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1.
Jacques Laskar 《Celestial Mechanics and Dynamical Astronomy》2005,91(3-4):351-356
Recently, Breiter et al. [Celest. Mech. Dyn. Astron., 2004, 88, 153–161] reported the computation of Hansen coefficients X
k
γ ,m
for non-integer values of γ. In fact, the Hansen coefficients are closely related to the Laplace b
s
(m), and generalized Laplace coefficients b
s,r
(m) [Laskar and Robutel, 1995, Celest. Mech. Dyn. Astron., 62, 193–217] that do not require s,r to be integers. In particular, the coefficients X
0
γ ,m
have very simple expressions in terms of the usual Laplace coefficients b
γ +2
(m), and all their properties derive easily from the known properties of the Laplace coefficients. 相似文献
2.
The Franck-Condon factors and r-centroids, which are very closely related to vibrational transition probabilities, have been evaluated by the more reliable
numerical integration procedure for the bands of B
2∑+ − X
2∑+, F
2∑+ − X
2∑+ systems of SrF and C
1∑+ − X
1∑+, G
1Π − X
1∑+ systems of ScF molecules of astrophysical interest, using a suitable potential. 相似文献
3.
We study the stability of motion in the 3-body Sitnikov problem, with the two equal mass primaries (m
1 = m
2 = 0.5) rotating in the x, y plane and vary the mass of the third particle, 0 ≤ m
3 < 10−3, placed initially on the z-axis. We begin by finding for the restricted problem (with m
3 = 0) an apparently infinite sequence of stability intervals on the z-axis, whose width grows and tends to a fixed non-zero value, as we move away from z = 0. We then estimate the extent of “islands” of bounded motion in x, y, z space about these intervals and show that it also increases as |z| grows. Turning to the so-called extended Sitnikov problem, where the third particle moves only along the z-axis, we find that, as m
3 increases, the domain of allowed motion grows significantly and chaotic regions in phase space appear through a series of
saddle-node bifurcations. Finally, we concentrate on the general 3-body problem and demonstrate that, for very small masses, m
3 ≈ 10−6, the “islands” of bounded motion about the z-axis stability intervals are larger than the ones for m
3 = 0. Furthermore, as m
3 increases, it is the regions of bounded motion closest to z = 0 that disappear first, while the ones further away “disperse” at larger m
3 values, thus providing further evidence of an increasing stability of the motion away from the plane of the two primaries,
as observed in the m
3 = 0 case. 相似文献
4.
D. Viswanath 《Celestial Mechanics and Dynamical Astronomy》2006,94(2):213-235
The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses
1− μ and μ that circle each other with period equal to 2π. For small μ, a resonant periodic motion of the massless particle
in the rotating frame can be described by relatively prime integers p and q, if its period around the heavier primary is approximately 2π p/q, and by its approximate eccentricity e. We give a method for the formal development of the stable and unstable manifolds associated with these resonant motions.
We prove the validity of this formal development and the existence of homoclinic points in the resonant region. In the study
of the Kirkwood gaps in the asteroid belt, the separatrices of the averaged equations of the restricted three-body problem
are commonly used to derive analytical approximations to the boundaries of the resonances. We use the unaveraged equations
to find values of asteroid eccentricity below which these approximations will not hold for the Kirkwood gaps with q/p equal to 2/1, 7/3, 5/2, 3/1, and 4/1. Another application is to the existence of asymmetric librations in the exterior resonances.
We give values of asteroid eccentricity below which asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3,
and 1/2 resonances for any μ however small. But if the eccentricity exceeds these thresholds, asymmetric librations will exist
for μ small enough in the unaveraged restricted three-body problem. 相似文献
5.
O. O. Vasilkova 《Astronomy Letters》2010,36(3):227-230
Dynamical behaviour of a small binary with equal components, each of mass m, is considered under attraction of a heavy body of mass M. Differential equations of the general three-body problem are integrated numerically using the code by S. J. Aarseth (Aarseth,
Zare 1974) for mass ratios m/M within 10−11–10−4 range. The direct and retrograde orbits of light bodies about each other are considered which lie either in the plane of
moving their center of mass or in the plane perpendicular to it. It is shown numerically that the critical separation between
the binary components which leads to disruption of binary is proportional to (m/M)1/3. The criterion can be used for studying (in the first approximation) the motion of double stars and binary asteroids or computing
the parameters of magnetic monopol and antimonopol pairs. 相似文献
6.
In the problem of 2+2 bodies in the Robe’s setup, one of the primaries of mass m*1m^{*}_{1} is a rigid spherical shell filled with a homogeneous incompressible fluid of density ρ
1. The second primary is a mass point m
2 outside the shell. The third and the fourth bodies (of mass m
3 and m
4 respectively) are small solid spheres of density ρ
3 and ρ
4 respectively inside the shell, with the assumption that the mass and the radius of third and fourth body are infinitesimal.
