共查询到20条相似文献，搜索用时 31 毫秒
1.
H. Greiner-Mai 《Astronomische Nachrichten》1986,307(3):201-208
The theoreticl treatment of several geophysical problems presupposes the solution of field equations of the magnetic field in the Earth's mantle. The field equations are given in a scalar form for a spherical model of the Earth. It will be shown that analytical solutions are possible in all cases. The boundary conditions are discussed with regard to the dynamo process in the Earth's core and the existence of a field representation, which is investigated on the Earth's surface. The question is discussed, to what extend the mantle's field is given by this field representation, when some special assumptions about the Earth's model are made. 相似文献
2.
V. Mioc 《Astronomische Nachrichten》1994,315(2):175-180
The elliptic-type motion in the gravitational field found by Fock as exact solution of Einstein's vacuum equations in the case of spherical symmetry (Solution called here Fock's gravitational field) is studied by means of a classic method based on the perturbation theory. Regarding the deviations of the orbit from a Kepleian orbit as perturbations, the first and second order variations of the Keplerian orbital elements over one nodal period as well as those of the nodal period itself are determined. 相似文献
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Brandon A. Jones Gregory Beylkin George H. Born Robert S. Provence 《Celestial Mechanics and Dynamical Astronomy》2011,111(3):309-335
A new model, dubbed the MRQSphere, provides a multiresolution representation of the gravity field designed for its estimation.
The multiresolution representation uses an approximation via Gaussians of the solution of the Laplace’s equation in the exterior
of a sphere. Also, instead of the spherical harmonics, variations in the angular variables are modeled by a set of functions
constructed using quadratures for the sphere invariant under the icosahedral group. When combined, these tools specify the
spatial resolution of the gravity field as a function of altitude and required accuracy. We define this model, and apply it
to representing and estimating the gravity field of the asteroid 433 Eros. We verified that a MRQSphere model derived directly
from the true spherical harmonics gravity model satisfies the user defined precision. We also use the MRQSphere model to estimate
the gravity field of Eros for a simulated satellite mission, yielding a solution with accuracy only limited by measurement
errors and their spatial distribution. 相似文献
6.
In two earlier papers (BRÄUER and RÄDLER 1986, 1987) the evolution of a magnetic field was considered which pervades an electrically conducting fluid and its non-conducting surroundings. A construction principle for Green's functions of the corresponding initial value problem was proposed, and worked out for the case in which the fluid fills a spherical region. Now the principle is applied to the case of a fluid body occupying a half-space. Green's functions are constructed for arbitrary motions of the fluid. More concrete results are derived for shear flow, and explicit expressions of Green's functions are given for rigid body motion. 相似文献
7.
田谐项摄动是分析法轨道预报中的重要部分,其中包含大量倾角函数及其偏导数的计算.由于具有精度更高、速度更快的优点,倾角函数一般通过递推方法计算.以文献中提出的改进Gooding方法为基础,将其给出的程序稍加改进,在计算2–50阶倾角函数时缩短了约24%的计算时间.考虑到分析法预报过程中轨道平倾角变化很小,以泰勒展开式计算倾角函数,可极大提高计算速度,较大程度地减小分析法预报耗时,且引力场阶次越高,减小幅度越大,取50阶时预报耗时缩短了48%.另一方面,以2阶展开式计算倾角函数时,与改进Gooding法相比,分析法预报星历偏差很小.对于500 km高度的低轨卫星,分别以改进Gooding法和2阶泰勒展开式计算倾角函数,预报3天,当地球引力场阶次不高于50时,二者预报星历偏差RMS (Root Mean Square)低于1 mm,且随着轨道高度的增加,预报星历偏差RMS逐渐减小. 相似文献
8.
We establish the solution of the ninth order — in masses — canonical J-S equations of motion by Hori-Lie technique — i.e., by expressing the initial Poincaré canonical variables as functions of the new variables through the Hori-Lie canonical transformation. Terms of order higher than 9 in the masses are neglected. 相似文献
9.
