Stability of the solar system     

Zdeněk Kopal 《Earth, Moon, and Planets》1980,22(1):5-11

If the solar system is considered as a mechanical clockwork consisting of its present members which attract each other as mass-points, the extent of its present approach to secular stability (i.e., the state of minimum potential energy) — manifested by the existence of a number of nearcommensurabilities of the present orbital periods, not only of the planets, but also of their satellites —could not have been attained in a time-span of 4.6×10⁹ yr of its age by gravitational perturbations alone.The existence of such commensurabilities — striking in many instances— could then be understood only on the assumption that either (a) the solar system was actually born with the present 2-, 3- and 4-term couplings between the orbital period of the planets already built-in from the outset (which is improbable on any known grounds); or (b) that these couplings — in particular, the 25 Jupiter-Saturn commensurability — have arisen as a result of tidal interaction between proto-planetary globes of much larger dimensions than these planets possess today. For the present dimensions and mutual distances of these planets, their tidal interaction in 10⁹ yr would exert but negligible effects; and during that time neither their masses, nor the scale of the solar system underwent any essential change.Therefore, a hypothesis is proposed that the situation now obtaining had its origin in the early days of the formation of the solar system, when the planetary globes — in particular, those of Jupiter and Saturn (now in the terminal stage of Kelvin contraction) — were very much larger than they are today; and when, as a result, the tidal coupling between them operated at a much higher rate than at the present time.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.  相似文献   

Investigation of the instability of graveyard orbits due to the earth's gravitational perturbations     

Jan Kostelecký  Jaroslav Klokočník 《Studia Geophysica et Geodaetica》1992,36(4):297-301

Summary The Banach theorem is applied to the Lagrange planetary equation for the semimajor axis of a geostationary satellite orbit to estimate the stability of near-geostationary satellite orbits. To achieve a graveyard (disposal) orbit, which will not interfere (=cross) the initial geostationary orbit, the geostationary semi-major axis a_g have to be increased at least by 50 km. Numerical results for a variety of graveyard orbits show that the increase of a_g by about 100 km will yield sufficiently stable orbits (accounting for the Earth's gravitational perturbations only) during the next 150 years.Dedicated to the 75th Birthday of Professor Academician Tibor Kolbenheyer  相似文献   

A combined study of macroseismic data and focal mechanisms applied to the West-Bohemian earthquake,Czechoslovakia     

J. Zahradník  M. Antonini  G. Grünthal  J. Janský  D. Procházková  E. Schmedes  A. Špičak  J. Zedník 《Pure and Applied Geophysics》1990,133(1):53-71

The main shock of the West-Bohemian earthquake swarm, Czechoslovakia, (magnitudem=4.5, depthh=10 km) exhibits an irregular areal distribution of macroseismic intensities 6° to 7° MSK-64. Four lobes of the 6° isoseismal are found and the maximum observed intensity is located at a distance of 8 km from the instrumentally determined epicentre. This distribution can be explained by the energy flux of the directS wave generated by a circular source, the hypocentral location and focal mechanism of which are taken from independent instrumental studies. The theoretical intensity, which is assumed to be logarithmically proportional to the integrated squared ground-motion velocity (i.e.,I=const+log v ² (t)dt), fits the observed intensity with an overall root-mean-square error less than 0.5°. It is important that the present intensity data can also be equally well explained by the isotropic source. The fit was attained by means of a horizontally layered model though large fault zones and an extended sedimentary basin suggest a significant lateral heterogeneity of the epicentral region. The results encourage a broader application of the simple modelling technique used.  相似文献   