We assume m
2 is describing a circle around m*1m^{*}_{1}. The masses m
3 and m
4 mutually attract each other, do not influence the motion of m*1m^{*}_{1} and m
2 but are influenced by them. We also assume masses m
3 and m
4 are moving in the plane of motion of mass m
2. In the paper, the equations of motion, equilibrium solutions, linear stability of m
3 and m
4 are analyzed. There are four collinear equilibrium solutions for the given system. The collinear equilibrium solutions are
unstable for all values of the mass parameters μ,μ
3,μ
4. There exist an infinite number of non collinear equilibrium solutions each for m
3 and m
4, lying on circles of radii λ,λ′ respectively (if the densities of m
3 and m
4 are different) and the centre at the second primary. These solutions are also unstable for all values of the parameters μ,μ
3,μ
4, φ, φ′. Such a model may be useful to study the motion of submarines due to the attraction of earth and moon. 相似文献
7.
8.
We estimate the values of the cosmological parameters using the data about peculiar velocities of 1493 flat edge-on spirals
from the RFGC catalogue. The obtained values Ω
m
= 0.21− 0.09
+ 0.22, σ8 = 1.07− 0.24
+ 0.28 differ from the WMAP values by approximately 2–3σ, but well agree with modern constraints on these parameters. Due to a strong
correlation between these quantities the shape of the 1σ, 2σ and 3σ-boundaries are rather narrow. This gives us the opportunity
to use this estimation to verify the corresponding values, obtained by different methods. 相似文献
9.
We present the results of our infrared observations of WR 140 (=V1687 Cyg) in 2001–2010. Analysis of the observations has
shown that the J brightness at maximum increased near the periastron by about 0
m
.3; the M brightness increased by ∼2
m
in less than 50 days. The minimum J brightness and the minimum L and M brightnesses were observed 550–600 and 1300–1400 days after the maximum, respectively. The JHKLM brightness minimum was observed in the range of orbital phases 0.7–0.9. The parameters of the primary O5 component of the
binary have been estimated to be the following: R(O5) ≈ 24.7R
⊙, L(O5) ≈ 8 × 105
L
⊙, and M
bol(O5) ≈ −10
m
. At the infrared brightness minimum, T
g ∼ 820–880 K, R
g ≈ 2.6 × 105
R
⊙, the optical depth of the shell at 3.5 μm is ∼5.3 × 10−6, and its mass is ≈1.4 × 10−8
M
⊙. At the maximum, the corresponding parameters are ∼1300 K, 8.6 × 104
R
⊙, ∼2 × 10−4, and ∼6 × 10−8
M
⊙; the mean rate of dust inflow (condensation) into the dust structure is ∼3.3 × 10−8
M
⊙ yr−1. The mean escape velocity of the shell from the heating source is ∼103 km s−1 and the mean dispersal rate of the shell is ∼1.1 × 10−8
M
⊙ yr−1. 相似文献
10.
We present two new luminous blue variable (LBV) candidate stars discovered in the M33 galaxy. We identified these stars as
massive star candidates at the final stages of evolution, presumably with a notable interstellar extinction. The candidates
were selected from the Massey et al. catalog based on the following criteria: emission in H
α
, V<18./m 5 and 0.m 35 < (B - V) < 1.m 2. The spectra of both stars reveal a broad and strong H
α
emission with extended wings (770 and 1000 kms−1). Based on the spectra we estimated the main parameters of the stars. Object N45901 has a bolometric luminosity log(L/L⊙) = 6.0–6.2 with the value of interstellar extinction A
V
= 2.3 ± 0.1. The temperature of the star’s photosphere is estimated as T⋆ ∼ 13000–15000 K, its probable mass on the Zero
Age Main Sequence is M∼ 60–80 M⊙. The infrared excess in N 45901 corresponds to the emission of warm dust with the temperature Twarm ∼ 1000 K, and amounts
to 0.1%of the bolometric luminosity. A comparison of stellar magnitude estimates from different catalogs points to the probable
variability of the object N45901. Bolometric luminosity of the second object, N125093, is log(L/L⊙) = 6.3 − 6.6, the value of interstellar extinction is A
V
= 2.75 ± 0.15. We estimate its photosphere’s temperature as T⋆∼ 13000–16000K, the initial mass as M ∼ 90–120 M⊙. The infrared excess in N125093 amounts to 5–6% of the bolometric luminosity. Its spectral energy distribution reveals two
thermal components with the temperatures Twarm ∼ 1000K and Tcold ∼ 480 K. The [Ca II] λλ7291, 7323 lines, observed in LBV-like stars Var A and N93351 in M33 are also present in the spectrum of N 125093. These lines
indicate relatively recent gas eruptions and dust activity linked with them. High bolometric luminosity of these stars and
broad H
α emissions allow classifying the studied objects as LBV candidates. 相似文献
11.