We propose the Ptolemaic transformation: a canonical change of variables reducing the Keplerian motion to the form of a perturbed Hamiltonian problem. As a solution of the unperturbed case, the Ptolemaic variables define an intermediary orbit, accurate up to the first power of eccentricity, like in the kinematic model of Claudius Ptolemy. In order to normalize the perturbed Hamiltonian we modify the recurrent Lie series algorithm of HoriuuMersman. The modified algorithm accounts for the loss of a term's order during the evaluation of a Poisson bracket, and thus can be also applied in resonance problems. The normalized Hamiltonian consists of a single Keplerian term; the mean Ptolemaic variables occur to be trivial, linear functions of the Delaunay actions and angles. The generator of the transformation may serve to expand various functions in Poisson series of eccentricity and mean anomaly. 相似文献
10.
FIEDLER and SCHIMMING (1983) proved that the fourth order gravitational field equations with a linear combination of Bach's and Einstein's tensors on the left-hand side, which were proposed by TREDER , admit static centrally symmetric solutions which are analytical and non-flat in some neighbourhood of the centre of symmetry. The existence of these solutions, known at first only in a small neighbourhood of r = o (r radius), can now be extended to intervals o ≦ r ≦ α with arbitrarily large α , using the abstract theorem on inverse functions. Further it is proved that the Schwarzschild metrics are in a certain sense the only solutions of the above equations that are analytic, asymptotically flat, static and centrally symmetric around r = +∞. 相似文献
11.
In order to study the apparent ‘super-rotation’ of the Earth's upper atmosphere, we examine a non-linear solution to the continuity, momentum conservation and state equations of gasdynamics for the steady state motion of a gravitationally stratified, cylindrical, inviscid atmosphere under the influence of a steady state, local time dependent temperature distribution. The resultant flow field can be understood in terms of angular momentum conservation of air masses: heated, rising air decreases its rotation rate and cooled, falling air increases its rotation rate. The local-time average of the differential rotation rate may given rise to an apparent altitude dependent ‘super-rotation’. Comparison with observations is presented. 相似文献
12.
T. V. Ivanova 《Solar System Research》2013,47(5):359-362
In order to generate an analytical theory of the motion of the Moon by considering planetary perturbations, a procedure of general planetary theory (GPT) is used. In this case, the Moon is considered as an addition planet to the eight principal planets. Therefore, according to the GPT procedure, the theory of the Moon’s orbital motion can be presented in the form of series with respect to the evolution of eccentric and oblique variables with quasi-periodic coefficients, which are the functions of mean longitudes for principal planets and the Moon. The relationship between evolution variables and the time is determined by a trigonometric solution for the independent secular system that describes the secular motion of a perigee and the Moon node by considering secular planetary inequalities. Principal planetary coordinates required for generating the theory of the motion of the Moon includes only Keplerian terms, the intermediate orbit, and the linear theory with respect to eccentricities and inclinations in the first order relative to the masses. All analytical calculations are performed by means of the specialized echeloned Poisson Series Processor EPSP. 相似文献
13.
In order to choose a numerical method for solving the time dependent equations of radiative transport, we obtain an exact
solution for the time dependent radiation field in a one dimensional infinite medium with monochromatic, isotropic scattering
for sources with an arbitrary spatial distribution and an arbitrary time variation of their power. The Lax-Wendroff method
seems to be the most suitable. Because it is assumed that radiation delay is caused by the finite speed of light, the following
difficulty arises when the numerical method is used: the region of variation of the variables (position τ and time t) is triangular (the inequality τ ≤ t). This difficulty is overcome by expanding the unknown functions in series in terms of small values of the time and position.
By comparing the numerical and exact solutions for a point source with a given time dependence for its power and with pure
scattering, the number of steps in the variables required to obtain a desired accuracy is estimated. This numerical method
can be used to calculate the intensity and polarization of the radiation from sources in the early universe during epochs
close to the recombination epoch.
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Translated from Astrofizika, Vol. 51, No. 1, pp. 109–123 (February 2008). 相似文献
14.
U. Dyllong 《Astronomische Nachrichten》1979,300(3):147-149
An exact solution of EINSTEIN 's field equations with cosmological constant coupled with the field equations of a massive vector field is given. The model has zero expansion and shear, but nonvanishing constant rotation. 相似文献
15.
《Chinese Astronomy and Astrophysics》2005,29(1):20-38
The equations of the electromagnetic field of a slowly rotating magnetized neutron star in Saa's gravitation model with torsion are derived and their exterior solution is investigated. The following conclusions are obtained: first, there is a specific solution for the electromagnetic field when Aô = 0; second, there is no solution at all when Aô ≠ 0. Therefore, we can judge whether or not torsion exists by observing the exterior electromagnetic field of the neutron star. 相似文献
16.
