Stability of outer planetary orbits around binary stars: A comparison of Hill's and Laplace's stability criteria

A comparison is made between the stability criteria of Hill and that of Laplace to determine the stability of outer planetary orbits encircling binary stars. The restricted, analytically determined results of Hill's method by Szebehely and co-workers and the general, numerically integrated results of Laplace's method by Graziani and Black are compared for varying values of the mass parameter =m ₂/(m ₁+m ₂). For 00.15, the closest orbit (lower limit of radius) an outer planet in a binary system can have and still remain stable is determined by Hill's stability criterion. For >0.15, the critical radius is determined by Laplace's stability criterion. It appears that the Graziani-Black stability criterion describes the critical orbit within a few percent for all values of .     

Asteroid motion near the 3 : 1 resonance

A mapping model is constructed to describe asteroid motion near the 3 : 1 mean motion resonance with Jupiter, in the plane. The topology of the phase space of this mapping coincides with that of the real system, which is considered to be the elliptic restricted three body problem with the Sun and Jupiter as primaries. This model is valid for all values of the eccentricity. This is achieved by the introduction of a correcting term to the averaged Hamiltonian which is valid for small values of the ecentricity.We start with a two dimensional mapping which represents the circular restricted three body problem. This provides the basic framework for the complete model, but cannot explain the generation of a gap in the distribution of the asteroids at this resonance. The next approximation is a four dimensional mapping, corresponding to the elliptic restricted problem. It is found that chaotic regions exist near the 3 : 1 resonance, due to the interaction between the two degrees of freedom, for initial conditions close to a critical curve of the circular model. As a consequence of the chaotic motion, the eccentricity of the asteroid jumps to high values and close encounters with Mars and even Earth may occur, thus generating a gap. It is found that the generation of chaos depends also on the phase (i.e. the angles andv) and as a consequence, there exist islands of ordered motion inside the sea of chaotic motion near the 3 : 1 resonance. Thus, the model of the elliptic restricted three body problem cannot explain completely the generation of a gap, although the density in the distribution of the asteroids will be much less than far from the resonance. Finally, we take into account the effect of the gravitational attraction of Saturn on Jupiter's orbit, and in particular the variation of the eccentricity and the argument of perihelion. This generates a mixing of the phases and as a consequence the whole phase space near the 3 : 1 resonance becomes chaotic. This chaotic zone is in good agreement with the observations.     

Theoretical infrared spectra of some model polycyclic aromatic hydrocarbons: effect of ionization

In order to test the hypothesis of ionized polycyclic aromatic hydrocarbons (PAHs) as possible carriers of the UIR bands, we realized a computational exploration on selected PAHs of small dimension in order to identify which changes ionization would induce on their IR spectra. In this study we performed ab initio calculations of the spectra of neutral and positively ionized naphthalene, anthracene, and pyrene. The results are significantly important. The frequencies in the cations are slightly shifted with respect to the neutral species, but no general conclusion can be reached from the three molecules considered. By contrast, the relative intensities of most vibrations are strongly affected by ionization, leading to a much better agreement between the calculated CH/CC vibration intensity ratios and those deduced from observations.     

Preservation of biological information in thermal spring deposits: developing a strategy for the search for fossil life on Mars

Current interpretations of the early history of Mars suggest many similarities with the early Earth and therefore raise the possibility that the Archean and Proterozoic history of life on Earth could have a counterpart on Mars. Terrestrial experience suggests that, with techniques that can be employed remotely, ancient springs, including thermal springs, could well yield important information. By delivering water and various dissolved species to the sunlit surface of Mars, springs very likely created an environment suitable for life, which could have been difficult, if not impossible, to attain elsewhere. The chemical and temperature gradients associated with thermal springs sort organisms into sharply delineated, distinctive and different communities, and so diverse organisms are concentrated into relatively small areas in a predictable and informative fashion. A wide range of metabolic strategies are concentrated into small areas, thus furnishing a useful and representative sampling of the existing biota. Mineral-charged springwaters frequently deposit chemical precipitates of silica and/or carbonate which incorporate microorganisms and preserve them as fossils. The juxtaposition of stream valley headwaters with volcanoes and impact craters on Mars strongly implies that subsurface heating of groundwater created thermal springs. On Earth, thermal springs create distinctive geomorphic features and chemical signatures which can be detected by remote sensing. Spring deposits can be quite different chemically from adjacent rocks. Individual springs can be hundreds of meters wide, and complexes of springs occupy areas up to several kilometers wide. Benthic microbial mats and the resultant stromatolites occupy a large fraction of the available area. The relatively high densities of fossils and microbial mat fabrics within these deposits make them highly prospective in any search for morphological evidence of life, and there are examples of microbial fossils in spring deposits as old as 300 Myr.     

The effect of Antarctic O3 decline on night airglow intensity of Na5893Å, O5577Å, OH emissions and its correlation with total solar flare numbers

The paper presents the effect of O₃ depletion on different night airglow emission lines. Calculations based on chemical kinetics show that the airglow intensity of Na5893Å, O5577Å and OH band emissions will also be affected due to the depletion of O₃ concentration. Intensity of Na5893Å is calculated theoretically for Halley Bay (76° S,27° W), British Antarctic Survey Station, during the period 1973 to 1984. It is concluded from the covariation of different emission lines that O5577Å and OH emissions also follow the same trend of variation. A study has been made to find the correlation between the depletion of O₃ concentration and total solar flare numbers. Important results are as follows:

The new Russian minorities: a statistical overview

The author "presents a succinct review of the newly constituted Russian minorities situated in the former Soviet republics. Based on census data series (1897 to 1989) and original computations, the paper covers location (highest proportion of Russians in Kazakhstan, Latvia, and Estonia), concentration (predominantly urban), occupational structure (largely in industry and science), and related data on issues such as language affinities and migration."     

