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1.
In this paper we study only the perturbation due to the deformation of the elastic mantle by a tidal body force. In a previous
publication (Getino and Ferrándiz, 1989a) we defined two canonical systems of variables - we gave them the names ofelastic variables of Euler and Andoyer respectively. Next, using them, we obtained the canonical expression of rotational kinetic
energy.
In the present paper, using the same variables, we build up the elastic energy which is produced by the deformation of the
elastic mantle. We show that the three termsm = 0, 1, 2 corresponding to the second order of the development in spherical harmonics of the perturbing potential, a tidal
potential, are of the same order of magnitude. In addition, the numerical integration for a particular Earth Model (Takeuchi's
Model 2) is performed, with the aim of obtaining a numerical estimate of the coefficients which intervene in both this energy
and the previously mentioned kinetic energy. 相似文献
2.
In this article an approximate analytical integration is performed of the Hamiltonian corresponding to the rotational motion
of an Earth whose elastic mantle is deformed by rotation and lunisolar attraction, using Deprit's perturbation method for
the first order. Besides the usual terms, this Hamiltonian includes the perturbation of the kinetic energy and the elastic
energy produced with the deformation, as well as their causes, the tidal and the centrifugal potential; these new terms have
already been studied for the tidal deformation in previous articles (Getino and Ferrándiz, 1990a, 1990b). The effects of the
deformation due to the centrifugal potential are studied in this article, following the same method as that used for the tidal
deformation. Numerical tables of the periodic perturbations corresponding to the nutation in obliquity and longitude are obtained.
As for the secular effects, a theoretical value of 457 days is obtained for Chandler's period. 相似文献
3.
C. Z. Zhang 《Earth, Moon, and Planets》1991,54(2):129-143
In view of the elastic deformation of the Earth we performed the comparative study for the Earth's models 1066 A and PREM, calculated the static Love numbers from degree 2 to 30, and discussed the relative variations of the second degree Love numbers and their combinations due to the variation of the position of the core-mantle boundary, due to the redistribution of V
p, V
s, and in the lower mantle, and due to the possible rigidity in the outer core. From the above-mentioned discussions we recommended that the Standard Earth Model (SEM) should include two kinds of models—one is oceanless, and another has an oceanic surface. Finally, we calculated the astronomicgeodetic parameters, which are consistent with the primary constants in the IERS Standards, of the SEM. 相似文献
4.
5.
C. Z. Zhang 《Earth, Moon, and Planets》1992,56(3):193-207
In the IERS Standards (1989), for the Moon the adopted value of the tide Love number, k
2, is equal to 0.0222. In this paper using the latest geodetic parameters of the Moon a group of internal structure models are constructed for this celestial body (see Table V), then the dependence of the Moon's core size on calculated value of k
2 is explored. The obtained results indicate that the second degree Love number, k
2 = 0.02664, of the lunar model 91–04 is near its observed value (0.027 ± 0.006). This implies that the Moon may possess an outer core of 660 km radius and of 300 kbar mean rigidity. With the same method the static Love numbers from degree 2 to 30 are computed for the terrestrial planets — Mercury, Venus, and Mars (see Table VII), and the influence of some parameters (such as the rigidity) of the outer core on low degree Love numbers is discussed. Finally, the likely range of the second degree Love numbers is determined for the terrestrial planets (see Table XI). It seems that if low degree Love numbers of a terrestrial planet can be detected in the future space explorations, there is some possibility to improve the planetary internal structure model. For example, as soon as space techniques yield an observed value of k
2 > 0.10 for Mercury, there will be reason to anticipate that a partly melted iron core exists in this planet. 相似文献
6.
滞弹地球自转速率的潮汐变化 总被引：5，自引：0，他引：5
本文根据勒夫数和负荷载夫数的数值扰动原理，利用ｈａｎｄｌｅｒ摆动的理论周期作为滞弹吸收带模型参数估计的约束条件，讨论了地幔滞弹性对有效勒夫数ｋ的直接影响，以及滞弹地球对平均海潮的响应所产生的间接扰动，分析了它们对带谐潮尺度因子ｋ／Ｃ的影响，由此定义了一个具有动力学海潮、滞弹地幔和液核地球的世界时ＵＴ１潮汐变化序列，与天文新技术观测结果相比较表明，高频带谐潮变化的理论值与实测值是一致的。频散效应对低 相似文献
7.
