On the instability of “folded” equilibria of a flexible nonstretchable thread attached to the satellite in a circular orbit

The author considers a problem of Lyapunov's stability of relative equilibria of a flexible nonstretchable thread attached to the satellite moving in a circular Keplerian orbit in the first approximation. When it is in the position of relative equilibrium, the thread is known to be situated either along the radius vector of the orbit (the radial equilibrium) or along the circular orbit (the tangential equilibrium) and in each case the thread can be in a folded state. The author shows that folded radial equilibria of the thread are always unstable while tangential ones are unstable if the thread is sufficiently short in comparison with the radius of the orbit. The generalized Chetaev functional has been constructed to prove the instability.     

Connection between X-ray and optical variability in NGC 4151

We have used long light curves in the X-ray (ARIEL V, EXOSAT, Ginga and others), UV (IUE), and optical (data of intensive ground-based monitoring) ranges of NGC 4151 to investigate connections between variations in these spectral fields. Applying Fourier (CLEAN algorithm) and modern cross-correlation analysis, we revealed the different character of the variability and the cross-correlation between high and low states of the nucleus. In contrast to earlier results, we found that X-ray and optical fluxes correlate in the active state without any apparent delay.In the power spectrum of the optical and X-ray light curves in the high state we found the existence of the same period of about 65 days, which disappeared in the low state.We confirmed previous data that X-ray variations correlate more strongly with UV and optical continuum variability during the low state, but it is possible that the optical variations appear to lag behind those involving X-rays by several tens of days.Strong variations in H line profile and [Fe X]6374 line intensity variations correlate with the observed X-ray covering dip in 1990 (Yaqoobet al., 1993).We discuss briefly the implications of these results.     

Application of a global polytropic model to the Jupiter's system of satellites: a numerical treatment

We study the so-called inverse planetary problem (i.e., given the distances from the centre, masses, and radii of, say, three planets of a planetary system, find the optimum polytropic index, mass, and radius of their star, and also other quantities of interest, which depend either explicitly or implicitly on the foregoing ones, e.g., central and mean density, central and mean pressure, central and mean temperature, etc.) for the system of satellites of Jupiter. In particular, Jupiter is considered as star and its satellites as planets of a proper planetary system, which is then treated numerically on the basis of the so-called global polytropic model, developed recently by the first author.     

The photogravitational restricted three-body problem

The photogravitational restricted three-body problem is reviewed and the case of the out-of-plane equilibrium points is analysed. It is found that, when the motion of an infinitesimal body is determined only by the gravitational forces and effects of the radiation pressure, there are no out-of-plane stable equilibrium points.     

Cataclysmic Variables in the “Period Gap”

This article reviews observational data on cataclysmic variables (CVs) whose orbital periods fall within the so-called period gap between 2 and 3 hours. The orbital period distribution of cataclysmic variables and the filling of the period gap by various types of CVs are demonstrated. Roughly half the stars in the period gap are magnetic, of which the majority are polars, while the other half (except a few stars) are SU UMa-type stars characterized by superbursts and superhumps. It is also interesting to note that those intermediate polars whose periods fall within the gap are among the stars with constant superhumps. The height above the galactic plane is estimated for the nonmagnetic stars and it is shown that, contrary to predictions, the stars in the period gap do not belong (except for one) to the spherical component of the galaxy. Light curves, some characteristic times, burst amplitudes, etc. are given for a number of Su UMa-type stars observed by the authors. The evolution of superbursts from the stars NY Ser, V725 Aql, and Var73 Dra is described. Observational data are presented on the classical nova V Per, a star whose period lies right in the middle of the period gap but whose status (magnetic or nonmagnetic) has still unclear.     

Evolution, punctuational crises and the threat to civilization

The relationship between punctuated equilibrium and impact crises is critically examined in the light of our present knowledge of asteroids and comets. It turns out that the emphasis on relatively narrow epochs associated with occasional NEO impacts is probably misplaced. Rather priority should be given to the wider and more frequent epochs associated with multiple NEO debris impacts which result in so-called punctuational crises afflicting the planets. These comprise the global coolings, super-Tunguska events and generally enhanced fireball flux produced by the larger orbital debris whenever an active, dormant or dead comet fragments and produces a trail. Taken as a whole and in conjunction with the target, the response function is inevitably complex. Nevertheless we broadly expect that the strength of a punctuational crisis will vary as the progenitor comet mass, the inverse dispersion of its debris and the inverse delay since fragmentation. The encounter of P/SL-9 with Jupiter may be taken as representing an extreme punctuational crisis where the dispersion and delay were exceptionally small. The more familiar crises affecting the Earth with less extreme values of dispersion and delay, which have resulted in civilization being disturbed a good many times during recent millennia, are no less important however. Indeed, the next such threat to civilization ostensibly has a roughly 1 in 4 lifetime chance. Any support for the Spaceguard programme which detracts from consideration of these punctuational crises, whatever their strength, would seem now to be peculiarly wide of the mark.     

