Triple encounters in the linear three-body problem with equal masses

The paper considers triple encounters in the linear three-body problem for the case of equal masses. Triple encounters are described using two parameters: the virial coefficient k and the angle ? such that tan $\varphi = \dot r/\dot \rho$ , where $\dot r$ and $\dot \rho$ are the velocities of the “central” body relative to each of the “outer” bodies. The equations of motion are integrated numerically up to one of the following times: the time for a receding body to turn, the time for this body to reach some critical distance, the time for some escape criterion to be fulfilled, or to some critical time. Evolutionary scenarios for the triple system are determined as a function of the initial conditions. The dependences of the ejection length on k and $\dot \varphi$ are derived. The initial conditions corresponding to escape form a continuous region with k>0.5. The regions into which the right and left bodies depart alternate and are symmetrical about the lines of triple close encounters (?=45°,225°). Regions of stable motions in the vicinity of the central periodic orbit of Schubart (k?0.206; ?=135°,315°) are identified. Linear structures emanate from the peak of the region of stability, which divide the region for the initial conditions into alternating zones with identical evolutionary scenarios.     

Dynamical stability of triple stars

The dynamical stability of 38 observed hierarchical triple stars with known orbital elements of the internal and external binary subsystems and component masses is considered. Four different criteria of dynamical stability are used. The observed stability parameters and their critical values are calculated by taking into account errors in the orbital elements and component masses. Most triple systems are stable. According to some criteria, several triple stars (ADS 440, ξ Tau, λ Tau, ADS 3358, VV Ori, ADS 10157, HZ Her, Gliese 795, ADS 15971, and ADS 16138) may be dynamically unstable. This result is probably associated with unreliability of the empirical stability criteria and/or with errors in the observed quantities.     

Optical depth of the Martian atmosphere and surface albedo from high-resolution orbiter images

In this paper we describe and evaluate the so-called shadow method. This method can be used to estimate the optical depth of the Martian atmosphere from the differences in brightness between shadowed and sunlit regions observed from an orbiter. We present elaborate and simplified versions of the method and analyze the capabilities and the sources of errors. It proves essential to choose shadowed and sunlit comparison regions with similar surface properties. Accurate knowledge of the observing geometry, including the slopes of the observed region, is important as well, since the procedure should be corrected for the non-horizontal surface. Moreover, the elaborate version of the shadow method can be sensitive to (i) the optical model of aerosols and (ii) the assumed bi-directional reflectance function of the surface. To obtain reliable estimates, the analyzed images must have a high spatial resolution, which the HiRISE camera onboard the MRO provides. We tested the shadow method on two HiRISE images of Victoria crater (TRA_0873_1780 and PSP_001414_1780) that were taken while this crater was the exploration site of the Opportunity rover. While the rover measured optical depth τ approximately in the ranges from 0.43 to 0.53 and from 0.53 to 0.59 by imaging the sun, our shadow procedure yielded τ about 0.50 and 0.575, respectively (from the HiRISE's red images). Thus, the agreement is quite good. The obtained estimates of the surface albedo are about 0.20 and 0.17, respectively.     

Rb-Sr and K-Ar isotopic systems of the Upper Devonian sediments in the Pripyat Trough,Belarus

The results of Rb-Sr and K-Ar isotope studies of the Famennian upper salt and suprasalt complexes sampled from the core material of exploratory boreholes drilled at the northwestern margin of the Pripyat Trough (Belarus) are presented. The suprasalt and saliferous portions of the sequence define an age of approximately 470 Ma. Despite multiple reworking of the material, we interpret this value as preservation of the provenance “memory.” Regardless of the Sr content in sample, the strontium isotope ratios obtained for low-Rb minerals (celestine, carbonate, and halite) varies throughout the section within 0.7083–0.7095, indicating the preservation of some primary features of the matter. The lowest isotope values obtained are slightly higher than those inferred for the upper Famennian. This fact confirms the concept that the studied complex was formed in a shallow-water setting. Data on sylvites show that the present-day isotopic characteristics of potassium salts were formed significantly later.     