初步探讨用日长和卫星轨道摄动方法研究半月潮Mf 和月潮Mm 的Love数k2 .结果表明 ,日长方法给出k2 =0 .30 32 i0 .0 0 2 8(Mf) ,0 .30 2 6 i0 .0 0 1 2 (Mm) ,卫星轨道摄动方法为k2 =0 .30 83-i0 .0 1 0 0 (Mf) ,0 .30 1 4-i0 .0 0 1 0 (Mm) ,并与理论固体潮计算结果较为相符 .另外 ,上述结果更接近滞弹地球模型计算的结果 ,因此精确地测定长期潮Love数将对固体潮理论和地幔滞弹性提供重要的结束 . 相似文献
8.
This paper is the first of a set of four, in which we shall develop the first part of a project dedicated to elaborating a Hamiltonian theory for the rotational motion of a deformable Earth. Here we study only the perturbation due to the deformation of the elastic mantle by tidal body force. In the present paper, we define two canonical systems of variables—we give these variables the names of elastic variables of Euler and Andoyer respectively. Next, using them, we obtain the canonical expression of rotational kinetic energy, which is valid for any Earth model satisfying hypotheses as general as those established in Section 2. 相似文献
9.
Orbital evolution of the elements of the comet Halley are calculated. The changes in the orbital elements are very small and caused by Jupiter's perturbation except in two periods in which are predominant those of Venus and Earth. 相似文献
10.
由PREM模型参数计算地球自转的周期变化 总被引：3，自引：1，他引：2
弹性地球在日月引潮力势作用下的形变引起其转动惯量的改变，从而导致地球自转速率的变化．本文利用PREM地球模型所给的物质密度和弹性等参数分布．计算日月引潮力势产生的地球形变附加势，进而计算转动惯量的变化．最后得到一系列包含周期同引潮势带谐项、振幅大于1微秒的自转速率周期变化系数． 相似文献
11.
The shape of the Earth and of planets depends on the exciting forces and on the rheology of the medium. From the equilibrium equation, we present the main modelisations of the viscous and inviscid fluids and we essentially describe the characteristics of linear viscoelastic deformations, for the Maxwell viscoelastic model of rheology. We use the elastic, viscoelastic and fluid Love numbers in order to investigate the associated relaxation modes. For these various kinds of rheology of the planets interior, we compute the geoid and the topography induced by an internal mass distribution. Finally, we show the importance of this viscoelastic deformation calculations in the study of the celestial body rotations. 相似文献
12.
The observed density of Venus is about 2% smaller than would be expected if Venus were a twin planet of the Earth, possessing an identical internal composition and structure. In principle, this could be explained by a process of physical segregation of metal particles from silicate particles in the solar nebula prior to accretion, so that Venus accreted from relatively metal-depleted material. However, this model encounters severe difficulties in explaining the nature of the physical segregation process and also the detailed chemical composition of the Earth's mantle. Two alternative hypotheses are examined, both of which attempt to explain the density difference in terms of chemical fractionation processes. Both of these hypotheses assume that the relative abundances of the major elements Fe, Si, Mg, Al, and Ca are similar in both planets. According to the first hypothesis, a larger proportion of the total iron in Venus is present as iron oxide in the mantle, so that the core-to-mantle ratio is smaller than in the Earth. This model implies that Venus is more oxidized than the Earth, with its lower intrinsic density (i.e., corrected to equivalent pressures and temperatures) due to the larger amount of oxygen present. The difference between oxidation states is attributed to differing degrees of accretional heating arising from the relatively smaller mass of Venus. On the other hand, the second hypothesis maintains that Venus is more reduced than the Earth, with its mantle essentially devoid of oxidized iron. The difference intrinsic densities is attributed to the Earth accreting at a lower temperature than Venus as a result of the Earth's greater distance from the center of the nebula. As a result, large amounts of sulfur accreted on the Earth but not on Venus. The sulfur, which entered the core, is believed to have increased the mean density of the Earth because of its relatively high atomic weight. The hypothesis also implies that most of the Earth's potassium, because of its chalcophile properties, entered the core.These hypotheses are evaluated in the light of existing data. The second hypothesis leads to an intrinsic density for Venus which is only 0.4% smaller than that of the Earth. This difference is much smaller than is believed to exist. A wide range of chemical evidence is found to be unfavorable to this second hypothesis, but to be consistent with the interpretation that Venus is more oxidized than the Earth, as required by the first hypothesis. 相似文献
13.
