共查询到20条相似文献，搜索用时 31 毫秒
1.
Osman M. Kamel 《Earth, Moon, and Planets》1989,45(2):127-137
We construct a U-N secular canonical planetary theory of the third order with respect to planetary masses. The Hori-Lie procedure is adopted to solve the problem. Expansions have been carried out by hand, neglecting powers higher than the second with respect to the eccentricity-inclination. We take into account the principal as well as the indirect part of the planetary disturbing function. The theory is expressed in terms of the Poincaré canonical variables, referring to the Jacobi-Radau set of origins. We assume that the 1:2 U-N critical terms and its multiples are the only periodic terms. 相似文献
2.
Osman M. Kamel 《Earth, Moon, and Planets》1992,59(2):111-140
We eliminate the 1:2 critical terms — after a previous elimination of the short period terms — in the Hamiltonian of a first order U-N theory. We take into account terms of degree 0, 1, 2, 3, 4 in the eccentricity-inclination. We apply for this elimination the Hori-Lie technique through the Poincaré canonical variables and the Jacobi coordinates. The purely principal first order secular U-N Hamiltonian admits a complete solution. We obtained the U-N equations of motion generated by the principal first order long period U-N Hamiltonian which will be solved later. This part III is closely related to the two previous papers (Kamel, 1982, 1983). 相似文献
3.
Osman M. Kamel 《Earth, Moon, and Planets》1990,49(3):259-267
We construct the outline of a third order secular theory for the four major planets. We apply the Hori-Lie technique to solve the problem. We take into consideration both parts of the perturbing function. Our canonical variables are those of H. Poincaré. Our periodic terms are the only 2:5 and 1:2 critical terms of J-S and U-N respectively. Terms of degree higher than the second in the Poincaré canonical variables H, K, P, Q are neglected. 相似文献
4.
Abdel Aziz Bakry 《Earth, Moon, and Planets》1988,42(1):77-106
In this paper of the third order Uranus-Neptune planetary theory which is the third part of this work for the third order theory, we compute the Poisson brackets in the Lie series which is used to transform canonical variables. We apply Hori-Lie technique in this work and neglect all powers higher than the second in Poincaré variables H, K, P, Q. We restrict this work to the principal part of the disturbing function. 相似文献
5.
We calculate in this paper the secular and critical terms arising from the principal part of the classical planetary Hamiltonian. This is the first step to establish a third order canonical planetary theory of Uranus-Neptune through the Hori-Lie technique. We truncate our expansions at the second degree of eccentricity-inclination. Our planetary theory is expressed in terms of the canonical variables of H. Poincaré. 相似文献
6.
In this paper, we have used a square root formulation of the Wheeler-De Witt equation to quantize a minisuperspace model consisting of the Bianchi-I type universe with a radiation field source. We have derived a wavefunction with a conserved current and a positive-definite probability density.
We have also explored the third quantization of the Bianchi type universe using a procedure usual in the quantum field theory of curved space-time. We have given the wave function that satisfies the Wheeler-De Witt equation. By regarding the wave function as the universe field operator in a minisuperspace, we have not only circumvented the difficulty of a probabilistic interpretation in quantum cosmology, we have also reached the conclusion that multiple universes would result. We have estimated the average number of universes produced from ‘nothing’, and have given their distribution, which turned out to be a Planck distribution. 相似文献
7.
A. Shalchi 《Monthly notices of the Royal Astronomical Society》2006,371(4):1898-1902
Besides parallel and perpendicular spatial diffusion, momentum diffusion can be seen as the third important process of cosmic ray transport. In this paper, the recently derived weakly non-linear theory is applied for a simple quasi-magnetostatic composite model to determine the momentum diffusion coefficient. It is demonstrated that non-linear effects are essential and cannot be neglected. Therefore, the weakly non-linear transport theory has to be preferred over the traditional quasi-linear approach. Within this improved theory, we find for the rigidity dependence of the momentum diffusion coefficient A ∼ R 1.4 for relativistic and A ∼ R 0.4 for non-relativistic cosmic rays. 相似文献
8.
