple intersections of these families with other families. 相似文献
17.
We prove that, in general, a given two-dimensional inhomogeneous potential V(x,y) does not allow for the creation of homogeneous families of orbits. Yet, depending on the case at hand, if the given potential satisfies certain conditions, this potential is compatible either with one (or two) monoparametric homogeneous families of orbits or at most with five such familes. The orbits are then found on the grounds of the given potential. 相似文献
18.
In the present article, a family of static spherical symmetric well behaved interior solutions is derived by considering the
metric potential g
44=B(1−Cr
2)−n
for the various values of n, such that (1+n)/(1−n) is positive integer. The solutions so obtained are utilised to construct the heavenly bodies’ like quasi-black holes such
as white dwarfs, neutron stars, quarks etc., by taking the surface density 2×1014 gm/cm3. The red shifts at the centre and on the surface are also computed for the different star models. Moreover the adiabatic
index is calculated in each case. In this process the authors come across the quarks star only. Least and maximum mass are
fond to be 3.4348M
Θ and 4.410454M
Θ along with the radii 21.0932 km and 23.7245 km respectively. 相似文献
19.
G. Hahn C. -I. Lagerkvist B. A. Lindblad 《Celestial Mechanics and Dynamical Astronomy》1993,56(1-2):131-141
By using theD-criterion Lindblad (1992) has identified 14 asteroid families from a sample of 4100 numbered asteroids with proper elements from Milani and Kneevi (1990). Taxonomic types and other physical properties for a significant number of objects in five of the families show strong homogeneity within each family, further strengthening their internal relationship.To test the hypothesis of a common origin in, e.g., a catastrophic collision event, we have set out to integrate the orbits of the members of the Maria, Dora and Oppavia-Gefion families over some 106 years. The mean distance for the Maria family is close to the 3:1 mean-motion resonance with Jupiter, while the other two families lie close to the 5:2 resonance.We used a simplified solar system model which included the perturbations by Jupiter and Saturn only and implemented Everhart's variable stepsize integrator RA15. All close encounters between the family members (within 0.1 AU) were recorded as well. Preliminary results from integrations over 4×105 years are presented here.The statistics of close encounters show pronounced peaks for several members within each family, while for others no significant levels above the background of random encounters or even very low frequencies were found. This indicates a subclustering within the families. Quite a lot of very close (<0.005 AU) mutual encounters are found, which suggest that, at least for the larger members in a family, the mutual gravitational interactions could be of some importance for the real orbital evolutions.The encounter statistics between the Dora and Oppavia family members suggest a possible interrelationship between this two groups. 相似文献
20.
Intersections of families of three-dimensional periodic orbits which define bifurcation points are studied. The existence conditions for bifurcation points are discussed and an algorithm for the numerical continuation of such points is developed. Two sequences of bifurcation points are given concerning the family of periodic orbits which starts and terminates at the triangular equilibrium pointsL
4,L
5. On these sequences two trifurcation points are identified forµ = 0.124214 andµ = 0.399335. The caseµ = 0.5 is studied in particular and it is found that the space families originating at the equilibrium pointsL
2,L
3,L
4,L
5 terminate on the same planar orbitm
1v of the familym. 相似文献