E.A. Perdios 《Astrophysics and Space Science》2003,286(3-4):501-513
In this paper, we determine series of horizontally critical symmetric periodic orbits of the six basic families, f,g,h,i,l,m, of the photogravitational restricted three-body problem, and computetheir vertical stability. We restrict our study in the
case where only the first primary is radiating, namely q
1≠1 andq
2=1. We also compare our results with those of Hénon and Guyot (1970) so as to study the effect of radiation to this kind of
orbits.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
12.
We have two mass points of equal masses m
1=m
2 > 0 moving under Newton’s law of attraction in a non-collision parabolic orbit while their center of mass is at rest. We
consider a third mass point, of mass m
3=0, moving on the straight line L perpendicular to the plane of motion of the first two mass points and passing through their
center of mass. Since m
3=0, the motion of m
1 and m
2 is not affected by the third and from the symmetry of the motion it is clear that m
3 will remain on the line L. The parabolic restricted three-body problem describes the motion of m
3. Our main result is the characterization of the global flow of this problem. 相似文献
13.
This paper investigates the stability of equilibrium points in the restricted three-body problem, in which the masses of the
luminous primaries vary isotropically in accordance with the unified Meshcherskii law, and their motion takes place within
the framework of the Gylden–Meshcherskii problem. For the autonomized system, it is found that collinear and coplanar points
are unstable, while the triangular points are conditionally stable. It is also observed that, in the triangular case, the
presence of a constant κ, of a particular integral of the Gylden–Meshcherskii problem, makes the destabilizing tendency of the radiation pressures
strong. The stability of equilibrium points varying with time is tested using the Lyapunov Characteristic Numbers (LCN). It
is seen that the range of stability or instability depends on the parameter κ. The motion around the equilibrium points L
i
(i=1,2,…,7) for the restricted three-body problem with variable masses is in general unstable. 相似文献
14.
The effect of small perturbation in the Coriolis and centrifugal forces on the location of libration point in the ‘Robe (1977)
restricted problem of three bodies’ has been studied. In this problem one body,m
1, is a rigid spherical shell filled with an homogeneous incompressible fluid of densityϱ
1. The second one,m
2, is a mass point outside the shell andm
3 is a small solid sphere of densityϱ
3 supposed to be moving inside the shell subject to the attraction ofm
2 and buoyancy force due to fluidϱ
1. Here we assumem
3 to be an infinitesimal mass and the orbit of the massm
2 to be circular, and we also suppose the densitiesϱ
1, andϱ
3 to be equal. Then there exists an equilibrium point (−μ + (ɛ′μ)/(1 + 2μ), 0, 0). 相似文献
15.
Josep Maria Cors César Castilho Claudio Vidal 《Celestial Mechanics and Dynamical Astronomy》2009,103(2):163-177
We consider a restricted three-body problem consisting of two positive equal masses m
1 = m
2 moving, under the mutual gravitational attraction, in a collision orbit and a third infinitesimal mass m
3 moving in the plane P perpendicular to the line joining m
1 and m
2. The plane P is assumed to pass through the center of mass of m
1 and m
2. Since the motion of m
1 and m
2 is not affected by m
3, from the symmetry of the configuration it is clear that m
3 remains in the plane P and the three masses are at the vertices of an isosceles triangle for all time. The restricted planar isosceles three-body
problem describes the motion of m
3 when its angular momentum is different from zero and the motion of m
1 and m
2 is not periodic. Our main result is the characterization of the global flow of this problem. 相似文献
16.
S. Chatterjee 《Journal of Astrophysics and Astronomy》1991,12(4):269-280
We present here rigorous analytical solutions for the Boltzmann-Poisson equation concerning the distribution of stars above
the galactic plane. The number density of stars is considered to follow a behaviour n(m,0) ∼H(m - m0)m−x, wherem is the mass of a star andx an arbitrary exponent greater than 2 and also the velocity dispersion of the stars is assumed to behave as < v2(m)> ∼ m−θ the exponent θ being arbitrary and positive. It is shown that an analytic expression can be found for the gravitational field
Kz, in terms of confluent hypergeometric functions, the limiting trends being Kz∼z for z →0, while Kz
→ constant for z → infinity. We also study the behaviour of < |z(m)|2>,i.e. the dispersion of the distance from the galactic disc for the stars of massm. It is seen that the quantity < |z(m)|2>∼ mt-θ, for m→ t, while it departs significantly from this harmonic oscillator behaviour for stars of lighter masses. It is suggested
that observation of < |z(m)|2> can be used as a probe to findx and hence obtain information about the mass spectrum. 相似文献
17.