In this paper, we deal with the stellar three body problem, that is one star is far away from the other two stars. The outer
orbit is assumed to be Keplerian. To analyze the effect of the distant star on the orbit of the close stars, we use the Gauss
method; this method consist in replacing the gravitational attraction of the third star by the gravitational attraction of
an infinitesimal non-homogeneous elliptic ring. We obtain the force vector for the Gauss method in terms of elliptic integrals.
Finally we compare the results obtained by this model with the classical third body model.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
9.
We constructed an analytical theory of satellite motion up to the third order relative to the oblateness parameter of the Earth (J 2). Equations of secular variations was developed for the first three orbital elements (a, e, i) of an artificial satellite. The secular variations are solved in a closed form. 相似文献
10.
M. Moons 《Earth, Moon, and Planets》1982,27(3):257-284
This paper presents a new theory of the libration of the Moon, completely analytical with respect to the harmonic coefficients of the lunar gravity field. This field is represented through its third degree harmonics for the torque due to the Earth (second degree for the torque due to the Sun).The orbital motion of the Moon is described by the ELP 2000 solution (Chapront-Touzé, 1980) of the main problem of lunar theory.the physical libration variables are obtained as Poisson series and comparisons with the results of Eckhardt (Eckhardt, 1981) and Migus (Migus, 1980) are presented. 相似文献
11.
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
12.
The paper aims at removing the restriction x ? 1 (where x is the cosine of the equatorial pitch angle) in the theory of pitch angle diffusion by bounce resonance. When the fourth order anharmonicity term is included in the expansion of the magnetic field around the equator, the parallel displacement of a particle becomes a superposition of the first and third harmonics of the fundamental frequency. The diffusion coefficient for pitch angle scattering by bounce resonance has been evaluated by taking into consideration the anharmonicity effects, and this expression can be expected to be valid for particles which mirror at higher latitudes also. 相似文献
13.
Arthur B. Congdon Charles R. Keeton C. Erik Nordgren 《Monthly notices of the Royal Astronomical Society》2008,389(1):398-406
Gravitational lensing provides a unique and powerful probe of the mass distributions of distant galaxies. Four-image lens systems with fold and cusp configurations have two or three bright images near a critical point. Within the framework of singularity theory, we derive analytic relations that are satisfied for a light source that lies a small but finite distance from the astroid caustic of a four-image lens. Using a perturbative expansion of the image positions, we show that the time delay between the close pair of images in a fold lens scales with the cube of the image separation, with a constant of proportionality that depends on a particular third derivative of the lens potential. We also apply our formalism to cusp lenses, where we develop perturbative expressions for the image positions, magnifications and time delays of the images in a cusp triplet. Some of these results were derived previously for a source asymptotically close to a cusp point, but using a simplified form of the lens equation whose validity may be in doubt for sources that lie at astrophysically relevant distances from the caustic. Along with the work of Keeton, Gaudi & Petters, this paper demonstrates that perturbation theory plays an important role in theoretical lensing studies. 相似文献
14.
V. De Bruyne F. Leeuwin H. Dejonghe 《Monthly notices of the Royal Astronomical Society》2000,311(2):297-306
We use a set of Stäckel potentials to obtain a local approximation for an effective third integral in axisymmetric systems. We present a study on the feasibility and effectiveness of this approach. We apply it to three trial potentials of various flattenings, corresponding to nearly ellipsoidal, discy and boxy density isophotes. In all three cases, a good fit to the potential requires only a small set of Stäckel potentials, and the associated Stäckel third integral provides a very satisfactory, yet analytically simple, approximation to the trial potentials effective third integral. 相似文献
15.
We generalize our results of a second order Jupiter-Saturn planetary theory to be applicable for the case of the four major planets.We use the Von Zeipel method and we neglect powers higher than the third with respect to the eccentricities and sines of the inclinations in our expansions. We consider the critical terms as the only periodic terms. 相似文献
16.
