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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.
VLBI-based offsets of the Celestial Pole positions, as well as the variations of UT (series of Goddard Space Flight Center, 1984–2005) are processed applying the Earth’s rotation theory (ERA) 2005 constructed by the numerical integration of the differential equations of rotation of the deformable Earth. The equations were published earlier (Krasinsky 2006) as the first part of the work. The resulting weighted root mean square (WRMS) errors of the residuals , for the angles of nutation and precession are 0.136 and 0.129 mas, respectively. They are significantly less than the corresponding values 0.172 and 0.165 mas for the IAU 2000 model adopted as the international standard. In ERA 2005, the angles , are related to the inertial ecliptical frame J2000, the angle including the precessional secular motion. As the published observational data are theory-dependent being related to IAU 2000, a procedure to confront the numerical theory to the observed Celestial Pole offsets and UT variations is developed. Processing the VLBI data has shown that beside the well known 435-day FCN mode of the free core nutation, there exits a second mode, FICN, caused by the inner part of the fluid core, with the period of 420 day close to that of the FCN mode. Beatings between the two modes are responsible for the apparent damping and excitation of the free oscillations, and are implicitly modeled by ERA 2005. The nutational and precessional motions in ERA 2005 are proved to be mutually consistent but only in case the relativistic correction for the geodetic precession is applied. Otherwise, the overall WRMS error of the residuals would increase by 35%. Thus, the effect of the geodetic precession in the Earth rotation is confirmed experimentally. The other finding is the reliable estimation δc = 3.844 ± 0.028° of the phase lag δc of the tides in the fluid core. When processing the UT variations, a simple model of the elastic interaction between the mantle and fluid core at their common boundary made it possible to satisfactory describe the largest observed oscillations of UT with the period of 18.6 year, reducing the WRMS error of the UT residuals to the value 0.18 ms (after removing the secular, annual and semi-annual terms). 相似文献
4.
From the analysis of all available radiometric measurements of distances between the Earth and the major planets (including
observations of martian landers and orbiters over 1971–2003 with the errors of few meters) the positive secular trend in the
Astronomical Unit AU is estimated as
. The given uncertainty is the 10 times enlarged formal error of the least-squares estimate and so accounts for possible
systematic errors of measurements and deficiencies of the mathematical model. The reliability of this estimate as well as
its physical meaning are discussed. A priori most plausible attribution of this effect to the cosmological expansion of the
Universe turns out inadequate. A model of the observables developed in the frame of the relativistic background metric of
the uniform isotropic Universe shows that the corresponding dynamical perturbations in the major planet motions are completely
canceled out by the Einstein effect of dependence of the rate of the observer’s clock (that keeps the proper time) on the
gravitational field, though separately values of these two effects are quite large and attainable with the accuracy achieved.
Another tentative source of the secular rate of AU is the loss of the solar mass due to the solar wind and electromagnetic
radiation but it amounts in
only to 0.3 m/cy. Excluding other explanations that seem exotic (such as secular decrease of the gravitational constant)
at present there is no satisfactory explanation of the detected secular increase of AU, at least in the frame of the considered
uniform models of the Universe. 相似文献
5.
6.
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
7.
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
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.
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
10.
Michael Efroimsky 《Celestial Mechanics and Dynamical Astronomy》2006,96(3-4):259-288
We continue the study undertaken in Efroimsky [Celest. Mech. Dyn. Astron. 91, 75–108 (2005a)] where we explored the influence of spin-axis variations of an oblate planet on satellite orbits. Near-equatorial satellites had long been believed to keep up with the oblate primary’s equator in the cause of its spin-axis variations. As demonstrated by Efroimsky and Goldreich [Astron. Astrophys. 415, 1187–1199 (2004)], this opinion had stemmed from an inexact interpretation of a correct result by Goldreich [Astron. J. 70, 5–9 (1965)]. Although Goldreich [Astron. J. 70, 5–9 (1965)] mentioned that his result (preservation of the initial inclination, up to small oscillations about the moving equatorial plane) was obtained for non-osculating inclination, his admonition had been persistently ignored for forty years. It was explained in Efroimsky and Goldreich [Astron. Astrophys. 415, 1187–1199 (2004)] that the equator precession influences the osculating inclination of a satellite orbit already in the first order over the perturbation caused by a transition from an inertial to an equatorial coordinate system. It was later shown in Efroimsky [Celest. Mech. Dyn. Astron. 91, 75–108 (2005a)] that the secular part of the inclination is affected only in the second order. This fact, anticipated by Goldreich [Astron. J. 70, 5–9 (1965)], remains valid for a constant rate of the precession. It turns out that non-uniform variations of the planetary spin state generate changes in the osculating elements, that are linear in , where is the planetary equator’s total precession rate that includes the equinoctial precession, nutation, the Chandler wobble, and the polar wander. We work out a formalism which will help us to determine if these factors cause a drift of a satellite orbit away from the evolving planetary equator.By “precession,” in its most general sense, we mean any change of the direction of the spin axis of the planet—from its long-term variations down to nutations down to the Chandler wobble and polar wander. 相似文献
11.