Vibrational stability of rotating stars     

Zdeněk Kopal 《Astrophysics and Space Science》1981,76(1):187-212

The aim of the present paper will be to detail the explicit form of the equations which govern first-order oscillations of fast-rotating globes of self-gravitating fluids; with due account taken of the effects arising from the centrifugal as well as Coriolis force. As such configurations oscillate in general about distorted figures of equilibrium, the equations governing them can be conveniently expressed in terms of the Clairaut coordinates, associated with distorted spheroidal figures, and introduced in our previous paper (Kopal, 1980) for this purpose.In Section 2 which follows a brief outline of our problem, the equilibrium properties of fast-rotating configurations or arbitrary structure will be formulated. In Section 3 we shall carry out a separation of the variables in the equations of motion, and reduce the partial differential equations of the problem to an equivalent system of ordinary differential equations, by an expansion of expressions for the velocity componentsU, V, W in terms of tesseral harmonicsY _n ^m (, ). The explicit form of such a system, including the effects of all tesseral harmonics of orders up tom=n=4, will be specified in Section 3 for configurations whose equilibrium form is a sphere; while in Section 4 this latter condition will be relaxed to allow for the equilibrium configuration to become a rotational spheroid.In the concluding Section 5 we shall convert the complex form of our equations of motion into real terms, amenable to a solution-analytical or numerical-in terms of real variables; and shall establish the boundary conditions necessary for a specification of the characteristic frequencies of oscillation.  相似文献   

Editorial     

Cornelis De Jager  Zdeněk Švestka 《Solar physics》1978,56(1):3-4

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Fourier analysis of the light curves of eclipsing variables,IX     

Zdeněk Kopal 《Astrophysics and Space Science》1976,45(2):269-281

The aim of the present paper will be to detail the procedure outlined in our previous investigations (Kopal, 1975; Kopalet al., 1976) for a solution of the elements of distorted eclipsing systems by a Fourier analysis of their light changes. This procedure—which constitutes an equivalent, in the frequency-domain, of rectification hitherto practised in the time-domain — should enable us to free the observed momentsA _2m of the light curves from all photometric effects of distortion (between minima as well as within eclipses) — a feat impossible in the time-domain except under very restricted conditions — and thus to make it possible to obtain the geometrical elements of the eclipses which should be free from any obvious source of systematic errors.  相似文献   

Fourier analysis of the light curves of eclipsing variables,II     

Zdeněk Kopal 《Astrophysics and Space Science》1975,35(1):159-170

The aim of the present paper will be to extend the Fourier methods of analysis of the light curves of eclipsing binaries, outlined in our previous communication (Kopal, 1975) in connection with systems whose components would appear as uniformly bright discs, to systems whose components exhibit discs characterized by an arbitrary radially-symmetrical distribution of brightness —i.e., an arbitrary law of darkening towards the limb — be it linear or nonlinear.In Section 2 which follows a few brief introductory remarks, fundamental equations will be set up which govern the light changes arising from the mutual eclipses of limb-darkened stars — be such eclipses total, partial or annular; and Section 3 will contain a closed algebraic solution for the elements of the occulation eclipses terminating in total phase. Such a solution proves to be no more complicated than it turned out to be for uniformly bright discs in our previous paper; and calls for no special functions for the purpose — as will be put in proper perspective in the concluding Section 4.The cases of transit eclipses terminating in an annular phase, of partial eclipses of occulation or transit type, will be similarly dealt with by Fourier methods in the next paper of the present series.  相似文献   

Acid leaching of ash and coal: Time dependence and trace element occurrences     

Mehtap Paul  Meryem Seferinoğlu  Gul Asiye Ayçık  Åke Sandström  Michael L. Smith  Jan Paul 《International Journal of Mineral Processing》2006