A.J. Coates R.A. Frahm D.O. Kataria G. Collinson J.D. Winningham S. Barabash R. Lundin Y. Futaana A. Grigoriev H. Gunell J.-J. Thocaven W. Baumjohann H. Koskinen J.U. Kozyra Y. Ma A. Galli P. Bochsler E.C. Roelof N. Krupp M. Fraenz S. McKenna-Lawlor R. Cerulli-Irelli A. Milillo C.C. Curtis K.C. Hsieh A. Asamura 《Planetary and Space Science》2008,56(6):802-806
We report the detection of electrons due to photo-ionization of atomic oxygen and carbon dioxide in the Venus atmosphere by solar helium 30.4 nm photons. The detection was by the Analyzer of Space Plasma and Energetic Atoms (ASPERA-4) Electron Spectrometer (ELS) on the Venus Express (VEx) European Space Agency (ESA) mission. Characteristic peaks in energy for such photoelectrons have been predicted by Venus atmosphere/ionosphere models. The ELS energy resolution (ΔE/E∼7%) means that these are the first detailed measurements of such electrons. Considerations of ion production and transport in the atmosphere of Venus suggest that the observed photoelectron peaks are due primarily to ionization of atomic oxygen. 相似文献
14.
Juan Getino 《Celestial Mechanics and Dynamical Astronomy》1992,53(1):11-36
This work is the first in the second part of a project dedicated to elaborating a Hamiltonian theory for the rotational motion of a deformable Earth. In the four works which make up the first part the basis of this theory is laid down, studying the effects produced when the Earth's elastic mantle is deformed by lunisolar attraction. More specifically, in Getino and Ferrándiz (1991), the elastic energy which is produced on the deformation of the Earth's mantle is studied, considering solely the second order in the development in spherical harmonics of the perturbing potential (tidal potential).The present article can be considered as an amplification of the above mentioned, obtaining, under the same hypotheses, but also very general, the general expression of the said elastic energy for any order of the development of the tidal potential. Although at first this expression, in its general form, is very complicated, the final result is extremely simple, and for the case n = 2, it coincides, obviously, with that already found by the above mentioned authors. 相似文献
15.
M. Burša 《Earth, Moon, and Planets》1984,31(2):135-140
The secular Love numbers of planets and of the Moon have been computed by use of the recent satellite data. It has been demonstrated that Venus, Mercury, and the Moon are far from the ideal hydrostatic equilibrium; the angular velocities (rotation periods) which correspond to the hydrostatic equilibrium have been computed. 相似文献
16.
Yoshio Kubo 《Celestial Mechanics and Dynamical Astronomy》2012,112(1):99-106
Kubo (Celest Mech Dyn Astron 110:143–168, 2011) investigated the kinematical structure of the perturbation in the rotation of the elastic Earth due to the deformation caused
by the outer bodies. In that paper, while the mechanism for the perturbation of the figure axis was made clear, that for the
rotational axis was not shown explicitly. In the present study, following the same method, the structure of the perturbation
of the rotational axis is investigated. This perturbation consists of the direct perturbation and the convective perturbation.
First the direct perturbation is shown to be (A − C)/A times as large as that of the figure axis, coinciding with the analytical expressions obtained in preceding studies by other
authors. As for the convective perturbation, which appears only in the perturbation of the rotational axis but not in that
of the figure axis, it is shown to be (A − C)/A times the angular separation between the original figure axis and the induced figure axis produced by the elastic deformation,
A and C being the principal moments of inertia of the Earth. If the perturbing bodies are motionless, the conclusion of Kubo (Celest
Mech Dyn Astron 105:261–274, 2009) holds strictly, i.e. the sum of the direct and the convective perturbations of the rotational axis coincides with the perturbation
of the figure axis. 相似文献
17.
