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1.
G. A. Krasinsky 《Celestial Mechanics and Dynamical Astronomy》2008,101(4):325-336
The long-term systematic errors of the analytical theories IAU 2000 and IAU 2006 of the Earth’s precession–nutational motion
are studied making use of the VLBI data of 1984–2007. Several independent methods give indubitable evidence of the significant
quadratic error in the IAU 2000 residuals of the precessional angle while the adopted value of the secular decrease /cy of the Earth’s ellipticity e (derived from Satellite Laser Ranging data) should manifest itself in the residuals of as the negative quadratic trend . The problem with the precession of the IAU 2006 theory adopted as a new international standard and based on the precession
model P03 (Capitaine et al., Astron Astrophys 432:355–367, 2005) appears to be even more serious because the above mentioned quadratic term has already been incorporated into the P03 precession. Our analysis of the VLBI data demonstrates that the quadratic trend
of the IAU 2006 residuals does amount to the expected value (30.0 ± 3) mas/cy2. It means, first, that the theoretical precession rate of IAU 2006 should be augmented by the large secular correction and, second, that the available VLBI data have potentiality of estimating the rate . And indeed, processing these data by the numerical theory ERA of the Earth’s rotation (Krasinsky, Celest Mech Dyn Astron
96:169–217, 2006, Krasinsky and Vasilyev, Celest Mech Dyn Astron 96:219–237, 2006) yields the estimate /cy statistically in accordance with the satellite-based . On the other hand, applying IAU 2000/2006 models, the positive value /cy is found which is incompatible with the SLR estimate and, evidently, has no physical meaning. The large and steadily increasing
error of the precession motion of the IAU 2006 theory makes the task of replacing IAU 2006 by a more accurate model be most
pressing. 相似文献
2.
We perform the bifurcation analysis of the Kepler problem on
and
. An analog of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of a Newtonian
center moving along a geodesic on
and
(the restricted two-body problem). For the case of a small curvature, the pericenter shift is computed using the perturbation
theory. We also present the results of numerical analysis based on an analogy with the motion of a rigid body. 相似文献
3.
In this paper, dilaton in Weyl-Scaled induced gravitational theory is regarded as a candidate of dark energy. When the potential of dilaton field is taken as the form of a double exponential , we find that there exist attractor solutions in dilatonic dark energy model, and these attractors correspond to an equations of state and a cosmic density parameter , which are important features for a dark energy model that can meet the current observations. We find out the sufficient condition of the existence of a late time de Sitter attractor. 相似文献
4.
5.
Irina N. Kitiashvili Alexander Gusev 《Celestial Mechanics and Dynamical Astronomy》2008,100(2):121-140
We investigate the evolution of the rotational axes of exoplanets under the action of gravitational and magnetic perturbations.
The planet is assumed to be dynamically symmetrical and to be magnetised along its dynamical-symmetry axis. By qualitative
methods of the bifurcation theory of multiparametric PDEs, we have derived a gallery of 69 phase portraits. The portraits
illustrate evolutionary trajectories of the angular momentum of a planet for a variety of the initial conditions, for different values of the ratio between parameters describing gravitational
and magnetic perturbations, and for different rates of the orbital evolution. We provide examples of the phase portraits,
that reveal the differences in topology and the evolutionary track of in the vicinity of an equilibrium state. We determine the bifurcation properties, i.e., the way of reorganisation of phase
trajectories in the vicinities of equilibria; and we point out the combinations of parameters’ values that permit ip-overs
from a prograde to a retrograde spin mode. 相似文献
6.
G. A. krasinsky 《Celestial Mechanics and Dynamical Astronomy》1999,75(1):39-66
Analytical expressions for tidal torques induced by a tide‐arising planet which perturbs rotation of a nonrigid body are derived.
Corresponding expressions both for secular and periodic perturbations of the Euler's angles are given for the case of the
earth's rotation. Centennial secular rates of the nutation angle θ and of the earth's angular velocity ω, as well as the centennial
logarithmic decrement ν of the Chandler wobble are evaluated:
mas,
.
