共查询到20条相似文献，搜索用时 35 毫秒
1.
S. Kasperczuk 《Celestial Mechanics and Dynamical Astronomy》1994,58(4):387-391
This paper considers the integrability of generalized Yang-Mills system with the HamiltonianH
a
(p, q)=1/2(p
1
2
+p
2
2
+a
1
q
1
2
+a
2
q
2
2
)+1/4q
1
4
+1/4a
3
q
2
4
+ 1/2a
4
q
1
2
q
2
2
. We prove that the system is integrable for the cases: (A)a
1=a
2,a
3=a
4=1; (b)a
1=a
2,a
3=1,a
4=3; (C)a
1=a
2/4,a
3=16,a
4=6. Our main result is the presentation of these integrals. Only for cases A and B does the Yang-Mills Hamiltonian possess the Painlevé property. Therefore the Painlevé test does not take account of the integrability for the case C. 相似文献
2.
The Hill stability of the low mass binary system in the presence of a massive third body moving on a wider inclined orbit is investigated analytically. It is found that, in the case of the third body being on a nearly circular orbit, the region of Hill stability expands as the binary/third body mass ratio increases and the inclination (i) decreases. This i-dependence decreases very quickly with increasing eccentricity (e 2) of the third body relative to the binary barycentre. In fact, if e 2 is not extremely small, the Hill stable region can be approximately expressed in a closed form by setting i = 90°, and it contracts with increasing e 2 as ${e_2^2}$ for sufficiently low mass binary. Our analytic results are then applied to the observed triple star systems and the Kuiper belt binaries. 相似文献
3.
J. Anosova 《Astrophysics and Space Science》1996,238(2):223-238
The dynamical evolution of about 1.5 million planar hierarchical triple systems with a negative total energy and different-mass bodies is investigated by computer simulations. We considered both cases — prograde and retrograde motions of bodies. For every system, calculations were carried out either till a time when the Marchal'set al. (1984) criterion of escape of a body from a triple system was satisfied (the unstable triple systems) or during 1000 rotations of a total system (the stable triple systems). Computations were carried out on three computers-Sunstations in the Physical Research Laboratory, Ahmedabad, India during several months continuously. We changed smoothly the initial value of the coefficient of hierarchy of triples $$q = r_{3 - 12} /r_{12} $$ Wherer 12 is a distance between close bodiesM1,M2 andr 3–12 is a distance between their center of masses and a distant bodyM3. We define critical (minimum) values of the coefficientq of hierarchy of stable triple systems with a relative accuracy δq=1%. Ratios of masses of bodies belong to the interval [0.13, 244.00]. A possibility of extention of these results for hierarchical subsystems with different multiplicities inside clusters is discussed. 相似文献
4.
Two CCD epochs of light minimum and a complete R light curve of SS Ari are presented. The light curve obtained in 2007 was
analyzed with the 2003 version of the W-D code. It is shown that SS Ari is a shallow contact binary system with a mass ratio
q=3.25 and a degree of contact factor f=9.4%(±0.8%). A period investigation based on all available data shows that there may exist two distinct solutions about the
assumed third body. One, assuming eccentric orbit of the third body and constant orbital period of the eclipsing pair, results
in a massive third body with M
3=1.73M
⊙ and P
3=87.0 yr. On the contrary, assuming continuous period changes of the eclipsing pair the orbital period of tertiary is 37.75
yr and its mass is about 0.278M
⊙. Both of the cases suggest the presence of an unseen third component in the system. 相似文献
5.
M. Clutton-Brock 《Astrophysics and Space Science》1972,19(1):225-247
The aim of this series of papers is to develop straightforward methods of computing the response of flat galaxies to small perturbations. This Paper I considers steady state problems; Paper II considers time varying perturbations and the effects of resonances; and Paper III applies the methods developed in Papers I and II to a numerical study of the stability of flat galaxies.The general approach is to study the dynamics of each individual orbit. The orbits are described by their apocentric and pericentric radii,r
a
andr
p
, and the distribution function of an equilibrium model is a function ofr
a
andr
p
. The mass density and potential corresponding to a distribution function is found by means of an expansion in Hankel-Laguerre functions; the coefficients of the expansion being found by taking moments of the mass density of the individual orbits. This leads to a simple method of constructing equilibrium models.The response to a small perturbation is found by seeking the response of each orbit. When the perturbations are axisymmetric and slowly varying, the response can be easily found using adiabatic invariants. The potential is expanded in a series of Hankel-Laguerre functions, and the response operator becomes a discrete matrix. The condition that the model is stable against adiabatic radial perturbations is that the largest eigenvalue of the response matrix should be less than one.An analytic approximation to the response matrix is derived, and applied to estimate the eccentricity needed for stability against local perturbations. 相似文献
6.
