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1.
Boris Bardin 《Celestial Mechanics and Dynamical Astronomy》2002,82(2):163-177
We deal with the planar restricted circular problem of three bodies. We study trajectories in a small neighborhood of the Lagrange equilibrium point L
4 when mass ratio is close to Routh's value. In particular, we show that the case of proper degeneracy takes place and for most initial conditions trajectories are conditionally-periodic. We obtain an approximate representation of families of periodic solution emanating from the equilibrium point L
4. We also show that in the case of instability of L
4 the trajectories starting in a vicinity of L
4 remain in a finite domain forever. We give an upper bound of this domain. To carry out our investigation, we analyze the dynamics of a general Hamiltonian system with two degrees of freedom in the case of 1 : 1 resonance in detail.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
2.
In this paper we consider a restricted equilateral four-body problem where a particle of negligible mass is moving under the Newtonian gravitational attraction of three masses (called primaries) which move on circular orbits around their center of masses such that their configuration is always an equilateral triangle (Lagrangian configuration). We consider the case of two bodies of equal masses, which in adimensional units is the parameter of the problem. We study numerically the existence of families of unstable periodic orbits, whose invariant stable and unstable manifolds are responsible for the existence of homoclinic and heteroclinic connections, as well as of transit orbits traveling from and to different regions. We explore, for three different values of the mass parameter, what kind of transits and energy levels exist for which there are orbits with prescribed itineraries visiting the neighborhood of different primaries. 相似文献
3.
Shannon L. Coffey André Deprit Etienne Deprit 《Celestial Mechanics and Dynamical Astronomy》1994,59(1):37-72
We say that a planet is Earth-like if the coefficient of the second order zonal harmonic dominates all other coefficients in the gravity field. This paper concerns the zonal problem for satellites around an Earth-like planet, all other perturbations excluded. The potential contains all zonal coefficientsJ
2 throughJ
9. The model problem is averaged over the mean anomaly by a Lie transformation to the second order; we produce the resulting Hamiltonian as a Fourier series in the argument of perigee whose coefficients are algebraic functions of the eccentricity — not truncated power series. We then proceed to a global exploration of the equilibria in the averaged problem. These singularities which aerospace engineers know by the name of frozen orbits are located by solving the equilibria equations in two ways, (1) analytically in the neighborhood of either the zero eccentricity or the critical inclination, and (2) numerically by a Newton-Raphson iteration applied to an approximate position read from the color map of the phase flow. The analytical solutions we supply in full to assist space engineers in designing survey missions. We pay special attention to the manner in which additional zonal coefficients affect the evolution of bifurcations we had traced earlier in the main problem (J
2 only). In particular, we examine the manner in which the odd zonalJ
3 breaks the discrete symmetry inherent to the even zonal problem. In the even case, we find that Vinti's problem (J
4+J
2
2
=0) presents a degeneracy in the form of non-isolated equilibria; we surmise that the degeneracy is a reflection of the fact that Vinti's problem is separable. By numerical continuation we have discovered three families of frozen orbits in the full zonal problem under consideration; (1) a family of stable equilibria starting from the equatorial plane and tending to the critical inclination; (2) an unstable family arising from the bifurcation at the critical inclination; (3) a stable family also arising from that bifurcation and terminating with a polar orbit. Except in the neighborhood of the critical inclination, orbits in the stable families have very small eccentricities, and are thus well suited for survey missions. 相似文献
4.
E. D. Kuznetsov P. E. Zakharova D. V. Glamazda A. I. Shagabutdinov S. O. Kudryavtsev 《Solar System Research》2012,46(6):442-449
The hardware-software complex of the SBG telescope of the Kourovka astronomical observatory of the Ural Federal University is described. The area-to-mass ratio of high-orbit objects was estimated from the results of positional observations at the SBG telescope. Positions and sizes of resonance zones are determined from the numerical simulation results depending on the area-to-mass ratio in the case of low-order resonances (1 : 1, 1 : 2, and 1 : 3). Secular perturbations of semimajor axes of orbits, caused by the Poynting-Robertson effect, are estimated in the neighborhood of low-order resonance zones at different area-to-mass ratios. 相似文献
5.
P. Bély L. Petro R. Burg L. Wade C. Beichman J. Gay P. Baudoz Y. Rabbia J.-M. Perrin 《Experimental Astronomy》1999,9(4):189-204
We present a concept for a space mission designed to make a mid-IR survey of potential zodiacal dust disks around nearby stars. We show that a two-aperture (0.6 m diameter), 10-m baseline, nulling interferometer located in a 1 × 4 AU, 4-yr solar orbit would allow for the survey of 400 stars in the solar neighborhood and permit a first-order determination of the disk inclination and radial dependences of density and temperature. The high dynamic range of the instrument may also be used to study additional astrophysical phenomena. Beyond its own scientific merit, such a mission would serve as a technological precursor to a larger interferometer of the type being considered for the detection of earth-like planets. 相似文献
6.
