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1.
D. V. Mikryukov 《Astronomy Letters》2018,44(5):337-350
A system of averaged equations of planetary motion around a central star is constructed. An astrocentric coordinate system is used. The two-planet problem is considered, but all constructions are easily generalized to an arbitrary number N of planets. The motion is investigated in modified (complex) Poincarécanonical elements. The averaging is performed by the Hori–Deprit method over the fast mean longitudes to the second order relative to the planetary masses. An expansion of the disturbing function is constructed using the Laplace coefficients. Some terms of the expansion of the disturbing function and the first terms of the expansion of the averaged Hamiltonian are given. The results of this paper can be used to investigate the evolution of orbits with moderate eccentricities and inclinations in various planetary systems. 相似文献
2.
An analytical expansion of the disturbing function arising from direct planetary perturbations on the motion of satellites is derived. As a Fourier series, it allows the investigation of the secular effects of these direct perturbations, as well as of every argument present in the perturbation. In particular, we construct an analytical model describing the evection resonance between the longitude of pericenter of the satellite orbit and the longitude of a planet, and study briefly its dynamic. The expansion developed in this paper is valid in the case of planar and circular planetary orbits, but not limited in eccentricity or inclination of the satellite orbit. 相似文献
3.
The study of the evolution of planetary systems, primarily of the Solar System, is one of the basic problems of celestial mechanics. The stability of motion of giant planets on cosmogonic time scales was established by numerical and analytical methods, but the question about the evolution of orbits of terrestrial planets and arbitrary solar-type planetary systems remained open. This work initiates a series of papers allowing one to advance in solving the problem of the evolution of the solar-type planetary systems on cosmogonic time scales by using powerful analytical tools. In the first paper of this series, we choose the optimum reference system and obtain the Poisson series expansion of the Hamiltonian of the problem in all Keplerian elements. We propose to use the integral representation of the corresponding coefficients or the Poisson processor means instead of conventionally addressing any possible special functions. This approach extremely simplifies the algorithm. The next paper of this series deals with the calculation of the expansion coefficients. 相似文献
4.
D. H. Morgan Q. A. Parker Martin Cohen 《Monthly notices of the Royal Astronomical Society》2003,346(3):719-730
We report the discovery of the first probable Galactic [WN] central star of a planetary nebula (CSPN). The planetary nebula candidate was found during our systematic scans of the AAO/UKST Hα Survey of the Milky Way. Subsequent confirmatory spectroscopy of the nebula and central star reveals the remarkable nature of this object. The nebular spectrum shows emission lines with large expansion velocities exceeding 150 km s−1 , suggesting that perhaps the object is not a conventional planetary nebula. The central star itself is very red and is identified as being of the [WN] class, which makes it unique in the Galaxy. A large body of supplementary observational data supports the hypothesis that this object is indeed a planetary nebula and not a Population I Wolf–Rayet star with a ring nebula. 相似文献
5.
A plasma simulation code is applied to interpret the instabilities in an expanding planetary nebula. The temperature of the
central star of a planetary nebula is assumed as above 50,000 K. Most of the atoms are ionized at this temperature. Since
ionization cannot be neglected for such a hot plasma, the electrostatic instability should be taken into account. In the one
dimensional electrostatic simulation, Maxwell and Vlasov equations are used and the fast Fourier transform is applied. The
calculated drift velocity in the simulation is found comparable with the expansion velocity of a planetary nebula. The linear
and non-linear behaviors of the simulated nebular plasma have been investigated in phase space; the simulation results agree
with the theory.
This revised version was published online in September 2006 with corrections to the Cover Date. 相似文献
6.
The interactions of the solar wind with planetary magnetic fields: Basic principles and observations
D.B. Beard 《Planetary and Space Science》1973,21(9):1475-1496
A planetary magnetic field obstructs the supersonic expansion of the solar coronol ions and electrons and creates a cigar shaped bubble in the solar wind. The pressure of the solar wind on the bubble compresses and seriously distorts the planetary magnetic field. A review is given here of the theoretical calculation and experimental observation of the shape of the bubble and the configuration of the compressed magnetic field inside the surface. Other effects, namely the shock structure on the surface, the radiation belts, and the current in the antisolar side of the bubble are described as well as a simplified account of electric fields and the connection of the planetary field lines with interplanetary field lines. 相似文献
7.
A set of differential equations is derived that has a number of advantages in special perturbation work. In particular, the equations remain valid for all values of the orbital eccentricity and inclination including zero. They are therefore applicable to parabolic- and hyperbolic-type orbits as well as elliptic-type; a scheme for use when the orbit is rectilinear or nearly so is provided. The equations are also much simpler in form than the Lagrange planetary equations and the transformations of the osculating elements to and from the rectangular coordinates are straightforward. 相似文献
8.