The linear stability of the triangular equilibrium points in the photogravitational elliptic restricted three-body problem is examined and the stability regions are determined in the space of the parameters of mass, eccentricity, and radiation pressure, in the case of equal radiation factors of the two primaries. The full range of values of the common radiation factor is explored, from the gravitational caseq
1 =q
2 =q = 1 down to the critical value ofq = 1/8 at which the triangular equilibria disappear by coalescing on the rotating axis of the primaries. It is found that radiation pressure exerts a significant influence on the stability regions. For certain intervals of radiation values these regions become qualitatively different from the gravitational case as well as the solar system case considered in Paper I. There exist values of the common radiation factor, in the range considered, for which the triangular equilibrium points are stable for the entire range of mass distribution among the primaries and for large eccentricities of their orbits. 相似文献
7.
Sake J. Hogeveen 《Astrophysics and Space Science》1992,196(2):299-336
In order to determine the mass-ratio distribution of spectroscopic binary stars, the selection effects that govern the observations of this class of binary systems are investigated. The selection effects are modelled numerically and analytically. The results of the models are compared to the data inThe Eighth Catalogue of the Orbital Elements of Spectroscopic Binary Stars (DAO8) compiled by Battenet al. (1989). The investigations involve binary systems with Main-Sequence primary components only, in order to avoid confusion of evolutionary and selection effects.For single-lined spectroscopic binaries (SBI) it is found that the mass ratios (q=M
sec/M
prim) in general adhere to a distribution
q
q
-2 forq>q
0, withq
0=0.3. The observations are consistent with a distribution that is flat forq<q
0. The turn-over value varies fromq
0=0.3 for systems with B-type primaries, toq
0=0.55 for systems with K-type primaries. The semi-major axesa
1 are distributed according to
a
(a
1)a
1
-a
with an average value of
a
=1.3. The power varies from
a
=1.7 for systems with B-type primaries to
a
=0 for systems with K-type primaries. The eccentricitiese of the orbits of SBI systems are distributed according to
e
(e)e
-1.For double-lined spectroscopic binary stars (SBII) it is found that the shape of theq-distribution, as derived from observations, is almost entirely determined by selection effects. It is shown that the distribution is compatible with theq-distribution found for SBI systems. A sub-sample, consisting of the SBII systems from DAO8 with magnitudesm
V
5
m
, is less hampered by selection effects, and shows the same shape of theq-distribution as the SBI systems, at theq-interval (0.67, 1).It is estimated that 19–45% of the stars in the solar neighbourhood are spectroscopic binary systems. 相似文献
8.
The linear stability of the inner collinear equilibrium point of the photogravitational elliptic restricted three-body problem is examined and the stability regions are determined in the space of the parameters of mass, eccentricity and radiation pressure. The case of equal radiation factors of the two primaries is considered and the full range of values of the common radiation factor is explored, from the caseq
1 =q
2 =q = 1/8 at which the triangular equilibria disappear by coalescing on the rotating axis of the primaries transferring their stability to the collinear point, down toq = 0 at which value the stability regions in theµ - e plane disappear by shrinking down to zero size. It is found that radiation pressure exerts a significant influence on the stability regions. For certain intervals of radiation values these regions become qualitatively different from the gravitational case as well as the solar system case. They evolve as in the case of the triangular equilibrium point considered in a previous paper. There exist values of the common radiation factor, in the range considered, for which the collinear equilibrium point is stable for the entire range of mass distribution among the primaries and for large eccentricities of their orbits. 相似文献
9.
Rodica Roman 《Astrophysics and Space Science》2001,275(4):425-429
In the photogravitational restricted three-body problem, the role of theradiation-pressure is reviewed. By the analytical considerations, the existence of the `spatial' equilibrium points is analysed. In order to avoid the unknown parameters of the infinitesimal body, for the two component stars an analytical function 2 =f(1 ) is established.In contrast to results given by other authors, here only one pair of suchpoints is found. A numerical simulation for RW Monocerotis is undertakenand it is found L
6(–0.055; 0; +1.07) and L
7(–0.055; 0; –1.07). 相似文献
10.