Specific features of the mineral composition and petromagnetic properties of rocks from the Minami-Khiosi submarine volcano (Mariana island arc)

Complex studies of the mineral composition and petromagnetic properties of the rocks which compose an edifice of the Minami–Khiosi submarine volcano located in the Mariana island arc are carried out for the first time. The Minami–Khiosi Volcano is a part of the Khiosi volcanic complex within the alkaline province of the Idzu–Bonin and Mariana island arcs. All of the rocks analyzed are enriched in K₂O (1.34–3.30%), Ba (370–806 ppm), and Sr (204–748 ppm). The basalt has a porhyric texture and contains mosTy olivine phenocrysts as individual crystals and growths with a size up to 2 cm; the groundmass is finecrystalline. The samples studied contain at least three Fe-bearing oxide minerals. These are predominant magnetite and less abundant ilmenite and Fe hydroxides. It is established that the samples studied are magnetically isotropic and have high values of natural remanent magnetization and Königsberger ratio. Similarly to the other island-arc Late Cenozoic submarine volcanoes in the western part of the Pacific Ocean, the samples studied are strongly differentiated by the value of natural remanent magnetization and magnetic susceptibility. The low-coercivity magnetic minerals (titanomagnetite and magnetite) of the pseudo-single-domain structure, as well as high-coercivity minerals (hematite) are the main carriers of magnetization. The high values of natural remanent magnetization are explained by the pseudo-single-domain structure of the titanomagnetite grains, whereas the high values of magnetic susceptibility result from the high concentration of ferromagnetic grains.     

Light scattering by morphologically complex objects and opposition effects (a review)

Over the last decade, considerable progress has been achieved in the theory of light scattering by morphologically complex objects, which extends the potential of correct interpretation of photometric and polarimetric observations. This especially concerns the backscattering domain, where the opposition effects in brightness and polarization are observed. Although the equations of radiative transfer and weak localization (coherent backscattering) are rigorously valid only for sparse media, the results of exact computer solutions of the Maxwell equations for a macroscopic volume filled with randomly positioned particles show that their application area can be wider. In particular, the observations can be correctly interpreted if the packing density of particles in the medium reaches 20–30%. The recently suggested approximate solution of the coherent backscattering problem allowed interesting effects in the spectra of Saturn’s satellites to be explained. In the densely packed media, the effects that are impossible in the sparse media and caused by the near-field contribution can be observed. To calculate the characteristics of radiation reflected by such a medium, it is not sufficient to solve the radiative transfer and weak localization equations, even if they are written in a form without the far-zone limitations. Nowadays, the influence of the interaction of particles in the near field can be analyzed only for the restricted ensembles of particles. It shows that the substantial increase of the packing density essentially changes the phase functions of intensity and polarization in the backscattering domain. This allows the packing density of particles in the medium and their absorbing properties to be estimated from the shape of the phase curves measured. However, the task of quantitative interpretation of the measurements of radiation reflected by a densely packed medium, in terms of sizes of particles, their refractive index, and packing density, still remains unsolved.     

On the dynamics and structure of Earth’s oscillations in December 2004 from seismic gravimeter observations in St. Petersburg

The paper describes phenomena of large-scale deformations, in particular, long-term deformation, observed on the planet during December 1–12, 2004, before a cycle of enhanced seismic activity. The spectrum of seismic vibrations with periods of 1 to 9 hr is calculated. A high correlation is established between the frequency distribution of significant vibrations recognizable in this spectrum and vibrations that should be excited most frequently in accordance with the statistical spectrum of the seismogravitational oscillations of the Earth.     

Potassium Tobelite As Indicator of the Postsedimentary Transformation of Coal-Bearing Sedimentary Complexes

The rare mineral, potassium tobelite being the NH₄-bearing mica, was first described in Lower Carboniferous coal-bearing rocks of the Egorshin–Kamensk district on the eastern slope of the Urals. It was formed from kaolinite and pyrophyllite at temperature less than 500°C and pressure about 2000 atm. The formation of tobelite was probably favored by postsedimentary stresses. Owing to sharp increase in pressure, gases were released from organic matter of the coal-bearing sequence and transformed into ammonia, which was subsequently incorporated as NH⁺ ₄in the structure of clay minerals. The potassium tobelite is an indicator of high-grade metamorphism (up to anthracite rank) of the organic matter in coal-bearing sequences.