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1.
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   

2.
It is known that the observed secular accelerations of the Sun and Moon are not consistent with the tidal interactions of the Earth with the Sun and Moon. Following Dicke, the hypothesis of variable constant of gravity is adopted and expressions for the accelerations are derived. It is shown that if the theoretical ratio of the acceleration is equated the observed one, a unique value for —/G can be calculated. Adopting the accelerations obtained by Fotheringham, Newton, Muller and Stephenson, and Stephenson, it is found that — /G ranges from 1.4 × 10–11 to 3.3 × 10–11 yr–1. This estimate is consistent with the one based upon the comparison of the lunar accelerations measured with respect to atomic and ephemis times.  相似文献   

3.
An analytic model for third-body perturbations and for the second zonal harmonic of the central body's gravitational field is presented. A simplified version of this model applied to the Earth-Moon-Sun system indicates the existence of high-altitude and highly-inclined orbits with their apsides in the equator plane, for which the apsidal as well as the nodal motion ceases. For special positions of the node, secular changes of eccentricity and inclination disappear too (balanced orbits). For an ascending node at vernal equinox, the inclination of balanced orbits is 94.56°, for a node at autumnal equinox 85.44°, independent of the eccentricity of the orbit. For a node perpendicular to the equinox, there exist circular balanced orbits at 90° inclination. By slightly adjusting the initial inclination as suggested by the simplified model, orbits can be found — calculated by the full model or by different methods — that show only minor variations in eccentricity, inclination, argument of perigee, and longitude of the ascending node for 105 revolutions and more. Orbits near the unstable equilibria at 94.56° and 85.44° inclination show very long periodic librations and oscillations between retrogade and prograde motion.Retired from IBM Vienna Software Development Laboratory.  相似文献   

4.
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   

5.
In this article, our previous Hamiltonian theory for the rotation of an Earth whose elastic mantle is deformed by rotation and linisolar attraction is applied to the study of the secular acceleration of the Earth's rotation. Since it is a result of the inelasticity, the theory is extended to include a phase lag. So, we obtain, in a theoretical way, a value of –5.6 × 10–22 rd sec–2, which agrees perfectly with the latest observational results.  相似文献   

6.
Heterogeneities in terrestrial samples for 182W/183W and 142Nd/144Nd are only preserved in Hadean and Archean rocks while heterogeneities in 129Xe/130Xe and 136Xe/130Xe persist to very young mantle‐derived rocks. In contrast, meteorites from Mars show that the Martian mantle preserves heterogeneities in 182W/183W and 142Nd/144Nd up to the present. As a consequence of the probable “deep magma ocean” core formation process, we assume that the Earth and Mars both had a very early two‐mantle‐reservoir structure with different initial extinct nuclide isotopic compositions (different 182W/183W, 142Nd/144Nd, 129Xe/130Xe, 136Xe/130Xe ratios). Based on this assumption, we developed a simple stochastic model to trace the evolution of a mantle with two initially distinct layers for the extinct isotopes and its development into a heterogeneous mantle by convective mixing and stretching of these two layers. Using the extinct isotope system 182Hf‐182W, we find that the mantles of Earth and Mars exhibit substantially different mixing or stirring rates. This is consistent with Mars having cooled faster than the Earth due to its smaller size, resulting in less efficient mantle mixing for Mars. Moreover, the mantle stirring rate obtained for Earth using 182Hf‐182W is consistent with the mantle stirring rate of ~500 Myr constrained by the long‐lived isotope system, 87Rb‐87Sr and 147Sm‐143Nd. The apparent absence of 182W/183W isotopic heterogeneity in modern terrestrial rocks is attributed to very active mantle stirring which reduced the 182W/183W isotopic heterogeneity to a relatively small scale (~83 m for a mantle stirring rate of 500 Myr) compared to the common sampling scale of terrestrial basalts (~30 or 100 km). Our results also support the “deep magma ocean” core formation model as being applicable to both Mars and Earth.  相似文献   

7.
In this paper, two factors — the redistribution of the density and the variation in the angular velocity of the Earth rotation, that affect the adopted value of the flattening for equidensity surface within the Earth, are discussed. The computational results show that the contribution of the redistribution of the density in the Earth interior (especially in the core) on the change of the flattening at the core-mantle boundary (CMB) is marginal, and that the calculated value of the flattening at the CMB can be in good agreement with the VLBI observed value so long as the fact that the angular velocity of the Earth rotation has undergone the tidal evolution is taken into account. As a result, this paper presents a set of recommended values of the dynamical parameters of the Earth (see Table III) for computing Earth's forced nutation series.  相似文献   