Comparative Analysis of “Exact” and “Approximate” Methods for Estimating the Absolute and Relative Elements of Detached Close Binary Systems

In this paper the star characteristics (luminosities, spectra, masses, absolute and relative radii of the components, mass ratio, major semiaxis, and orbital inclination) of close binary systems (CBS) with detached components are compared element-by-element. Svechnikov and Perevozkina's Catalog of the orbital elements, masses, and luminosities of pre-main sequence-type eclipsing variable stars with known photometric and spectroscopic elements and Svechnikov and Kuznetsova's Catalog of approximate photometric and absolute elements of eclipsing variable stars are used as initial data. The orbital elements contained in the first catalog are determined from solutions of the known photometric light curves and the known radial velocity curves, while the orbital elements for the second catalog were estimated using data from the General Catalog of Variable Stars (GCVS) IV employing approximate statistical relationships such as mass-radius, mass-luminosity, and mass-spectrum, along with the dependence of the orbital inclination on the depth of the principal minimum and others. Possible reasons for discrepancies among the compared quantities are discussed.     

Stability of a Riemann S Ellipsoid with a Spheroidal Halo

The stability of Riemann S ellipsoids inside an oblate halo with respect to the second form of oscillations is investigated. It is shown that some ellipsoids with reverse internal circulation of matter, which are stable inside a spherical halo or in its absence, become unstable with respect to second odd forms of oscillation inside an oblate halo. Here there is asymmetry between conjugate ellipsoids from the standpoint of their stability. Only those conjugate ellipsoids that correspond to higher frequencies of reverse circulation of matter than their corresponding angular rotation rates are unstable. The domains of instability of light and heavy conjugate embedded ellipsoids are obtained as a function of the oblateness measure and relative density of the halo.     

Polarimetry of comets: A review

Some attempts of polarimetric sounding of Comet Halley will be undertaken from the flyby probes. In order to facilitate the final planning and the future interpretation of these experiments we have done a thorough analysis of practically all available polarimetric observations. An emphasis is made on interpretation attempts and their discussion. The results of the phase dependence of polarization investigations are presented covering a wide range of phase angles . The chief peculiarities of this dependence are: maximum polarization at = 90, diminishing through zero at 20, negative values up to several per cent and a final growth to zero at zero . A division into gaseous and dusty comets on polarimetric basis is revealed. The wavelength dependence of polarization is discussed. The numerous results of detailed polarimetry are compared to the negative results of attempts to detect the elliptical polarization. New observational problems arising from the evidence given by the negative polarization at small phase angles and by the opposition effect recently discovered are discussed.     

The mid-infrared structure of the bipolar nebulae AFGL 915, AFGL 618, and AFGL 2688

We have obtained near diffraction-limited images of three bipolar PPN at UKIRT in October, 1993: AFGL 915 (the Red Rectangle), AFGL 618, and AFGL 2688 (the Egg Nebula). Images were taken at unidentified infrared (UIR) emission feature wavelengths and at several continuum wavelengths in the 10 and 20µm atmospheric windows. In all three PPN the emission is dominated by a central point source with fainter emission extending for several arcsec. In AFGL 2688, the mid-IR emission is extended in the same direction as the main optical lobes. In AFGL 915, the UIR feature emission is spatially separated from the central source. The spikes that have been observed at 2µm and give the nebula its rectangular appearance are also visible at 10µm.     

Frequency Distribution Function of Stellar Flares for Faint Stars in the Pleiades Cluster

It is shown that to derive the distribution function of the average frequency of stellar flares in a case in which the number of flares observed in an aggregatation is small, a chronology of third flares can be used to confirm the chronology of first flares. A concrete solution for faint stars of the Pleiades cluster is given.     

Study of alpha component dynamics in the solar wind using the Prognoz satellite

The analysis of solar wind He⁺⁺ and H⁺ ion distribution functions, collected over five months by the satellite Prognoz 1, shows that these are in general maxwellian but that often tails appear at higher speeds. The existing relation V-T, the observation of ratios of T/Tp 3.83 and V/Vp 1.035 give evidence of preferential He⁺⁺ ion heating and acceleration. The criteria for heating by dissipation of hydromagnetic waves proposed by Barnes and Hung (1973) are tested experimentally. Finally, multifluid models are likely to predict certain observations such as dependence of the velocity ratio V/Vp on the solar wind flux.     