We investigate the neighborhood of the periodic eight-like orbit found by Moore (1993) and Chenciner and Montgomery (2000). One-, two-, and three-dimensional scans in body coordinates, velocities, and masses were constructed. We found the regions of initial conditions in which the maximum mutual separation did not exceed 5 distance units during 2000 time units (about 300 periods of the initial solution). Larger deviations from the periodic solution lead to distant body ejections and escapes. The identified regions of finite motions are complex in structure. In some sections, these are simple-connected manifolds, while in other sections, stability zones alternate with escape zones. We estimated the fractal dimensions of the stability regions in three-dimensional scans: it typically ranges from 2 to 3. In some cases, we found transitions between motions along the figure of eight in its neighborhood and motions in the vicinity of a periodic Broucke orbit in the isosceles three-body problem. 相似文献
7.
J. Roels 《Celestial Mechanics and Dynamical Astronomy》1975,12(3):327-336
The planar restricted 3-body problem, linearized in the neighborhood of Lagrangian equilibriaL 4 andL 5, has in general two distinct eigenvalues and their opposites. When they are pure imaginary and not multiples of each other, they generate two families of periodic solutions called long and short periodic families. This is essentially a consequence of the famous theorem of Liapunov (Siegel, 1956). We showed (Roels, 1971b) how to solve the problem when the eigenvalues are multiples of each other in building series with negative exponents instead of the integer expansions of Siegel (Roels and Lauterman, 1970). When the eigenvalues are equal, which is the case for the mass ratio of Routh, the problem was solved by Deprit and Henrard (1968) using formal series in ordinary unnormalized variables. That leads to very complicated series because of the use of variables that are not well adapted to the problem. The convergence of the series was proven by Meyer and Schmidt (1971). In this paper we solve the problem by using normalized variables. This brings us to build expansions with fractional exponents. So in summary, normalized variables generate integer series in the non-resonant cases, series with negative exponents in the case of resonancek≥3, and series with fractional exponents when the resonance is 1. 相似文献
8.
We consider a spatially homogeneous and isotropic flat Robertson-Walker model filled with a scalar (or tachyonic) field minimally
coupled to gravity in the framework of higher derivative theory. We discuss the possibility of the emergent universe with
normal and phantom scalar fields (or normal and phantom tachynoic fields) in higher derivative theory. We find the exact solution
of field equations in normal and phantom scalar fields and observe that the emergent universe is not possible in normal scalar
field as the kinetic term is negative. However, the emergent universe exists in phantom scalar field in which the model has
no time-like singularity at infinite past. The model evolves into an inflationary stage and finally admits an accelerating
phase at late time. The equation of state parameter is found to be less than −1 in early time and tends to −1 in late time
of the evolution. The scalar potential increases from zero at infinite past to a flat potential in late time. More precisely,
we discuss the particular case for phantom field in detail. We also carry out a similar analysis in case of normal and phantom
tachyonic field and observe that only phantom tachyonic field solution represents an emergent universe. We find that the coupling
parameter of higher order correction affects the evolution of the emergent universe. The stability of solutions and their
physical behaviors are discussed in detail. 相似文献
9.
O. Yu. Malkov 《Astrophysics》1994,37(3):256-260
Assuming that local missing mass exists, we consider its total amount, its nature, and its spatial distribution, emphasizing brown dwarfs and less massive objects. We show that under these assumptions the problem of local missing mass is essentially the problem of determining the lower limit of the masses of stars in the process of formation.We propose in addition one other possible source of local missing mass: photometrically unresovable double systems. We show that under certain conditions they can make a significant contribution to the visible matter in the solar neighborhood.Translated fromAstrofizika, Vol. 37, No. 3, 1994.In this paper we have also shown that under certain conditions photometrically unresolved double systems may make an important contribution to the amount of visible matter in the solar neighborhood.In the present paper we have attempted to explain only local missing mass. However, it may be that the nature of missing mass is the same on the whole range of scales of astronomical systems.The author is grateful to A. G. Masevich for a number of useful observations. This work was supported by the Russian Fund for Basic Research (RFFI 93-02-2942). 相似文献
10.