K. E. Papadakis 《Astrophysics and Space Science》1995,232(2):337-354
The aim of the paper is to study the geometry of the Roche curvilinear coordinates (, , ) in the photogravitational circular restricted three-body problem, with varying radiation pressure, and special attention is given to the geometry of zero-velocity curves specified by the coordinate. The radiation pressure exerted by the primary bodies on the infinitesimal third body is considered the same (q
1 =q
2), and the primaries are taken to have equal masses (m
1 =m
2). The full range of values of the common radiation factor is explored, from the valueq
1 =q
2 = 1 (the gravitational three-body problem) down toq
1 =q
2 0. It is found that radiation has a strong influence on the geometry of the Roche coordinates and the zero-velocity curves. 相似文献
11.
12.
N. Delsate P. Robutel A. Lemaître T. Carletti 《Celestial Mechanics and Dynamical Astronomy》2010,108(3):275-300
We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed
by a third body, assumed to lay in the equatorial plane (Sun or Jupiter for example) using a Hamiltonian formalism. We are
able to determine, in the parameters space, the location of the frozen orbits, namely orbits whose orbital elements remain
constant on average, to characterize their stability/unstability and to compute the periods of the equilibria. The proposed
theory is general enough, to be applied to a wide range of probes around planet or natural planetary satellites. The BepiColombo
mission is used to motivate our analysis and to provide specific numerical data to check our analytical results. Finally,
we also bring to the light that the coefficient J
2 is able to protect against the increasing of the eccentricity due to the Kozai-Lidov effect and the coefficient J
3 determines a shift of the equilibria. 相似文献
13.
A period study of the young binary AR Aur based on the extensive series of published photoelectric/ccd minima times indicates the cyclic (O – C) variation for the system. This continuous oscillatory variation covers almost three cycles, about 6000 orbital periods, by the present observational data. It can be attributed to the light‐time effect due to a third body with a period of 23.68 ± 0.17 years in the system. The analysis yields a light‐time semi‐amplitude of 0.0084 ± 0.0002 day and an orbital eccentricity of 0.20 ± 0.04. Adopting the total mass of AR Aur, the mass of the third body assumed in the co‐planar orbit with the binary is M3 = 0.54 ± 0.03 M⊙ and the semimajor axis of its orbit is a3 = 13.0 + 0.2 AU. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
14.
Results of ourmeasurements of the longitudinal magnetic field B
z
for the young star RWAur A are presented. B
z
measured from the so-called narrow component of the He I 5876 line varies in the range from −1.47 ± 0.15 to +1.10 ± 0.15
kG. Our data are consistent with a stellar rotation period of }~5.6 days and the model of two hot spots with opposite magnetic
field polarities spaced about 180° apart in longitude. Relative to the Earth, the spot with B
z
< 0 lies in the hemisphere above the midplane of the accretion disk, while the spot with B
z
> 0 is below the midplane. The upper limit for B
z
(at the 3σ level) obtained by averaging all observations is 180 G for the photosphere and 220 and 230 G for the Hα and [OI] 6300 line formation regions, respectively. We have also failed to detect a field in the formation region of broad
emission line components: the upper limit for B
z
is 600 G. In two of 11 cases, we have detected a magnetic field in the formation region of the blue absorption wing of the
Na I D doublet lines, i.e., in the wind from RW Aur A: B
z
= −180 ± 50 and −810 ± 80 G. The radial velocity of the photospheric lines in RW Aur A averaged over all our observations
is }~+10.5 km s−1, i.e., a value lower than that obtained by Petrov et al. (2001) ten years earlier by 5.5 km s−1. Therefore, we discuss the possibility that RW Aur is not a binary but a triple system. 相似文献
15.
John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》1975,12(3):255-276
A method is developed to study the stability of periodic motions of the three-body problem in a rotating frame of reference, based on the notion of surface of section. The method is linear and involves the computation of a 4×4 variational matrix by integrating numerically the differential equations for time intervals of the order of a period. Several properties of this matrix are proved and also it is shown that for a symmetric periodic motion it can be computed by integrating for half the period only.This linear stability analysis is used to study the stability of a family of periodic motions of three bodies with equal masses, in a rotating frame of reference. This family represents motion such that two bodies revolve around each other and the third body revolves around this binary system in the same direction to a distance which varies along the members of the family. It was found that a large part of the family, corresponding to the case where the distance of the third body from the binary system is larger than the dimensions of the binary system, represents stable motion. The nonlinear effects to the linear stability analysis are studied by computing the intersections of several perturbed orbits with the surface of sectiony
3=0. In some cases more than 1000 intersections are computed. These numerical results indicate that linear stability implies stability to all orders, and this is true for quite large perturbations. 相似文献
16.