Julien Dufey Anne Lemaître Nicolas Rambaux 《Celestial Mechanics and Dynamical Astronomy》2008,101(1-2):141-157
Two space missions dedicated to Mercury (MESSENGER and BepiColombo) aim at understanding its rotation and confirming the existence of a liquid core. This double challenge requires much more accurate models for the spin-orbit resonant rotation of Mercury. The purpose of this paper is to introduce planetary perturbations on Mercury’s rotation using an analytical method and to analyse the influence of the perturbations on the libration in longitude. Applying a perturbation theory based on the Lie triangle, we were able to re-introduce short periodic terms into the averaged Hamiltonian and to compute the evolution of the rotational variables. The perturbations on Mercury’s forced libration in longitude mainly come from the orbital motion of Mercury (with an amplitude around 41 arcsec that depends on the momenta of inertia). It is completed by various effects from Jupiter (11.86 and 5.93 year-periods), Venus (with a 5.66 year-period), Saturn (14.73 year-period), and the Earth (6.58 year-period). The amplitudes of the oscillations due to Jupiter and Venus are approximately 33% and 10% of those from the orbital motion of Mercury and the amplitudes of the oscillations due to Saturn and the Earth are approximately 3% and 2%. We compare the analytical results with the solution obtained from the spin-orbit numerical model SONYR. 相似文献
18.
Dynamical evolution of the rotation of Venus 总被引：1，自引：0，他引：1
By considering the torque of the bodily tides, the effect of the core-mantle viscous coupling and the torque of the atmospheric tides have been obtained by numerical calculation: the evolution of the spin angular velocity and the obliquity of the Venus are calculated numerically with the step-variable Runge-Kutta method of 7th order; and 7 sets of the probable Cytherean spin evolution have been obtained. It is indicated that the present spin state of Venus is the result of long-term evolution within the reasonable ranges of some disposable parameters. The early spin period is between 7 h to 2 d and the corresponding obliquity is about 90 ° ~ 100 °. The effects of the torques of body and atmospheric tides and the core-mantle viscous coupling of Venus on its spin angular velocity could nearly cancel out each other about a billion years ago. Therefore, Venus could have been captured in a spin-orbit resonant state by the gravitational torque of the Earth on the permanent deformation part of Venus; and this resonant state has lasted up to the present time. 相似文献
19.
M. N. Izakov 《Solar System Research》2012,46(4):278-290
Vertical profiles of the turbulence parameters calculated for the planet-averaged conditions from the experimental data on the turbulent fluctuations of temperature and wind velocity are presented. Improved formulas accounting for the difference between the atmospheric gas on Venus and an ideal one, and the large difference in its thermal capacity at different altitudes, are used. The commonly used formula for the potential temperature describing the atmospheres of the Earth and Mars is inapplicable to the atmosphere of Venus. It has been shown that the opinion on the absence of turbulence in the atmosphere of Venus is based on overestimated values of the dynamic Richardson number obtained from the smoothed profiles of wind velocity, while its actual values are below unity due to the large wind velocity gradients produced by buoyancy waves. To improve the global circulation models of the atmosphere of Venus, it is necessary to use the currently available turbulence parameters calculated from experimental data. 相似文献
20.
A model has been developed for the currents induced in the ionospheres of Venus and Mars by the flowing magnetized solar wind in a previous paper (Cloutier and Daniell, 1973). The altitudes of the ionopauses on both planets, determined from the electrodynamical models of the previous paper, are used here to calculate the total rates of atmospheric mass loss to the solar wind for Venus and Mars. These loss rates are compared to the rates calculated by Michel (1971) based upon the limit of mass loading of the solar wind flow determined from hydrodynamic constraints. The distributions of planetary ions in the downstream wakes of Venus and Mars are calculated, and the interpretation of ion spectrometer measurements from close planetary encounters is discussed. 相似文献