Arbab I. Arbab 《Astrophysics and Space Science》2008,314(1-3):35-39
We have developed a cosmological model for the Earth rotation and planetary acceleration that gives a good account (data)
of the Earth astronomical parameters. These data can be compared with the ones obtained using space-base telescopes. The expansion
of the universe has shown to have an impact on the rotation of planets, and in particular, the Earth. The expansion of the
universe causes an acceleration that is exhibited by all planets. 相似文献
9.
We eliminate by the method of von Zeipel the short-period terms in a first order-with respect to planetary masses—general planetary Uranus-Neptune theory. We exclude in the expansion terms of eccentricities and sines of inclinations higher than the third power.Our variables are the Poincaré canonical variables. We use the Jacobi-Radau set of origins, and we refer the planes of the osculating ellipses to a common fixed plane, the longitudes to a common origin. The short-periodic terms arising from the indirect and principal parts of the disturbing functions, are eliminated separately. The Fourier series of the principal part of the disturbing function, is reduced to the sum of only the first three terms. 相似文献
10.
Some methods are described for the expansion of the disturbing function in planetary theory. One method uses the classical binomial expansion theorem or a successive approximation process derived from it. Another method is a direct application of the Laplace series expansions. For both methods it is proposed to first prepare the series to be manipulated by a scaling operation. These methods can be applied either in a literal or in a numerical form, or any combination of both, but they are especially designed for use on a large scale digital computer with standard Poisson series programs. No usage is made of Newcomb operators or derivatives of Laplace coefficients. 相似文献
11.
In this part we expand the indirect part of the planetary perturbing function by Smart's method, via Taylor's theorem. We neglect, in our expansion, terms of degree higher than the fourth with regard to the eccentricities and tangents of the inclinations. 相似文献
12.
We present an outline to calculate the principal and indirect portions of the planetary disturbing function, based on the method of W. M. Smart. We truncate the Taylor expansion at the third power of eccentricity-inclination. The outline of a new method to obtain the negative powers of the mutual distance between two planets is also given, neglecting powers higher than the fourth in the eccentricity-inclination. 相似文献
13.
We expand the principal part of the planetary disturbing function, by Smart's method, using Taylor's theorem. In our expansion we neglect terms of degree higher than the fourth in the eccentricities and tangents of the inclinations.Now at the JPL Pasadena, California. 相似文献
14.
Philippe Robutel 《Celestial Mechanics and Dynamical Astronomy》1995,62(3):193-217
We present a direct method for the expansion of the planetary Hamiltonian in Poincaré canonical elliptic variables with its effective implementation in computer algebra. This method allows us to demonstrate the existence of simplifications occurring in the analytical expression of the Hamiltonian coefficients. All the coefficients depending on the ratio of the semi major axis can thus be expressed in a concise and canonical form. 相似文献
15.
There are about 50 galactic planetary nebulae know to have [WR] type nuclei. We have compared their nebular properties with those of the other planetary nebulae in the Galaxy. We have found that the nebular morphological types are similarly distributed in the two groups. Bipolar nebulae constitute only 20% of the total in each group. The distribution of the nebular electron densities and abundance ratios N/O, He/H and C/O are the same in the two groups. The only marked difference is that nebular expansion velocities are larger in the group of planetary nebulae with [WR] central stars. We argue that the WR phenomenon does not preferentially occur in more massive central stars of planetary nebulae, contrary to what has been suggested in some former studies. We demonstrate that, for most of the observed [WR] type objects, the WR phenomenon cannot be triggered by a late helium shell flash event.The results of our investigation are published inAstronomy & Astrophysics
303, 893 (1995) and in the proceedings of the 2nd International Colloquium on Hydrogen-deficient Stars, C.S. Jeffery & U. Heber (eds), Astronomical Society of the Pacific Conference Series, Vol. 96, p. 209 (1996). 相似文献
16.
