Stability of the solar system

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.     

Vibrational stability of rotating stars

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.     

Fourier analysis of the light curves of eclipsing variables,IX

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.     

Fourier analysis of the light curves of eclipsing variables,II

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.     

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)

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.     

Optimized Seismic Threshold Monitoring – Part 2: Teleseismic Processing

v--vThis second paper (Part 2) pertaining to optimized site-specific threshold monitoring addresses the application of the method to regions covered by a teleseismic or a combined regional-teleseismic network. In the first paper (Part 1) we developed the method for the general case, and demonstrated its application to an area well-covered by a regional network (the Novaya Zemlya nuclear test site). In the present paper, we apply the method to the Indian and Pakistani nuclear test sites, and show results during the periods of nuclear testing by these two countries in May 1998. Since the coverage by regional stations in these areas is poor, an optimized approach requires the use of selected, high-quality stations at teleseismic distances.¶To optimize the threshold monitoring of these test sites, we use as calibration events either one of the nuclear explosions or a nearby earthquake. From analysis of the calibration events we derive values for array beamforming steering delays, filter bands, short-term averages (STA) lengths, phase travel times (P waves), and amplitude-magnitude relationships for each station. By applying these parameters, we obtain a monitoring capability of both test sites ranging from m_b 2.8-3.0 using teleseismic stations only. When including the nearby Nilore station to monitor the Indian tests, we show that the threshold can be reduced by about 0.4 magnitude units. In particular, we demonstrate that the Indian tests on 13 May, 1998, which were not detected by any known seismic station, must have corresponded to a magnitude (m_b) of less than 2.4.¶We also discuss the effect of a nearby aftershock sequence on the monitoring capability for the Pakistani test sites. Such an aftershock sequence occurred in fact on the day of the last Pakistani test (30 May, 1998), following a large (m_b 5.5) earthquake in Afghanistan located about 1100 km from the test site. We show that the threshold monitoring technique has sufficient resolution to suppress the signals from these interfering aftershocks without significantly affecting the true peak of the nuclear explosion on the threshold trace.     

Remote sensing detection of atmospheric pollutants by differential absorption LIDAR 510M/SODAR PA2 mobile system

Summary Air pollution problem in the Czech Republic is very complex due to large number of factors as turbulent dispersion and chemical reactions concurring in the status of the PBL. For this 3D distribution of pollutants is a key information that cannot be given by conventional monitoring stations. Combined use of DIAL lidar and sodar can give access to such information. Case studies of air pollutants transport are presented using 3D concentration fields of NO₂ and ozone measured by lidar and meteorological conditions monitored by Doppler Sodar.     

Paleontological records indicate the occurrence of open woodlands in a dry inland climate at the present-day Arctic coast in western Beringia during the Last Interglacial

Permafrost records, accessible at outcrops along the coast of Oyogos Yar at the Dmitry Laptev Strait, NE-Siberia, provide unique insights into the environmental history of Western Beringia during the Last Interglacial. The remains of terrestrial and freshwater organisms, including plants, coleopterans, chironomids, cladocerans, ostracods and molluscs, have been preserved in the frozen deposits of a shallow paleo-lake and indicate a boreal climate at the present-day arctic mainland coast during the Last Interglacial. Terrestrial beetle and plant remains suggest the former existence of open forest-tundra with larch (Larix dahurica), tree alder (Alnus incana), birch and alder shrubs (Duschekia fruticosa, Betula fruticosa, Betula divaricata, Betula nana), interspersed with patches of steppe and meadows. Consequently, the tree line was shifted to at least 270 km north of its current position. Aquatic organisms, such as chironomids, cladocerans, ostracods, molluscs and hydrophytes, indicate the formation of a shallow lake as the result of thermokarst processes. Steppe plants and beetles suggest low net precipitation. Littoral pioneer plants and chironomids indicate intense lake level fluctuations due to high evaporation. Many of the organisms are thermophilous, indicating a mean air temperature of the warmest month that was greater than 13 °C, which is above the minimum requirements for tree growth. These temperatures are in contrast to the modern values of less than 4 °C in the study area. The terrestrial and freshwater organism remains were found at a coastal exposure that was only 3.5 m above sea level and in a position where they should have been under sea during the Last Interglacial when the global sea level was 6–10 m higher than the current levels. The results suggest that during the last warm stage, the site was inland, and its modern coastal situation is the result of tectonic subsidence.