Cycle anatomy and variability in the storm-dominated type cincinnatian (Upper Ordovician): coming to grips with cycle delineation and genesis

Although parasequence and sequence are scale-independent terms, they are frequently applied only to specific scales of cycles. For example, meter-scale cycles are commonly assumed to be parasequences or PACs. In the Upper Ordovician Kope and Fairview Formations of northern Kentucky, we examined a succession of 50 meter-scale cycles that have been variously interpreted as deepening-upward, shallowing-upward, or showing no relationship with water depth. Our analysis shows that these cycles, characterized by shifts in storm-bed proximality, are highly variable in their thickness and internal construction. Most cycles are best considered high-frequency sequences, because deepening-upward intervals are common, and many cycles contain evidence of abrupt basinward shifts in facies as expected at sequence boundaries. A minority fit the parasequence model of shallowing-upward cycles bounded by flooding surfaces. Larger, 20 m scale cycles are defined by systematic thickening and thinning trends of meter-scale cycles. However, meter-scale cycles do not display any systematic trends in cycle anatomy as a function of position within the 20 m cycles or position within the Kope and Fairview Formations. The high cycle variability and the lack of systematic stratigraphic organization with respect to longer-term cyclicity reflect either the irregularity of relative sea-level changes, the poor recording of sea-level changes in this deep-water setting, or the generation of these cycles by climate-induced cyclicity in storm intensity. These three mechanisms would generate similar patterns at the outcrop scale, so it is not possible at the present to distinguish between them.     

Uncertainties in field-line tracing in the magnetosphere. Part II: the complete internal geomagnetic field

The discussion in the preceding paper is restricted to the uncertainties in magnetic-field-iine tracing in the magnetosphere resulting from published standard errors in the spherical harmonic coefficients that define the axisymmetric part of the internal geomagnetic field (i.e. g_n⁰ ± g_n⁰). Numerical estimates of these uncertainties based on an analytic equation for axisymmetric field lines are in excellent agreement with independent computational estimates based on stepwise numerical integration along magnetic field lines. This comparison confirms the accuracy of the computer program used in the present paper to estimate the uncertainties in magnetic-field-line tracing that arise from published standard errors in the full set of spherical harmonic coefficients, which define the complete (non-axisymmetric) internal geomagnetic field (i.e. g_n^m ± g_n^m and h_n^m ± h_n^m). An algorithm is formulated that greatly reduces the computing time required to estimate these uncertainties in magnetic-field-line tracing. The validity of this algorithm is checked numerically for both the axisymmetric part of the internal geomagnetic field in the general case (1 n 10) and the complete internal geomagnetic field in a restrictive case (0 m n, 1 n 3). On this basis it is assumed that the algorithm can be used with confidence in those cases for which the computing time would otherwise be prohibitively long. For the complete internal geomagnetic field, the maximum characteristic uncertainty in the geocentric distance of a field line that crosses the geomagnetic equator at a nominal dipolar distance of 2 R_E is typically 100 km. The corresponding characteristic uncertainty for a field line that crosses the geomagnetic equator at a nominal dipolar distance of 6 R_E is typically 500 km. Histograms and scatter plots showing the characteristic uncertainties associated with magnetic-field-line tracing in the magnetosphere are presented for a range of illustrative examples. Finally, estimates are given for the maximum uncertainties in the locations of the conjugate points of selected geophysical observatories. Numerical estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, including the associated uncertainties in thelocations of the conjugate points of geophysical observatories, should be regarded as first approximations in the sense that these estimates are only as accurate as the published standard errors in the full set of spherical harmomic coefficients. As in the preceding paper, howerver, all computational techniques developed in this paper can be used to derive more realistic estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, following further progress in the determination of more accurate standard errors in the spherical harmonic coefficients.Also Visiting Reader in Physics, University of Sussex, Palmer, Brighton, BN1 9QH, UK     

Sulfur isotope fractionation during bacterial sulfate reduction in organic-rich sediments

Isotope fractionation during sulfate reduction by natural populations of sulfate-reducing bacteria was investigated in the cyanobacterial microbial mats of Solar Lake, Sinai and the sediments of Logten Lagoon sulfuretum, Denmark. Fractionation was measured at different sediment depths, sulfate concentrations, and incubation temperatures. Rates of sulfate reduction varied between 0.1 and 37 micromoles cm-3 d-1, with the highest rates among the highest ever reported from natural sediments. The depletion of 34S during dissimilatory sulfate reduction ranged from 16% to 42%, with the largest 34S-depletions associated with the lowest rates of sulfate reduction and the lowest 34S-depletions with the highest rates. However, at high sulfate reduction rates (>10 micromoles cm-3 d-1) the lowest fractionation was 20% independent of the rates. Overall, there was a similarity between the fractionation obtained by the natural populations of sulfate reducers and previous measurements from pure cultures. This was somewhat surprising given the extremely high rates of sulfate reduction in the experiments. Our results are explained if we conclude that the fractionation was mainly controlled by the specific rate of sulfate reduction (mass cell-1 time-1) and not by the absolute rate (mass volume-1 time-1). Sedimentary sulfides (mainly FeS2) were on average 40% depleted in 34S compared to seawater sulfate. This amount of depletion was more than could be explained by the isotopic fractionations that we measured during bacterial sulfate reduction. Therefore, additional processes contributing to the fractionation of sulfur isotopes in the sediments are indicated. From both Solar Lake and Logten Lagoon we were able to enrich cultures of elemental sulfur-disproportionating bacteria. We suggest that isotope fractionation accompanying elemental sulfur disproportionation contributes to the 34S depletion of sedimentary sulfides at our study sites.