In the Universal Time (UT) a large out‐of‐phase (sine) dissipative term with the period 18.6 years and the amplitude 2.3 ms
is found. Corrections to nutation coefficients, which presumably have not been taken into account in IAU theory, are given.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
7.
Stanisław P. Kasperczuk 《Celestial Mechanics and Dynamical Astronomy》2000,76(4):215-227
In a recent paper Ballersteros and Ragnisco (1998) have proposed a new method of constructing integrable Hamiltonian systems.
A new class of integrable systems may be devised using the following sequence:
, where A is a Lie algebra
is a Lie–Poisson structure on R
3, C is a Casimir for
is a reduced Poisson bracket and (A, ▵) is a bialgebra. We study the relation between a Lie-Poisson stucture Λ and a reduced Poisson bracket
, which is a key element in using the Lie algebra A to constructing this sequence. New examples of Lie algebras and their
related integrable Hamiltonian systems are given.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
8.
Using a 12th order expansion of the perturbative potential in powers of the eccentricities and the inclinations, we study
the secular effects of two non-coplanar planets which are not in mean–motion resonance. By means of Lie transformations (which
introduce an action–angle formulation of the Hamiltonian), we find the four fundamental frequencies of the 3-D secular three-body
problem and compute the long-term time evolutions of the Keplerian elements. To find the relations between these elements,
the main combinations of the fundamental frequencies common to these evolutions are identified by frequency analysis. This
study is performed for two different reference frames: a general one and the Laplace plane. We underline the known limitations
of the linear Laplace–Lagrange theory and point out the great sensitivity of the 3-D secular three-body problem to its initial
values. This analytical approach is applied to the exoplanetary system Andromedae in order to search whether the eccentricities evolutions and the apsidal configuration (libration of ) observed in the coplanar case are maintained for increasing initial values of the mutual inclination of the two orbital
planes.
Anne-Sophie Libert is FNRS Research Fellow. 相似文献
9.
The measurements of pulsar frequency second derivatives have shown that they are 102−106 times larger than expected for standard pulsar spin-down law, and are even negative for about half of pulsars. We explain
these paradoxical results on the basis of the statistical analysis of the rotational parameters ν,
and
of the subset of 295 pulsars taken mostly from the ATNF database. We have found a strong correlation between
and
for both
and
, as well as between ν and
. We interpret these dependencies as evolutionary ones due to
being nearly proportional to the pulsars’ age. The derived statistical relations as well as “anomalous” values of
are well described by assuming the long-time variations of the spin-down rate. The pulsar frequency evolution, therefore,
consists of secular change of ν
ev(t),
and
according to the power law with n≈5, the irregularities, observed within a timespan as a timing noise, and the variations on the timescale larger than that—several
decades.
This work has been supported by the Russian Foundation for Basic Research (grant No 04-02-17555), Russian Academy of Sciences
(program “Evolution of Stars and Galaxies”), and by the Russian Science Support Foundation. The authors would also like to
thank the anonymous referee for valuable comments. 相似文献
10.
11.