Emilio J. Alfaro Federico Elias Jesús Cabrera-Caño 《Astrophysics and Space Science》2009,324(2-4):141-146
We perform a study into the spatial and kinematical distribution of young open clusters in the solar neighborhood, distinguishing between Gould Belt and local Galactic disk members. We use a previous estimate of the structural parameters of both systems obtained from a sample of O to B6 stars from Hipparcos. The two star-forming regions that dominate and give the Gould Belt its characteristic inclined shape show a striking difference in their content of star clusters: while Ori OB1 is richly populated by open clusters, not a single one can be found within the boundaries of Sco OB2. This is mirrored in velocity space, translating again into an abundance of clusters in the region of the kinematic space populated by the members of Ori OB1, and a marginal number of them associated with Sco OB2. We interpret all these differences by characterizing the Orion region as a cluster complex typically surrounded by a stellar halo, and the Sco-Cen region as an OB association in the outskirts of the complex. The different contents of star clusters, the different heights above the Galactic plane and the different residual velocities of Ori OB1 and Sco OB2 can be explained in terms of their relative position with respect to the density maximum of the Local Arm in the solar neighborhood. The origin of this feature could have been the interaction of a density wave with the local interstellar medium close to the Galactic co-rotation radius. 相似文献
11.
We consider the trajectories in the neighborhood of a 2: 1 resonance (in periods of osculating motions of the outer and inner binaries) in the plane equal-mass three-body problem. We identified the zones of motions that are stable on limited time intervals. All of them correspond to the retrograde motions of the outer and inner subsystems. The prograde motions are unstable: the triple system breaks up into a final binary and an escaping component. In the barycentric nonrotating coordinate system, the trajectories occasionally form symmetric structures composed of several leaves. These structures persist for a long time, and, subsequently, the trajectories of the bodies fill compact regions in coordinate space. 相似文献
12.
Tilemahos J. Kalvouridis 《Astrophysics and Space Science》2008,317(1-2):107-117
We deal with some new aspects of the photo-gravitational Copenhagen case of the restricted three-body problem; more particularly, the distribution and the attracting domains of the stationary solutions of small particles that move in the neighborhood of two major bodies with equal masses when one or both primaries are radiation sources with constant luminosity. Under these conditions, each particle is subjected not only to gravitational forces but to the radiation emitted from the primaries as well. 相似文献
13.
Celestial coordinate reference systems in curved space-time 总被引：1，自引：1，他引：0
S. M. Kopejkin 《Celestial Mechanics and Dynamical Astronomy》1988,44(1-2):87-115
14.
Nowadays the scientific community considers that more than a third of the asteroids are double. The study of the stability
of these systems is quite complex, because of their irregular shapes and tumbling rotations, and requires a full body–full
body approach. A particular case is analysed here, when the secondary body is sufficiently small and distant from the primary
to be considered as a point mass satellite. Gravitational resonances (between the revolution of the satellite and the rotation
of the asteroid) of a small body in fast or slow rotation around a rigid ellipsoid are studied. The same model can be used
for the motion of a probe around an irregular asteroid. The gravitational potential induced by the primary body is modelled
by the MacMillan potential. The stability of the satellite is measured thanks to the MEGNO indicator (Mean Exponential Growth
Factor of Nearby Orbits). We present stability maps in the plane
(\fracbd, \fraccd){\left(\frac{b}{d}, \frac{c}{d}\right)} where d, b, and c are the three semi-axes of the ellipsoid shaping the asteroid. Special stable conic-like curves are detected on these maps
and explained by an analytical model, based on a simplification of the MacMillan potential for some specific resonances (1
: 1 and 2 : 1). The efficiency of the MEGNO to detect stability is confirmed. 相似文献
15.
In this paper, we study the validity of the generalized second law (GSL) in phantom dominated universe in the presence of a Reissner-Nordström (RN) black hole. Our study is independent of the origin of the phantom like behavior of the considered universe. We also discuss the GSL in the neighborhood of transition from quintessence to phantom regime. We show that for a constant equation of state parameter, the GSL may be satisfied provided that the temperature is proportional to de Sitter temperature. It is shown that in models with (only) a transition from quintessence to phantom regime the generalized second law does not hold in the transition epoch. Next we show that if the phantom energy has a chemical potential, then the GSL will hold if the mass of black hole is above from a critical value. 相似文献
16.