D. Schnberner R. Jacob H. Lehmann G. Hildebrandt M. Steffen A. Zwanzig C. Sandin R.L.M. Corradi 《Astronomische Nachrichten》2014,335(4):378-408
We present the result of a study on the expansion properties and internal kinematics of round/elliptical planetary nebulae of the Milky Way disk, the halo, and of the globular cluster M 15. The purpose of this study is to considerably enlarge the small sample of nebulae with precisely determined expansion properties (Schönberner et al. 2005b). To this aim, we selected a representative sample of objects with different evolutionary stages and metallicities and conducted highresolution ´echelle spectroscopy. In most cases we succeeded in detecting the weak signals from the outer nebular shell which are attached to the main line emission from the bright nebular rim. Next to the measurement of the motion of the rim gas by decomposition of the main line components into Gaussians, we were able to measure separately, for most objects for the first time, the gas velocity immediately behind the leading shock of the shell, i.e. the post‐shock velocity. We more than doubled the number of objects for which the velocities of both rim and shell are known and confirm that the overall expansion of planetary nebulae is accelerating with time. There are, however, differences between the expansion behaviour of the shell and the rim: The post‐shock velocity is starting at values as low as around 20 km s–1 for the youngest nebulae, just above the AGB wind velocity of ∼ 10–15 km s–1, and is reaching values of about 40 km s–1 for the nebulae around hotter central stars. Contrarily, the rim matter is at first decelerated below the typical AGB‐wind velocity and remains at about 5–10 km s–1 for a while until finally a typical flow velocity of up to 30 km s–1 is reached. This observed distinct velocity evolution of both rim and shell is explained by radiation‐hydrodynamics simulations, at least qualitatively: It is due to the ever changing stellar radiation field and wind‐wind interaction together with the varying density profile ahead of the leading shock during the progress of evolution. The wind‐wind interaction works on the rim dynamics while the radiation field and upstream density gradient is responsible for the shell dynamics. Because of these time‐dependent boundary conditions, a planetary nebula will never evolve into a simple self‐similar expansion. Also the metal‐poor objects behave as theory predicts: The post‐shock velocities are higher and the rim flow velocities are equal or even lower compared to disk objects at similar evolutionary stage. The old nebula around low‐luminosity central stars contained in our sample expand still fast and are dominated by reionisation. We detected, for the first time, in some objects an asymmetric expansion behaviour: The relative expansions between rim and shell appear to be different for the receding and approaching parts of the nebular envelope. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
17.
Sergei A. Klioner 《Celestial Mechanics and Dynamical Astronomy》2000,77(3):215-238
Various Fourier expansions of the planetary disturbing function can be computed numerically with the use of numerical Fourier
analysis. The task to compute the most general five-dimensional Fourier expansion of disturbing function has become feasible
with typical server-class computers quite recently. In such an expansion two anomalies, two arguments of perihelions and two
longitudes of the node are independent angular variables, while two semi-major axes, two eccentricities and two inclinations
are fixed numerically. The semianalytical expansion of the disturbing function resulting from numerical Fourier analysis theoretically
converges for any values of the parameters except for those sets of parameters which allow the bodies to collide. Various
aspects of the numerical computation of the Fourier expansion are discussed. Theoretical and practical convergence of the
Fourier series is discussed and illustrated.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
18.
This paper is the third in a series of articles devoted to one of the basic problems of celestial mechanics: the study of the evolution of solar-type planetary systems. In the previous papers a brief review of the history and current state of the problem was given; the plan of the study was outlined; the Jacobi coordinates and the related osculating elements were introduced; the form of the Poisson expansion of the Hamiltonian in all elements was given; and the expansion coefficients for the Hamiltonian of the two-planetary Sun–Jupiter–Saturn problem were obtained (though with impure accuracy) by a simple algorithm that is reduced to the calculation of multiple integrals of elementary functions. In the present paper the expansion of the Hamiltonian of the two-planetary Sun–Jupiter–Saturn problem into the Poisson series in all elements is constructed with the help of the PSP Poisson series processor, which is capable of required accuracy. 相似文献
19.
Bruno Cordani 《Celestial Mechanics and Dynamical Astronomy》2004,89(2):165-179
A method for the expansion of the perturbative Hamiltonian in the planetary problem is presented, which allows one to immediately
detect the terms vanishing under the averaging process. The method bases itself on a geometrical analysis, through the groups
SO(3) and SU(2), of the Poincaré canonical variables or of the similar Laplace variables. As an outcome, one obtains a MAPLE
program, which calculates the first averaged terms of the perturbative Hamiltonian.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
20.
G. Tommei A. Milani D. Vokrouhlický 《Celestial Mechanics and Dynamical Astronomy》2010,107(1-2):285-298
The Radio Science Experiment is one of the on board experiments of the Mercury ESA mission BepiColombo that will be launched in 2014. The goals of the experiment are to determine the gravity field of Mercury and its rotation state, to determine the orbit of Mercury, to constrain the possible theories of gravitation (for example by determining the post-Newtonian parameters), to provide the spacecraft position for geodesy experiments and to contribute to planetary ephemerides improvement. This is possible thanks to a new technology which allows to reach great accuracies in the observables range and range rate; it is well known that a similar level of accuracy requires studying a suitable model taking into account numerous relativistic effects. In this paper we deal with the modelling of the space-time coordinate transformations needed for the light-time computations and the numerical methods adopted to avoid rounding-off errors in such computations. 相似文献