We study numerically the asymmetric periodic orbits which emanate from the triangular equilibrium points of the restricted
three-body problem under the assumption that the angular velocity ω varies and for the Sun–Jupiter mass distribution. The
symmetric periodic orbits emanating from the collinear Lagrangian point L
3, which are related to them, are also examined. The analytic determination of the initial conditions of the long- and short-period
Trojan families around the equilibrium points, is given. The corresponding families were examined, for a combination of the
mass ratio and the angular velocity (case of equal eigenfrequencies), and also for the critical value ω = 2
, at which the triangular equilibria disappear by coalescing with the inner collinear equilibrium point L
1. We also compute the horizontal and the vertical stability of these families for the angular velocity parameter ω under consideration.
Series of horizontal–critical periodic orbits of the short-Trojan families with the angular velocity ω and the mass ratio
μ as parameters, are given. 相似文献
18.
A. G. Tlatov 《Astrophysics and Space Science》2009,323(3):221-224
The parameter G, which is determined from the general number of sunspots groups N
g
according to the daily observations G=∑(1/N
g
)2, is offered. This parameter is calculated for the days when there is at least one sunspots group. It characterizes the minimum
epoch solar activity. Parameter G mounts to the maximum during the epoch close to the minimal activity of sunspots. According to the data of the sequence of
sunspots group in Greenwich–USAF/NOAA observatory format, observation data of Kislovodsk solar station and also daily Wolf
number, the changes of parameter G during 100 years were reconstructed. It is demonstrated in the paper that parameter G’s amplitude in minimal solar activity n is linked with the sunspot cycle’s amplitude W
n+1 or one and half cycles. The 24th activity cycle prediction is calculated, which makes W
24=135(±12). 相似文献
19.
It is shown (1) that the coefficients Ai of the limb darkening functions I(μ)/Icenter = P5 (μ) = ∑Ai μi (i = 0... 5; μ = cos ϑ), which had been published by Neckel and Labs (Solar Phys. 153, 91, 1994), can well be approximated by analytical functions of wavelength λ, and (2) that at first sight purely formal extrapolation
of the functions P5(μ) to the very limb (μ = 0.0) is not meaningless: in combination with absolute intensities for the disk center these functions
yield ‘limb intensities’ which all correspond to almost the same ‘limb temperature’, Tlimb≈4746 K. Together these results lead to ‘reference functions’ which can quickly yield rather reliable values of the Sun's
continuum intensities, for any values of μ and λ. 相似文献
20.
E. P. Pavlenko 《Astrophysics》2006,49(1):105-119
Series of photometric CCD observations of the asynchronous polar BY Cam in a low accretion state (R = 14m–16m) were made on the K-380 telescope at the Crimean Astrophysical Observatory (CrAO) over 100 hours in the course of 31 nights
during 2004–2005. A period of P
1 = 0.137120±0.000002 days was found for the variations in the brightness, along with less significant periods of P
2 = 0.139759±0.000003 and P3 = 0.138428±0.000002 days, where P2 and P3 are obviously the orbital and rotation periods, while the dominant period P1 is the sideband period. A modulation in the brightness and an amplitude of 0.137 days in the oscillations at the orbital-rotational
beat period (synodic cycle) of 14.568±0.003 day are found for the first time. The profile of the modulation period is four
humped. This indicates that the magnetic field has a quadrupole component, which shows up well during the low brightness state.
Accretion takes place simultaneously into two or three accretion zones, but at different rates. The times of the times of
maxima for the main accretion zone vary with the phase of the beat period. Three types of variation of this sort are distinguished:
linear, discontinuous, and chaotic, which indicate changes in the accretion regimes. At synodic phases 0.25 and 0.78 the bulk
of the stream switches by 180°, and at phase 0.55, by ∼75°. At phases of 0.25–0.55 and 0.55–0.78, the O-C shift with a period
of 0.1384 days, which can be explained by a retrograde shift of the main accretion zone relative to the magnetic pole and/or
a change in the angle between the field lines and the surface of the white dwarf owing to the asynchronous rotation. For phases
of 0.78–1.25 the motion of the accretion zone is quite chaotic. It is found that synchronization of the components occurs
at a rate of less than dProt/Prot∼10−9 day/day.
__________
Translated from Astrofizika, Vol. 49, No. 1, pp. 121–137 (February 2006). 相似文献