8.
The rheology of the Martian mantle and the planet's initial temperature is constrained with thermal evolution models that include crust growth and test the conditions for magnetic field generation in the core. As observations we use the present-day average crustal thickness of 50-120 km as estimated from the Mars Global Surveyor gravity and topography data, the evidence for the crust being produced mostly early, with a rate declining from the Noachian to the Hesperian, and the evidence for an early magnetic field that likely existed for less than a billion years. We use the fact that the rate of crust growth is a function of temperature, which must be above the solidus in the sub-lithosphere mantle, and the mantle convection speed because the latter determines the rate at which melt can be replenished. The convection speed is a strong function of viscosity which, in turn, is a strong function of temperature and also of the water content of the mantle. We use a viscosity parameterization with a reference viscosity evaluated at 1600 K the value of which can be characteristic of either a dry or a wet mantle. We further consider the Fe-FeS phase diagram for the core and compare the core liquidus estimated for a sulphur content of 14% as suggested by the SNC meteorite compositions with the core temperatures calculated for our cooling models. Two data sets of the Fe-FeS eutectic temperature have been used that differ by about 200 K [Böhler, R., 1996. Fe-FeS eutectic temperatures at 620 kbar. Phys. Earth Planet. Inter. 96, 181-186; Fei, Y., Bertka, C.M., Finger, L.W., 1997. High-pressure iron-sulphur compound, Fe3S2, and melting relations in the Fe-FeS system. Science 275, 1621-1623] at Martian core-mantle boundary pressure and in the eutectic composition by 5 wt%. The differences in eutectic temperature and composition translate into a difference of about 400 K in liquidus temperature for 14 wt% sulphur.We find it premature to rule out specific mantle rheologies on the basis of the presently available crustal thickness and crust growth evidence. Rather a trade-off exists between the initial mantle temperature and the reference viscosity. Both a wet mantle rheology with a reference viscosity less than 1020 Pas and a dry mantle rheology with a reference viscosity of 1021 Pas or more can be acceptable if initial mantle temperatures between roughly 1700 and 2000 K are allowed. To explain the magnetic field history, the differences in liquidus temperatures matter. For a liquidus temperature of about 1900 K at the Martian core-mantle boundary as calculated from the Böhler et al. eutectic, a dry mantle rheology can best explain the lack of a present-day dynamo. For a liquidus temperature of about 1500 K at the core-mantle boundary as calculated from the Fei et al. eutectic all models are consistent with the observed lack of dynamo action. The reason lies with the fact that at 14 wt% S the Martian core would be close to the eutectic composition if the Fei et al. data are correct. As inner core growth is unlikely for an almost eutectic core, the early field would have been generated by a thermally driven dynamo. Together with the measured strength of the Martian crustal magnetization this would prove the feasibility of a strong thermally driven dynamo.  相似文献   

9.
A multiple pinhole camera system has been designed and proposed for a small satellite of the SAS type for the detection and localization of gamma-ray bursts. The instrument consists of a three unit array of detectors each of which includes a semi-cylindrical collimator surrounding a twodimensional position-sensitive detector. The collimator contains slits of 1 mm width that are cut parallel to the axis of the cylinder. The slits are randomly arranged in azimuth around the cylinder. X-rays may enter the counter through several surfaces. The point at which photoelectric interaction takes place is determined in two dimensions in a plane perpendicular to the cylinder axis. Each unit of the system determines the position of a burst to a great circle. An intersection of two (or three) great circles provides the precise positions.The field of view of the instrument is 2.7 ster, essentially the entire region of sky not occulted by the Earth. It is designed to operate in the energy range 20–100 keV. An instrument sized to fit a SAS spacecraft has a sensitivity of better than 10–6 erg cm–2 for bursts whose intense phases occur in less than a total of three seconds. For stronger bursts (>10–5 erg cm–2) the location precision is better than a minute of arc.Paper presented at the COSPAR Symposium on Fast Transients in X-and Gamma-Rays, held at Varna, Bulgaria, 29–31 May, 1975.  相似文献   