R. A. Howland 《Celestial Mechanics and Dynamical Astronomy》1988,45(1-3):207-211
A new approach to the librational solution of the Ideal Resonance Problem has been devised--one in which a non-canonical transformation is applied to the classical Hamiltonian to bring it to the form of the simple harmonic oscillator. Although the traditional form of the canonical equations of motion no longer holds, a quasi-canonical form is retained in this single-degree-of-freedom system, with the customary equations being multiplied by a non-constant factor. While this makes the resulting system amenable to traditional transformation techniques, it must then be integrated directly. Singularities of the transformation in the circulation region limit application of the method to the librational region of motion.Computer-assisted algebra has been used in all three stages of the solution to fourth order of this problem: using a general-purpose FORTRAN program for the quadratic analytical solution of Hamiltonians in action-angle variables, the initial transformation is carried out by direct substitution and the resulting Hamiltonian transformed to eliminate angular variables. The resulting system of differential equations, requiring the expected elliptic functions as part of their solution, is currently in the process of being integrated using the LISP-based REDUCE software, by programming the required recursive rules for elliptic integration.Basic theory of this approach and the computer implementation of all these techniques is described. Extension to higher order of the solution is also discussed. 相似文献
17.
In an earlier paper the evolution of a magnetic field was considered which permeates an electrically conducting fluid and its non-conducting surroundings. It was shown how the tensorial Green's function of the initial value problem posed by the governing equations can be constructed. The present paper gives a more detailed analysis of the case where the fluid occupies the interior of a sphere. The construction is carried out for arbitrary motions of the fluid. More special results are derived for differential rotation with angular velocity depending only on the radius, and explicit expressions of Green's functions are given for rigid body rotation. 相似文献
18.
A quantitative re-formulation of Hoyle's theory on the formation of the solar system is attempted, according to a three-dimensional scheme based on the assumption that the original magnetic field of the star is a dipole field. This allows us to obtain analytic expressions for the main paraeters describing the different phases of the process. The protostar is assumed to evolve in gravitational contraction along the Hayashi track, along which, for a given value of the radiusR 0 depending on the total angular momentum, matter begins to be shed at the equator as a consequence of centrifugal instability. However, owing to the geometry of the dipole field and to Hoyle's assumption that, for a star with a convective envelope, the sign of the inward magnetic pressure determines whether the magnetic lines do wind up or not, it turns out that the magnetic coupling between the star and the disk formed at the equator starts only when the radius of the contracting star has reached the value ofR s=4/5R 0; and that the shedding of matter stops for a radius valueR d, depending on the strength of the magnetic field. One is thus able to calculate the total quantity of matter emitted at the solar equator and the distance reached by the rings thus formed as functions of the radius of the star, of the initial values of the magnetic field, of the total angular momentum and of the structural factors of the star. The quantitative results are discussed in order to see whether it is possible to deduce the main characteristics of the disk, from which the solar system should have originated, for reasonable values of these main parameters. 相似文献
19.
Carol A. Williams Thomas van Flandern Edward A. Wright 《Celestial Mechanics and Dynamical Astronomy》1987,40(3-4):367-391
The differential equations of planetary theory are solved analytically to first order for the two-dimensional case, using only Jacobian elliptic functions and the elliptic integrals of the first and second kind. This choice of functions leads to several new features potentially of importance for planetary theory. The first of these is that the solutions do not require the expansion of the reciprocal of the distance between two planets, even for those variables which depend on two angular arguments. A second result is that the solution is free from small divisors with the exception of two special resonances. In fact, not only are the solutions for resonant orbits free from small divisors, the perturbations for all variables are expressible in closed form. A subset of the resonant orbits maintains this form and in addition has the remarkable feature that the first order perturbations are purely periodic; they contain no secular terms. A solution for the 13 resonance case is given as an example. 相似文献
20.
An exact solution of the vacuum Brans-Dicke field equations is obtained for the metric tensor of a spatially-homogeneous and anisotropic Bianchi type I configuration. The solution has no analogy in Einstein's theory for the layer values of the BD parameter. Some properties of the solution are discussed. 相似文献