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1.
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.
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   

3.
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   

4.
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   

5.
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.
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   

7.
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   

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.
Explicit construction of the solutions of the Hamiltonian system given by H = H 0(J) – A(J) cos (ideal resonance problem), two orders of approximation beyond the well-known pendulum approximation. The given solutions are valid for libration amplitudes of order . The procedure used is extended to allow the construction of the solutions of Hamiltonians with perturbations involving two degrees of freedom; the post-pendulum solution of an example of this kind is constructed.  相似文献   

11.
Approximation formulas are found for and , wherex(t) satisfies ,x(0)=x 0,x(1)=x 1. The results are applied to an example of two-body motion.  相似文献   

12.
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.
Analytical techniques are employed to demonstrate certain invariant properties of families of moon-to-earth trajectories. The analytical expressions which demonstrate these properties have been derived from an earlier analytical solution of the restricted three-body problem which was developed by the method of matched asymptotic expansions. These expressions are given explicitly to orderµ 1/2 where is the dimensionless mass of the moon. It is also shown that the inclusion of higher order corrections does not affect the nature of the invariant properties but only increases the accuracy of the analytic expressions.The results are compared with the work of Hoelker, Braud, and Herring who first discovered invariant properties of earth-to-moon trajectories by exact numerical integration of the equations of motion. (Similar properties for moon-to-earth trajectories follow from the principle of reflection). In each instance the analytical expressions result in properties which are equivalent, to orderµ 1/2, with those found by numerical integration. Some quantitative comparisons are presented which show the analytical expressions to be quite accurate for calculating particular geometrical characteristics.

Nomenclature

Orbital Elements near the Moon energy - angular momentum - semi-major axis - eccentricity - inclination - argument of node - argument of pericynthion Orbital Elements near the Earth h e energy - l e angular momentum - i inclination - argument of node - argument of perigee - t f time of flight Other symbols parameters used in matehing - U a function of the energy near the earth - a function of the angular momentum near the earth - r p perigee radius - perincynthion radius - radius at node near moon - true anomaly of node near moon - initial angle between node near moon and earth-moon line - a function ofU, , andi - earth phase angle - dimensionless mass of the moon - U 0, U1 U=U 0+U 1 - i 0, i1/2, i1 i=i 0+µ 1/2 i 1/2+µ i 1 - 0, 1/2, 1 = 0+µ 1/2 i 1/2+µ i 1 - p longitude of vertex line - n latitude of vertex line - R o ,S o ,N o functions ofU 0 and - a function ofU 0, and   相似文献   

14.
The non-linear stability of L 4 in the restricted three-body problem has been studied when the bigger primary is a triaxial rigid body with its equatorial plane coincident with the plane of motion. It is found that L 4 is stable in the range of linear stability except for three mass ratios:
where A1, A2 depend upon the lengths of the semi axes of the triaxial rigid body. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

15.
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   

16.
Relations between integrable systems in plane and curved spaces   总被引：1，自引：0，他引：1  
We consider trajectory isomorphisms between various integrable systems on an n-dimensional sphere S n and a Euclidean space . Some of the systems are classical integrable problems of Celestial Mechanics in plane and curved spaces. All the systems under consideration have an additional first integral quadratic in momentum and can be integrated analytically by using the separation of variables. We show that some integrable problems in constant curvature spaces are not essentially new from the viewpoint of the theory of integration, and they can be analyzed using known results of classical Celestial Mechanics.  相似文献   

17.
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   

18.
Closely spaced microphotometer tracings parallel to the dispersion of one excellent frame of a K-line time sequence have been utilized for a study of the nature of the K2v , K2R intensities in the case of the solar chromosphere. The frequency of occurrence of the categories of intensity ratio are as follows: per cent; per cent; per cent; per cent; per cent. Two types of absorbing components are postulated to explain the pattern of observed K2v , k2R intensity ratios. One component with minor Doppler displacements acting on the normal K232 profile, where K2V >K2R , produces the cases K2v K2R , K2v = K2R , K2v <K2R . The other component arises from dark condensations which are of size 3500 kms as seen in K2R . They have principally large down flowing velocities in the range 5–8 km/sec and are seen on K3 spectroheliograms with sizes of about 5000 kms, within the coarse network of emission. These dark condensations give rise to the situation K2R = 0.K2-line widths are measured for all tracings where K2v , K2R are measurable simultaneously. The distribution curve of these widths is extremely sharp. The K2 emission source is identified with the bright fine mottles visible on the surface. Evidence for this interpretation comes from the study of auto-correlation functions of K2 intensity variations and the spacing between the bright fine mottles from both spectrograms and spectroheliograms. The life time of the fine mottling is 200 sec.The supergranular boundaries which constitute the coarse network come in two intensity classes. A low intensity network has the fine mottles as its principal contributor to the K emission. When the network is bright, the enhancement is caused by increased K emission due to the accumulation of magnetic fields at the supergranule boundary. The K2 widths of the low intensity supergranular boundary agree with the value found for the bright mottles. Those for the brighter network are lower than this value, similar to the K2 widths as seen in the active regions.It is concluded that bright fine mottling is responsible for the relation, found by Wilson and Bappu, between K emission line widths and absolute magnitudes of the stars.The paper discusses the solar cycle equivalents that stellar chromospheres can demonstrate and indicates a possible line of approach for successful detection of cyclic activity in stellar chromospheres.  相似文献   

19.
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   

20.
Résumé Une théorie a déjà été établie [3] concernant tout système lagrangienL(q, ,t) qui possède des intégrales premières ou plus généralement des formes invariantes, provenant par, exemple d'invariances géométriques. Cet article est une application concrète et directe aux équations aux variations du problème de Störmer qui intéressent actuellement des chercheurs en Mécanique [4].
The variational equations of Störmer's problem
A theory has already been established [3] concerning all lagrangiansL(q, ,t) which possess the integrals or more generally invariant forms, originating for example from geometric invariances. This paper is a direct application to the variational equations of Störmer's problem that has captured the interest of many researchers in celestial mechanics [4].
  相似文献   

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