G. A. Krasinsky 《Celestial Mechanics and Dynamical Astronomy》2006,96(3-4):169-217
Improved differential equations of the rotation of the deformable Earth with the two-layer fluid core are developed. The equations describe both the precession-nutational motion and the axial rotation (i.e. variations of the Universal Time UT). Poincaré’s method of modeling the dynamical effects of the fluid core, and Sasao’s approach for calculating the tidal interaction between the core and mantle in terms of the dynamical Love number are generalized for the case of the two-layer fluid core. Some important perturbations ignored in the currently adopted theory of the Earth’s rotation are considered. In particular, these are the perturbing torques induced by redistribution of the density within the Earth due to the tidal deformations of the Earth and its core (including the effects of the dissipative cross interaction of the lunar tides with the Sun and the solar tides with the Moon). Perturbations of this kind could not be accounted for in the adopted Nutation IAU 2000, in which the tidal variations of the moments of inertia of the mantle and core are the only body tide effects taken into consideration. The equations explicitly depend on the three tidal phase lags δ, δ
c, δ
i responsible for dissipation of energy in the Earth as a whole, and in its external and inner cores, respectively. Apart from the tidal effects, the differential equations account for the non-tidal interaction between the mantle and external core near their boundary. The equations are presented in a simple close form suitable for numerical integration. Such integration has been carried out with subsequent fitting the constructed numerical theory to the VLBI-based Celestial Pole positions and variations of UT for the time span 1984–2005. Details of the fitting are given in the second part of this work presented as a separate paper (Krasinsky and Vasilyev 2006) hereafter referred to as Paper 2. The resulting Weighted Root Mean Square (WRMS) errors of the residuals dθ, sin θd for the angles of nutation θ and precession are 0.136 mas and 0.129 mas, respectively. They are significantly less than the corresponding values 0.172 and 0.165 mas for IAU 2000 theory. The WRMS error of the UT residuals is 18 ms. 相似文献
12.
We consider multidimensional cosmological model with a higher-dimensional product manifold M = R × × /Γ, where is d
o-dimensional Ricci-flat external (our) space and /Γ is d
1-dimensional compact hyperbolic internal space. M2-brane solution for this model has the stage of accelerating expansion of the external space. We apply this model to explain
the late time acceleration of our Universe. Recent observational data (the Hubble parameter at the present time and the redshift
when the deceleration parameter changes its sign) fix fully all free parameters of the model. As a result, we find that considered
model has too big size of the internal space at the present time and variation of the effective four-dimensional fine structure
constant strongly exceeds the observational limits.
The article is published in the original. 相似文献
13.
Thomas J. Kelly 《Celestial Mechanics and Dynamical Astronomy》1989,46(1):19-25
Techniques are developed to facilitate the transformation of a perturbed Keplerian system into Deláunay normal form at first
order. The implicit dependence of the Hamiltonian on 1, the mean anomaly, through the explicit variable f, the true anomaly,
or E, the eccentric anomaly, is removed through first order for terms of the form:
|
相似文献
14.
Range of values of the Sun's mass quadrupole moment of coefficient J2 arising both from experimental and theoretical determinations enlarge across literature on two orders of magnitude, from
around 10-7 until to 10-5. The accurate knowledge of the Moon's physical librations, for which the Lunar Laser Ranging data reach an outstanding precision
level, prove to be appropriate to reduce the interval of J2 values by giving an upper bound of J2. A solar quadrupole moment as high as 1.1 10-5 given either from the upper bounds of the error bars of the observations, or from the Roche's theory, is not compatible with
the knowledge of the lunar librations accurately modeled and observed with the LLR experiment. The suitable values of J2 have to be smaller than 3.0 10-6.
As a consequence, this upper bound of 3.0 10-6 is accepted to study the impact of the Sun's quadrupole moment of mass on the dynamics of the Earth-Moon system. Such as
effect (with J2 = 5.5±1.3 × 10-6) has been already tested in 1983 by Campbell & Moffat using analytical approximate equations, and thus for the orbits of
Mercury, Venus, the Earth and Icarus. The approximate equations are no longer sufficient compared with present observational
data and exact equations are required. As if to compute the effect on the lunar librations, we have used our BJV relativistic
model of solar system integration including the spin-orbit coupled motion of the Moon. The model is solved by numerical integration.
The BJV model stems from general relativity by using the DSX formalism for purposes of celestial mechanics when it is about
to deal with a system of n extended, weakly self-gravitating, rotating and deformable bodies in mutual interactions.
The resulting effects on the orbital elements of the Earth have been computed and plotted over 160 and 1600 years. The impact
of the quadrupole moment of the Sun on the Earth's orbital motion is mainly characterized by variations of
,
, and
. As a consequence, the Sun's quadrupole moment of mass could play a sensible role over long time periods of integration of
solar system models.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
15.