The fundamental role of giant comets in earth history

We discuss some fundamental aspects of Earth history as predicted by what has come to be called coherent rather than stochastic catastrophism. The latter essentially seeks to provide an understanding of terrestrial evolution in terms of occasional kilometre-plus impactors from the asteroid belt whereas the former recognises a far more complex extraterrestrial regime arising from the streams of sub-kilometre and kilometre-plus debris due to the disintegration of successive giant comets in sub-Jovian orbits. Periodicities of 15 Myr during the later Phanerozoic (i.e. 250 to 0 Myr BP) and 200 yr during the Holocene (i.e. 10,000 to 0 yr 1313) are likely fundamental signatures in the terrestrial record relating to the action of past and present giant cornets respectively.     

The effect of toroidal magnetic field and differential rotation on self-gravitating polytropic models,II

In this paper we compute differentially rotating polytropic models distorted by toroidal magnetic field. In particular, we study rotating sequences, which do not terminate with a critical rotation. In the computations we use the so-called complex-plane strategy and multiple partition technique, which are numerical methods developed recently by the first author.     

Solar EUV flux variations near activity maxima

Data on solar emission variations in the extreme ultraviolet range <1300 (EUV-range) performed on board the Prognoz satellites and the Phobos spacecraft by the thermoluminescent method are presented. Flux variations from the 11-years cycle are factors of 2–2.5, and that by the 27-days cycle do not exceed 30%.     

Spectroscopic Observations of New Galaxies with a UV Excess. III

The results of the spectroscopic observation of 23 galaxies with a UV excess from Kazarian's lists are presented. The spectra were obtained on the 2.6-m telescope of Byurakan Observatory with a Byu FOSC-2 camera. Two grisms, red and green, were used in the observations. Emission lines are observed in the spectra of 21 of the galaxies.     

New kinematic distances of NGC 7009 and BD+30°3639 from UV and radio data

Measurements of the equivalent width of the interstellar Lyman line from IUE spectra in the direction of the planetary nebulae NGC 7009 and BD+30°3639 are used to infer the H column density in these directions. Hydrogen 21 cm profiles are also used in connection with the ultraviolet data so that the expected rotation velocities and distances can be determined. The results are compared with recently published distances, in an attempt to distinguish between the short and long PN distance scales as applied to these objects.     

Mhd Leaky Waves in a Layered Plasma: II Mechanisms of Leakage

The application of Fourier analysis to study leaky waves has the advantage of simplicity, but it is not clear why the complex roots of the dispersion relations represent leaky waves, nor how the leakage occurs. We investigate the different kinds of leakage that can occur in a three layer plasma, and to which Fourier pseudomodes they are associated. We find four basic mechanisms, called surface mode ..., single interface ..., trapped wave ... and lost insulation leakage. These mechanisms appear in pure form only near certain limiting cases, in which the parameters of the problem take some special values. As soon as the parameters depart significantly from the limiting values, the behavior of the leaky wave complicates and mixtures of the mechanisms occur, in varying amounts. In consequence different points of the same complex branch of the spectrum may correspond to different mechanisms. All the complex branches of the spectrum correspond to leaky waves, but in general it is not possible to classify them according to type of leakage, except close to a limiting case. Since in a three layer configuration there are many of these, the spectrum of leaky waves is very complicated.     

The critical inclination problem — 30 years of progress

The critical inclination problem in artificial satellite theory, first discovered 30 years ago, has aroused great interest and provoked much discussion and controversy in the intervening years. It was this problem which essentially provided the seed corn for the development of the theory of the Ideal Resonance Problem (IRP). The latter theory provides good first-approximation solutions to a number of important resonance problems in celestial mechanics. It is not applicable, however, to certain other interesting resonant systems within the solar system. For these resonances a new fundamental mathematical model of resonance, in the spirit of the IRP, has recently been formulated and successfully applied.This paper reviews the history of the critical inclination problem and highlights the controversies it has generated over the years. The Problem's strong connection with the IRP is outlined with both thenormal andabnormal forms featuring. Finally, with reference to the critical inclination problem, the essential properties of the newer fundamental model are described and compared with the IRP. A strong correspondence is established between recent independent investigations of a variety of resonance problems and earlier work of Andoyer.     

Star passages through the Oort cloud

Stars passing through the Oort cloud eject comets to interstellar space and initiate showers of comets into the planetary region. Monte Carlo simulations of such passages are performed on a representative distribution of cometary orbits. Ejected comets generally lie along a narrow tunnel drilled by the star through the cloud. However, shower comets come from the entire cloud, and do not give a strong signature of the star's passage, except in the inverse semimajor axis distribution for the shower comets. The planetary system is likely not experiencing a cometary shower at this time.