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
17.
Abstract— We describe results of 32 N‐body planetary accretion simulations that investigate the dependence of terrestrial‐planet formation on nebula surface density profile σ and evolution of the eccentricities of Jupiter and Saturn ej,s. Two surface density profiles are examined: a decaying profile with σ ∝ 1/a, where a is orbital semi‐major axis, and a peaked profile in which σ increases for a < 2 AU and decreases for a > 2 AU. The peaked profiles are generated by models of coagulation in an initially hot nebula. Models with initial ej,s = 0.05 (the current value) and 0.1 are considered. Simulations using the decaying profile with ej,s = 0.1 produce systems most like the observed planets in terms of mass‐weighted mean a and the absence of a planet in the asteroid belt. Simulations with doubled σ produce planets roughly twice as massive as the nominal case. Most initial embryos are removed in each simulation via ejection from the solar system or collision with the Sun. The asteroid belt is almost entirely cleared on a timescale of 10–100 Ma that depends sensitively on ej,s. Most initial mass with a < 2 AU survives, with the degree of mass loss increasing with a. Mass loss from the terrestrial region occurs on a timescale that is long compared to the mass loss time for the asteroid belt. Substantial radial mixing of material occurs in all simulations, but is greater in simulations with initital ej,s = 0.05. The degree of mixing is equivalent to a feeding zone of half width 1.5 and 0.9 AU for an Earth mass planet at 1 AU for the cases ej,s = 0.05 and 0.1, respectively. In simulations with ej,s = 0.05, roughly one‐third and 5–10% of the mass contained in final terrestrial planets originated in the region a > 2.5 AU for the decaying and peaked profiles, respectively. In the case ej,s = 0.1, the median mass accreted from a > 2.5 AU is zero for both profiles. 相似文献
18.
Marek Wolf P. G. Niarchos K. D. Gazeas V. N. Manimanis Lenka Kotková Anton Paschke Miloslav Zejda 《Astrophysics and Space Science》2006,304(1-4):181-183
Seven new precise times of minimum light have been gathered for the triple eccentric eclipsing binary YY Sgr (P = 2d.63, e = 0.16). Its O--C diagram is presented and improved elements of the apsidal motion and the light-time effect are given. We found a new short period of the third body of about 18.5 years in an eccentric orbit (e
3 ≃ 0.4). 相似文献
19.
R. K. Srivastava 《Astrophysics and Space Science》1987,139(2):373-387
A first detailed period study of the eclipsing RS CVn-binary system RW Com is presented. A new period (P=0d.2373455) based on 223 minima is given. The O–C diagrams of RW Com have been presented for the first time. Types of ten minima have been corrected judging the period trend. Period changes in different portions of the O–C diagram (Figure 2) have been estimated. The total change in period (P/P) ranges from 5.5×10–7 to 6.4×10–6. Thus, P ranges from 1.3×10–7 d to 1.5×10–6 d. Numerous minima are available in the time interval 1967 to 1986. This part of the O–C diagram (Figure 2) shows a sinusoidal variation, thus, it is suspected that RW Com could be a three-body system. The period of variation due to third body appears to be nearly 16 years. 相似文献
20.
We consider periodic halo orbits about artificial equilibrium points (AEP) near to the Lagrange points L
1 and L
2 in the circular restricted three body problem, where the third body is a low-thrust propulsion spacecraft in the Sun–Earth
system. Although such halo orbits about artificial equilibrium points can be generated using a solar sail, there are points
inside L
1 and beyond L
2 where a solar sail cannot be placed, so low-thrust, such as solar electric propulsion, is the only option to generate artificial
halo orbits around points inaccessible to a solar sail. Analytical and numerical halo orbits for such low-thrust propulsion
systems are obtained by using the Lindstedt Poincaré and differential corrector method respectively. Both the period and minimum
amplitude of halo orbits about artificial equilibrium points inside L
1 decreases with an increase in low-thrust acceleration. The halo orbits about artificial equilibrium points beyond L
2 in contrast show an increase in period with an increase in low-thrust acceleration. However, the minimum amplitude first
increases and then decreases after the thrust acceleration exceeds 0.415 mm/s2. Using a continuation method, we also find stable artificial halo orbits which can be sustained for long integration times
and require a reasonably small low-thrust acceleration 0.0593 mm/s2. 相似文献