The paper develops a hamiltonian formulation describing the coupled orbital and spin motions of a rigid Mercury rotation about
its axis of maximum moment of inertia in the frame of a 3:2 spin orbit resonance; the (ecliptic) obliquity is not constant,
the gravitational potential of mercury is developed up to the second degree terms (the only ones for which an approximate
numerical value can be given) and is reduced to a two degree of freedom model in the absence of planetary perturbations. Four
equilibria can be calculated, corresponding to four different values of the (ecliptic) obliquity. The present situation of
Mercury corresponds to one of them, which is proved to be stable. We introduce action-angle variables in the neighborhood
of this stable equilibrium, by several successive canonical transformations, so to get two constant frequencies, the first
one for the free spin-orbit libration, the other one for the 1:1 resonant precession of both nodes (orbital and rotational)
on the ecliptic plane. The numerical values obtained by this simplified model are in perfect agreement with those obtained
by Rambaux and Bois [Astron. Astrophys. 413, 381–393].
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
17.
We present the results of our study of the peculiar motions for 41 galaxy clusters and groups in the regions of the Hercules and Leo superclusters (0.027 < z < 0.045). For this purpose, based on SDSS (Data Release 8) data, we compiled a sample of early-type galaxies in the investigated clusters and groups, constructed their fundamental planes (FPs), and determined independent distances and peculiar velocities. The Hubble law between the radial velocities galaxy clusters and the distances derived from the FPs holds for the rich Hercules supercluster as a whole. At the same time, however, significant peculiar motions along the line of sight with rms deviations of 736 ± 50 and 584 ± 50 km s?1 are observed within this supercluster and in its immediate neighborhood. In the poor Leo supercluster, the rms deviation is also large, 625 ± 70 km s?1. Its Hubble diagram exhibits the approach of galaxy clusters and groups along the line of sight relative to the most massive cluster A1185. In the immediate neighborhood of the Leo supercluster (virtually in its field), the rms deviation of the peculiar velocities is minimal, 287 ± 60 km s?1. 相似文献
18.
J. P. S. Carvalho R. Vilhena de Moraes A. F. B. A. Prado 《Celestial Mechanics and Dynamical Astronomy》2010,108(4):371-388
In this paper we present an analytical theory with numerical simulations to study the orbital motion of lunar artificial satellites.
We consider the problem of an artificial satellite perturbed by the non-uniform distribution of mass of the Moon and by a
third-body in elliptical orbit (Earth is considered). Legendre polynomials are expanded in powers of the eccentricity up to
the degree four and are used for the disturbing potential due to the third-body. We show a new approximated equation to compute
the critical semi-major axis for the orbit of the satellite. Lie-Hori perturbation method up to the second-order is applied
to eliminate the terms of short-period of the disturbing potential. Coupling terms are analyzed. Emphasis is given to the
case of frozen orbits and critical inclination. Numerical simulations for hypothetical lunar artificial satellites are performed,
considering that the perturbations are acting together or one at a time. 相似文献
19.
Liang Xi-long Zhao Jing-kun Chen Yu-qin Zhao Gang 《Chinese Astronomy and Astrophysics》2018,42(1):1-19
The stellar streams originated from the Galactic halo may be detected when they pass by the solar neighborhood, and they still keep some information at their birth times. Thus, the investigation of halo streams in the solar neighborhood is very important for understanding the formation and evolution of our Galaxy. In this paper, the researches of halo streams in the solar neighborhood are briefly reviewed. We have introduced the methods how to detect the halo streams and identify their member stars, summarized the progresses in the observation of member stars of halo streams and in the study of their origins, introduced in detail how to analyze the origins of halo streams in the solar neighborhood by means of numerical simulation and chemical abundance, and finally discussed the prospects of the LAMOST and GAIA in the research of halo streams in the solar neighborhood. 相似文献
20.
V. L. Afanasiev S. N. Dodonov S. S. Khrapov V. V. Mustsevoi A. V. Moiseev 《Astrophysical Bulletin》2007,62(1):1-14
We discuss causes of the formation of the observed kinematics and morphology of cones of ionized matter in the neighborhood of the nuclei of Seyfert galaxies. The results of linear stability analysis of an optically thin conic jet where radiation cooling and gravity play an important part are reported. The allowance for radiation cooling is shown to result in strong damping of all acoustic modes and to have insignificant effect on unstable surface Kelvin-Helmholtz modes. In the case of waveguide-resonance internal gravity modes radiative cooling suppresses completely the instability of waves propagating away from the ejection source and, vice versa, reduces substantially the growth time scale of unstable sourceward propagating modes. The results obtained can be used to study ionization cones in Seyfert galaxies with radio jets. In particular, our analysis shows that surface Kelvin-Helmholtz modes and volume harmonics are capable of producing regular features observed in optical emission-line images of such galaxies. 相似文献