10.
The orbit of the Pageos 1 balloon satellite has been investigated in detail over the early part of the balloon's lifetime. The analysis herein focuses on how Pageos's orbit was affected by direct solar and albedo radiation pressure. Near the end of the second year of the satellite's lifetime, anomalous behavior was found in the orbital acceleration. This behavior may be the result of a change in the shape of the satellite: Pageos's original spherical shape had become slightly oblate, spinning about a minor axis and precessing about the direction to the sun. In fact, we have been able to represent this effect quite well by accounting for a small component of force in the plane perpendicular to the sun and allowing this component to rotate about the solar direction. By analyzing the balloon-inflation process, attained with sublimating compounds, and the consequent variation of the satellite's mass due to leakage through the holes caused by micrometeoroid bombardment, we have evaluated the near-earth micrometeoroid-particle flux, which turns out to be 5×10–8 cm–2 sec–1. With the assumptions we made for the satellite's area-to-mass ratio and reflection coefficient, we would need a solar constant of 1.95 cal cm–2 min–1 to give a best-fit to our data.  相似文献   

11.
Abstract— A review of problems related to Xe isotopic abundances in meteorites and terrestrial materials leads to four postulates which should be taken into account to build a model of the Earth's accretion and early evolution. 1. The pre-planetary accretion time scale was shorter than the 129I half-life, 17 Ma, so the initial ratio of 129I/127I had not been decreased considerably when planetary accretion started; therefore, this must also be the case for the 244Pu abundance. 2. The initial relative abundance of involatile refractory 244Pu in proto-planetary materials should be the same as in chondrites, that is, 244Pu/238U = 0.0068; this value corresponds to initial 244Pu 0.30 ppb in the bulk silicate earth. In contrast, I is a highly volatile element; its initial abundance, accretion history and even the present-day mean concentrations in principal terrestrial reservoirs are poorly known. 3. There is much less fission Xe in the upper mantle, crust, and atmosphere than is predictable from the fission of 244Pu (Xe(Pu)) based on the above argument. Therefore, Xe(Pu) has been mainly released from these reservoirs. 4. A mechanism for Xe(Pu) escape from the complementary upper mantle-crust-atmosphere reservoirs, for example, atmospheric escape via collisions of a growing Earth with large embryos and/or hydrodynamic hydrogen flux, etc., operated during the Earth's accretion. These postulates have been used as a background for a balance model of homogeneous Earth accretion which envisages: growth of the Earth due to accumulation of planetesimals; fractionation inside the Earth and segregation of the core; degassing via collision and fractionation; and escape of volatiles from the atmosphere. During the post-accretion terrestrial history, the processes described by the model are continuous fractionation, degassing and recycling of the upper mantle and crust. The lower mantle is considered as an isolated reservoir. Depending on the scenario invoked, the accretion time scale varies within the limits of 50–200 Ma. In the light of recent experimental data, the latter value is inferred to the most realistic version which explains a high Xe(U)/Xe(Pu) ratio in the upper mantle. Contrary to previous suggestions, the 129I-129Xe subsystem is considered to be meaningless with regard to the terrestrial accretion time scale. The terrestrial inventory of 129Xe(I) is controlled by the initial abundance of volatile elements (including I and Xe) in proto-terrestrial materials and the subsequent degassing history of the Earth. The residence time of a volatile element (e.g., Xe) in the bulk mantle (bm) during accretion, < t (Xe)bm>, is approximated by the ratio of < t (Xe)bm> m bm(t)/φbm, mf ≤ 10 Ma, where m bm(t) is the mantle mass, and φbm, mf is the rate of metal/silicate fractionation, which provided segregation of the core; φbm, mf is determined by involatile siderophile element abundances in the upper mantle. This relationship implies a link between the abundance of involatile siderophile and volatile incompatible elements. A short <t(Xe)bm> reflects a high degassing rate due to extremely high φbm, mf 1020 g/year. A small ratio of the atmospheric amount of Xe over the total amount of this gas in prototerrestrial materials, ≤0.01, is in accord with the process of Xe escape and fractionation in the primary Earth atmosphere.  相似文献   

12.
We use theoretical results derived in a previous paper (Lanzano, 1986) to numerically evaluate the temperature profile and radial deformation within a spherical, elastic Earth due to heat generated by the decay of radiogenic elements.We consider only the Uranium family and have assumed the diffusivity of the silicate mantle to be K = 8 × 10–3 cm2 s–1, the Poisson elastic ratio to be = 0.25 and the coefficient of thermal expansion to be = 2 × 10–5 (deg)–1. Our series solutions when applied to the interiors of the Moon, Mercury, and Mars yield results in agreement with Kopal's (1963) evaluations.  相似文献   