H. Asada 《Monthly notices of the Royal Astronomical Society》2009,394(2):818-830
This paper makes the first systematic attempt to determine using perturbation theory the positions of images by gravitational lensing due to arbitrary number of coplanar masses without any symmetry on a plane, as a function of lens and source parameters. We present a method of Taylor-series expansion to solve the lens equation under a small mass-ratio approximation. First, we investigate perturbative structures of a single-complex-variable polynomial, which has been commonly used. Perturbative roots are found. Some roots represent positions of lensed images, while the others are unphysical because they do not satisfy the lens equation. This is consistent with a fact that the degree of the polynomial, namely the number of zeros, exceeds the maximum number of lensed images if N = 3 (or more). The theorem never tells which roots are physical (or unphysical). In this paper, unphysical ones are identified. Secondly, to avoid unphysical roots, we re-examine the lens equation. The advantage of our method is that it allows a systematic iterative analysis. We determine image positions for binary lens systems up to the third order in mass ratios and for arbitrary N point masses up to the second order. This clarifies the dependence on parameters. Thirdly, the number of the images that admit a small mass-ratio limit is less than the maximum number. It is suggested that positions of extra images could not be expressed as Maclaurin series in mass ratios. Magnifications are finally discussed. 相似文献
17.
Paolo Lanzano 《Astrophysics and Space Science》1974,29(1):161-178
This paper extends Clairaut's theory of rotational equilibrium to third order terms in a small parameter and is meant to be a sequel to a 1962 publication by the author bearing on the same topic. It has been feasible to obtain the Clairaut equation, which governs the deformation of the equipotential surfaces within a rapidly rotating mass in hydrostatic equilibrium, as an ordinary differential equation. This has been achieved by eliminating the two integral terms which appeared in the original formulation. It is expected that the numerical integration of this newly obtained equation will contribute toward a more precise solution of certain geophysical problems — e.g., the determination of the geoid to an accuracy of ±1 m, and the correction to the travel-time of seismic waves; it should also assist in some planetary questions like the determination of the exterior shape for the rapidly rotating planets Jupiter and Saturn. 相似文献
18.
Osman M. Kamel 《Earth, Moon, and Planets》1993,62(2):131-138
Motivated by the recent proposals of A. Abian, we introduce the physical and dynamical considerations for producing a second Earth-like planet on which life sustaining conditions may exist, and hence we acquire multiplication of the cosmic resources of the human race. We investigate the perturbations in our solar system after alteration, through a third order Hamiltonian planetary theory for the eight principal planets. The Hori-Lie theorem, the Jacobi-Radau coordinates, and the canonical variables of H. Poincaré are adopted. 相似文献
19.
C. D. Andriesse 《Astrophysics and Space Science》1980,72(1):167-173
This third paper on the stellar mass loss as a fluctuation phenomenon addresses the refutations. It discusses the instability of the subphotosphere to outward mass flows, which develop into stochastic surges. By applying the principle of minimum free energy, the average outward velocity to which these flows are amplified is found to be just below the atmospheric escape velocity. Small fluctuations above this average value will therefore lead to mass loss. This justifies the Langevin equation, introduced previously to describe the mass loss, and a formal derivation of this equation is presented. The average value is, furthermore, related to the earlier postulated equipartition of kinetic and thermal power of the atmosphere. Finally, the paper discusses deviations of the stellar relaxation time fromGM
2
/RL, when a strong concentration of matter is at the centre. These deviations explain the anomalous behaviour of the mass loss rate of red (super)giants, so that the essential prediction of the fluctuation theory for the loss rate is not refuted. 相似文献
20.
F. Barone E. Covino L. Di Fiore L. Milano G. Russo 《Astrophysics and Space Science》1991,183(1):117-127
In this third paper of the series, we analyze five more EB-type eclipsing binaries with short periods (<1 day) and suspected to be contact, or near-contact systems.We find that V747 Cen and ZZ Aur are almost contact systems, RY Ind is a semi-detached system, while AX Vir and ST Car are both detached systems. 相似文献