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
12.
Bernard De Saedeleer 《Celestial Mechanics and Dynamical Astronomy》2006,95(1-4):407-423
We present here the first numerical results of our analytical theory of an artificial satellite of the Moon. The perturbation method used is the Lie Transform for averaging the Hamiltonian of the problem, in canonical variables: short-period terms (linked to l, the mean anomaly) are eliminated first. We achieved a quite complete averaged model with the main four perturbations, which are: the synchronous rotation of the Moon (rate
), the oblateness J
2 of the Moon, the triaxiality C
22 of the Moon (
) and the major third body effect of the Earth (ELP2000). The solution is developed in powers of small factors linked to these perturbations up to second-order; the initial perturbations being sorted ( is first-order while the others are second-order). The results are obtained in a closed form, without any series developments in eccentricity nor inclination, so the solution apply for a wide range of values. Numerical integrations are performed in order to validate our analytical theory. The effect of each perturbation is presented progressively and separately as far as possible, in order to achieve a better understanding of the underlying mechanisms. We also highlight the important fact that it is necessary to adapt the initial conditions from averaged to osculating values in order to validate our averaged model dedicated to mission analysis purposes. 相似文献
13.
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
14.
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
15.
F. Gonzalez-Gascon A. Gonzalez-Lopez P. J. Pascual-Broncano 《Celestial Mechanics and Dynamical Astronomy》1984,33(1):85-97
In this paper we prove that Szebehely's equation implies the condition necessary and sufficient in order that the Dainelli-Whittaker formulas be obtained from a potential function. Thus, we prove that Szebehely's equation is not only a necessary condition to be satisfied by the potential U
but is also a sufficient condition. This was shown by Broucke and Lass (1977) using a procedure different from ours. We obtain also a first order partial differential equation for the function g2
appearing in the paper of Broucke and Lass. This equation, being of a quite simple structure, is quite adequate for its integration, and this is shown by examples. 相似文献
16.
V. A. Brumberg 《Celestial Mechanics and Dynamical Astronomy》2003,85(3):269-291
The distinctive feature of the relativistic restricted three-body problem within the c
–5 order of accuracy (2
post-Newtonian approximation) is the presence of the gravitational radiation. To simplify the problem the motion of the massive binary components is assumed to be quasi-circular. In terms of time these orbits have linearly changing radii and quadratically changing phase angles. By substituting this motion into the Newtonian-like equations of motion one gets the quasi-Newtonian restricted quasi-circular three-body problem sufficient to take into account the main indirect perturbations caused by the binary radiation terms. Such problem admits the Lagrange-like quasi-libration solutions and rather simple quasi-circular orbits lying at large distance from the binary. 相似文献
17.
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:
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相似文献
18.
In this work, we shall confine ourselves to solve analytically the integrals called
,
for the two components of albedo radiation pressure on an Earth’s satellite. When the Earth’s albedo is variable, as far as
we know, this case has not been dealt with analytically. We shall solve these two integrals when the satellite’ horizon is
illuminated and when the sun lies on the equator. This approach will facilitate the evaluation of the mentioned two equations.
We will also compare our results with previous works obtained numerically. 相似文献
19.
Arbab I. Arbab 《Astrophysics and Space Science》2009,323(2):181-184
In the framework of unifying gravity and electromagnetism, we have shown that accelerating objects emit gravitational wave
as those determined by Larmor formula for the accelerating charged particle. We have found new formulae for the power of Gravitational
waves radiated by spinning and orbiting objects. The minimum wavelength of the gravitational wave emitted by an object of
mass m and radius R is
. 相似文献
20.
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
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