13.
Careful study by Owen of the displacements of the continents renders it likely that the Earth radius increased by almost 20% during the past 200 million years. Ramseys proposal that the Earth liquid core is a high-pressure phase of the mantle material is adopted to calculate the Earth radius under variableG. It is shown that ifG varies according to the large-numbers hypothesis of Dirac, the primordial Earth would have had radius 700 km less than the modern value. If it is assumed that the Earth began to respond and, hence, expand only 2 × 108 yr B.P., the expansion as large as 700 km is shown to be energetically plausible.  相似文献   

14.
Wegener concluded that the Earth's surface has suffered regionally variable westward displacement. Modern data support Wegener's conclusion, but a causative mechanism has not been evident. The retarding torque is too small to distort the viscous Earth. At the same time difficulty has been experienced in explaining the large value of the astronomically detected tidal dissipation. We have examined the effect of the secular rotational strain imposed by tidal bulge formation on convection in the mantle of arbitrary origin. The dissipation as measured by the lag in the bodily tides appears adequate to explain the missing part of the dissipation, some 8.5 × 1026 erg yr–1, without recourse to an unidentified mechanism in the seas. The convection must itself be influenced by the external force system. The effect to be expected is that circulation resulting in westward displacement at surface must be fostered at the expense of circulation in other directions. The history of the tidal couple, if this is based on dissipation in the mantle, is likely to differ greatly from that of a couple based on dissipation in the seas.  相似文献   

15.
The early phases of formation in the inner solar system were dominated by collisions and short-range dynamical interactions among planetesimals. But the later phases, which account for most of the differences among planets, are unsure because the dynamics are more subtle. Jupiter's influence became more important, leading to drastic clearing out of the asteroid belt and the stunting of Mars's growth. Further in, the effect of Jupiter-- both directly and indirectly, through ejection of mass in the outer solar system-- was probably to speed up the process without greatly affecting the outcome. The great variety in bulk properties of the terrestrial bodies indicate a terminal phase of great collisions, so that the outcome is the result of small-N statistics. Mercury, 65 percent iron, appears to be a residual core from a high-velocity collision. All planets appear to require a late phase of high energy impacts to erode their atmospheres: including the Earth, to remove CO2 so that its ocean could form by condensation of water.Consistent with this model is that the largest collision, about 0.2 Earth masses, was into the proto-Earth, although the only property that appears to require it is the great lack of iron in the Moon. The other large differences between the Earth and Venus, angular momentum (spin plus satellite) and inert gas abundances, must arise from origin circumstances, but neither require nor forbid the giant impact. Venus's higher ratio of light to heavy inert gases argues for it receiving a large icy impactor, about 10–6 Earth masses from far out, requiring some improbable dynamics to get a low enough approach velocity. Core formation in both planets probably started rather early during accretion.Some geochemical evidences argue for the Moon coming from the Earth's mantle, but are inconclusive. Large scale melting of the mantle by the giant impact would plausibly have led to stratification. But the "lock-up" at the end of turbulent mantle convection is a trade-off between rates: crystallization of constituents of small density difference versus overall freezing. Also, factors such as differences in melting temperatures and densities, melt compressibilities, and phase transitions may have had homogenizing effects in the subsequent mantle convection.  相似文献   