The leaching of coal and coal/asphaltite/wood-ashes in sulfuric acid (pH 1.0, 25 °C, S/L, 1:10) was studied as a function of time; acid consumption and extracted metal concentrations are presented. Whole coals consumed acid rapidly during the first few minutes, followed by slow acid consumption. Wood-, lignite-, and asphaltite-ashes consumed acid in two stages, the rapid phase extending < 30 min and the slow phase extended up to 10 days. The rapid phase was dominated by the dissolution of Ca, K and Mg ions for wood-ash, by Ca, Al and Mg ions for lignite-ash and Ca and Mg ions for asphaltite-ash. The sulfur concentration in solution and the concentrations of Ca, Fe, K, Mg, Na, P, Al and Mn in the aqueous phase verified the neutralizing capacity of the untreated ashes as well as the formation of insoluble sulfates in the residues. The slow phase kinetics differed for different fuels and exhibited leaching of several abundant elements—Fe, Al, K, Na and Mn. Trace elements (Ba, Cd, Co, Cr, Cu, Mo, Ni, Pb, Th, U, V, Zn) sometimes required up to 32 h for maximal extraction from ashes. Suggestions are presented regarding the chemical nature of trace elements in the untreated coals and ashes and suitable residence times for economical industrial processes. We think it possible to combine bacteriological oxidation of sulfidic concentrates of acid leaching from ash of various qualities or even whole coals.  相似文献   

Alpine reworking of Ordovician protoliths in the Western Carpathians: Geochronological and geochemical data on the Muráñ Gneiss Complex, Slovakia     

A.S. Gaab  M. Jank  U. Poller  W. Todt 《Lithos》2006,87(3-4):261-275

Magmatic protoliths of Ordovician age have been identified in the metamorphic rocks of the Muráñ Gneiss Complex, Veporic Unit (Central Western Carpathians). Vapor digestion single zircon U–Pb dating yields an intrusion age of 464 ± 35 Ma (upper intercept) for the granite protolith. A lower intercept age of 88 ± 40 Ma records amphibolite-facies metamorphic overprint in the Cretaceous, during the Alpine orogeny. Geochemical and isotopic data suggest crustal origin of the orthogneiss. Nd_initial are between − 2.6 and − 5.0 and T_DM^Nd between 1.3 and 1.5 Ga (two-step approach). ⁸⁷Sr / ⁸⁶Sr_initial ratios vary between 0.7247 and 0.7120, and a steep REE pattern further constrains the crustal affinity of these rocks. Associated amphibolite bodies have Nd_initial values of 6.5, ⁸⁷Sr / ⁸⁶Sr_initial ratio of 0.7017, and a flat REE pattern. They are interpreted as MORB derived metabasites. Whole-rock Pb isotope analyses define a linear array in a ²⁰⁶Pb / ²⁰⁴Pb vs. ²⁰⁷Pb / ²⁰⁴Pb diagram with an age of ca. 134 Ma, consistent with intense Alpine metamorphism and deformation.

These basement rocks of the Central Western Carpathians are interpreted as Ordovician magmatic rocks intruded at an active margin of Gondwana. They represent the eastern prolongation of Cambro–Ordovician units of the European Variscides, which were part of the peri-Gondwana superterrane and accreted to Laurussia during the Variscan orogeny. Variscan metamorphic overprint is not recorded by the isotopic data of the Muráñ Gneiss Complex. Alpine metamorphism is the most dominant overprint.  相似文献   

Will the river Irtysh survive the year 2030? Impact of long-term unsuitable land use and water management of the upper stretch of the river catchment (North Kazakhstan)     

Zbyněk Hrkal  Alain Gadalia  Pierre Rigaudiere 《Environmental Geology》2006,50(5):717-723

The Irtysh river basin all the way from river spring in China across Kazakhstan as far as the Russian part of Siberia is among the most ecologically endangered and affected regions on our planet. The study provides a summary of the historical reasons for anthropological interventions in this area, which began with the construction of plants of the military—industrial complexes in the forties of the last century during World War II. These plants have a major share in extreme high concentrations of heavy metals in surface as well in groundwaters locally. The Semipalatinsk nuclear polygon plays a specific role as a source of contamination of local waters. The release of top secret data enabled us to gain knowledge about serious problems related to high radioactivity of groundwaters, which should spread uncontrollably through a system of secondary fissures activated by nuclear blasts. Another serious problem in this region is the quantitative aspect of contamination. Model simulations of water balance indicate that large industrial development in the spring area in China and continuously increasing water consumption in Kazakhstan may lead to desiccation of the lower stretch of this large river in Siberia during the summer months of 2030.  相似文献