Despina Voyatzi Simos Ichtiaroglou 《Celestial Mechanics and Dynamical Astronomy》2005,93(1-4):331-342
We study the problem of the motion of a unit mass on the unit sphere
and examine the relation between integrability and certain monoparametric families of orbits. In particular we show that
if the potential is compatible with a family of meridians, it is integrable with an integral linear in the velocities, while
a family of parallels guarantees integrability with an integral quadratic in the velocities. 相似文献
16.
A. Z. Bonanos K. Z. Stanek R. P. Kudritzki L. Macri D. D. Sasselov J. Kaluzny D. Bersier F. Bresolin T. Matheson B. J. Mochejska N. Przybilla A. H. Szentgyorgyi J. Tonry G. Torres 《Astrophysics and Space Science》2006,304(1-4):207-209
We present the first direct distance determination to a detached eclipsing binary in M33, which was found by the DIRECT Project. Located in the OB 66 association, it was one of the most suitable detached eclipsing binaries found by DIRECT for distance determination, given its 4.8938 day period. We obtained follow-up BV photometry and spectroscopy from which we determined the parameters of the system. It contains two O7 main sequence stars with masses of and and radii of and , respectively. We derive temperatures of K and K and determine the reddening . Using HST photometry for flux calibration in the V band, we obtain a preliminary distance modulus of mag ( kpc). The photometry and thus distance is subject to revision in the final paper. 相似文献
17.
We explore self-similar hydrodynamic evolution of central voids embedded in an isothermal gas of spherical symmetry under
the self-gravity. More specifically, we study voids expanding at constant radial speeds in an isothermal gas and construct
all types of possible void solutions without or with shocks in surrounding envelopes. We examine properties of void boundaries
and outer envelopes. Voids without shocks are all bounded by overdense shells and either inflows or outflows in the outer
envelope may occur. These solutions, referred to as type
void solutions, are further divided into subtypes
and
according to their characteristic behaviours across the sonic critical line (SCL). Void solutions with shocks in envelopes
are referred to as type
voids and can have both dense and quasi-smooth edges. Asymptotically, outflows, breezes, inflows, accretions and static outer
envelopes may all surround such type
voids. Both cases of constant and varying temperatures across isothermal shock fronts are analyzed; they are referred to as
types
and
void shock solutions. We apply the ‘phase net matching procedure’ to construct various self-similar void solutions. We also
present analysis on void generation mechanisms and describe several astrophysical applications. By including self-gravity,
gas pressure and shocks, our isothermal self-similar void (ISSV) model is adaptable to various astrophysical systems such
as planetary nebulae, hot bubbles and superbubbles in the interstellar medium as well as supernova remnants.
相似文献
18.
The motion of spin particles in the Schwarzschild field is examined in this paper. It is shown that Mathisson-Papapetrou equations under additional conditions
, where
is the Lie derivative of the Killing vector
j
, permit only radial motion, motion in the equatorial plane and in the equilibrium points. All these types of motion are considered more in detail. 相似文献
19.
I. Stellmacher 《Celestial Mechanics and Dynamical Astronomy》1999,75(3):185-200
The motion of Hyperion is an almost perfect application of second kind and second genius orbit, according to Poincaré’s classification.
In order to construct such an orbit, we suppose that Titan’s motion is an elliptical one and that the observed frequencies
are such that 4n
H−3n
T+3n
ω=0, where n
H, n
T are the mean motions of Hyperion and Titan, n
ω is the rate of rotation of Hyperion’s pericenter. We admit that the observed motion of Hyperion is a
periodic motion
such as
. Then,
.N
H, N
T, k∈ N
+. With that hypothesis we show that Hyperion’s orbit tends to a particular periodic solution among the periodic solutions
of the Keplerian problem, when Titan’s mass tends to zero. The condition of periodicity allows us to construct this orbit
which represents the real motion with a very good approximation.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
20.
A linear correlation between the ratio of the[CII( $^{\text{2}}$ P
|