16.
C. Sotin  O. Grasset  A. Mocquet 《Icarus》2007,191(1):337-351
By comparison with the Earth-like planets and the large icy satellites of the Solar System, one can model the internal structure of extrasolar planets. The input parameters are the composition of the star (Fe/Si and Mg/Si), the Mg content of the mantle (Mg# = Mg/[Mg + Fe]), the amount of H2O and the total mass of the planet. Equation of State (EoS) of the different materials that are likely to be present within such planets have been obtained thanks to recent progress in high-pressure experiments. They are used to compute the planetary radius as a function of the total mass. Based on accretion models and data on planetary differentiation, the internal structure is likely to consist of an iron-rich core, a silicate mantle and an outer silicate crust resulting from magma formation in the mantle. The amount of H2O and the surface temperature control the possibility for these planets to harbor an ocean. In preparation to the interpretation of the forthcoming data from the CNES led CoRoT (Convection Rotation and Transit) mission and from ground-based observations, this paper investigates the relationship between radius and mass. If H2O is not an important component (less than 0.1%) of the total mass of the planet, then a relation (R/REarth)=ab(M/MEarth) is calculated with (a,b)=(1,0.306) and (a,b)=(1,0.274) for 10−2MEarth<M<MEarth and MEarth<M<10MEarth, respectively. Calculations for a planet that contains 50% H2O suggest that the radius would be more than 25% larger than that based on the Earth-like model, with (a,b)=(1.258,0.302) for 10−2MEarth<M<MEarth and (a,b)=(1.262,0.275) for MEarth<M<10MEarth, respectively. For a surface temperature of 300 K, the thickness of the ocean varies from 150 to 50 km for planets 1 to 10 times the Earth's mass, respectively. Application of this algorithm to bodies of the Solar System provides not only a good fit to most terrestrial planets and large icy satellites, but also insights for discussing future observations of exoplanets.  相似文献   

17.
The most conspicuous effects of non-gravitational forces in the Earth-Moon system are the accelerations of the Earth's spin and of the Moon's mean angular velocity. Evidence indicates that the present acceleration of the Moon is between –20 and –52 s of arc per century per century and that the present average acceleration of the Earth is between –5 and –23 parts in 109 per century. Over the past 2000 yr, the average for the Moon has been about –42 s per century per century and for the Earth has been about –28 parts in 109 per century; these values are probably correct within 10%. Evidence that does not involve any assumptions about the present values shows strongly that there was a square wave in the accelerations that lasted from about 700–1300, and that the accelerations were different by a factor of perhaps 5 during the time of this wave from what they were at neighboring times.An effect that seems to be changing the obliquity of the ecliptic has been reported in recent literature, on the basis of data obtained within the past century. The effect amounts to about 1/4 s of arc per century if it is real. Older data are not accurate enough to give information about an effect this small.There are no satisfactory explanations of the accelerations. Existing theories of tidal friction are quite inadequate.Paper presented at the AAAS Symposium on the Early History of the Earth and Moon in Philadelphia on 28 December 1971.  相似文献   

18.
The giant impact hypothesis for the origin of the Moon has been widely accepted. One of the most important features of this hypothesis is that the impactor's metallic core was incorporated in the Earth after impact. If the mass of the impactor is 0.82 × 1027 g, the mass of the impactor core was estimated to be 0.19 × 1027 g, which is about 1/10 of present Earth's core. Liu (1982) derived the bulk composition of the Earth from CI chondrites, and concluded that the Fe content of his model appears to be low in comparison with the present Earth, which, however, can be rationalized by the addition of impactor core into the proto-Earth developed by Liu (1982). If the impactor's mantle contains 14 wt% FeO as suggested, the mass ratio of impactor/proto-Earth should not exceed 0.22. The same ratio is not likely to exceed 0.30, if a giant blowoff did not occur during impact.  相似文献   

19.
In this paper we present a theory of the Earth rotation for a model composed of an inelastic mantle and a liquid core, including the dissipation in the core–mantle boundary (CMB). The main features of the theory are: (i) to be Hamiltonian, therefore the computation of some complex inner torques can be avoided; (ii) to be self-consistent and non-dependent on a previous rigid Earth theory, so there is no need to use transfer functions; (iii) to be analytical, the solution being derived by perturbation methods. Numerical nutation series deduced from the theory are compared with the IERS 96 empirical series, an accuracy better than 0.8 mas in providing celestial ephemeris pole (CEP) offsets .  相似文献   

20.
Conventional evolutionary models for Mars adopt a dry mantle solidus. Taking into account the condensation conditions in the preplanetary nebula in the accretion zone of Mars, it can be concluded that large amounts of water or hydrated silicates have condensed in those regions. Therefore, water influences significantly the melting behaviour and the viscosity of the silicatic material. A model for the calculation of the thermal history of a planet is constructed. On this basis, and use of water — saturated solidus — it is possible to derive that the core is not liquid, as given in models employing a dry mantle solidus, but solid to a large extent, which prevents the operation of a large-scale dynamo and explains in that way the lack of a magnetic field. With these assumptions one can construct a possible evolutionary scheme that covers early crust differentiation, a hot thermal past and the missing magnetic field at present.  相似文献   

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