A new approach to the librational solution in the Ideal Resonance Problem

The librational motion of the Ideal Resonance Problem (Garfinkel, 1966, Jupp, 1969) is treated through an initialnon-canonical transformation which, however, leaves the equations of motion in a quasi-canonical form, with Hamiltonian expressed in standard trigonometric functions amenable to traditional averaging techniques. The perturbed solutions, similarly expressed intrigonometric near-identity transformations, and their frequencies can be found to arbitrary order, with the elliptic integrals expected of the system introduced only in a final explicit quadrature for a Kepler-type equation in the angular variable. The specific transformations and resulting equations of motion are introduced, and explicit solutions for the original variables are found to second order, with mean motion accurate to fifth. Limitation of the present solution to the librational region, the extension of that solution to higher order, and observations on the form of the associated Hamiltonian are also discussed.     

The role of cavities and mantles in the ultraviolet extinction peak of graphite spheres with particular reference to a possibly discovered C60 structure

A computer routine using rigorous Güttler theory was developed to consider effects of concentric cavities and organic mantles within and around graphite spheres, with a view to assessing the stability of the extinction peak near 4.60 m^–1. The newly discovered stable carbon molecule of 60 atoms gives an absorption band at 4.60 m^–1 which closely agrees with the observed; moreover, it leads to the observed extinction rise in the far UV and can possibly explain the fine structure around the 5.5–7 m^–1 dip, while its own structure deals successfully with the main objections to previous carbon-graphite models. The role of the electric vector component perpendicular to the basal plane of the crystal in achieving the fit is stressed.     

A note on the total mass of comets in the solar system

The assumption that the very low albedo determined for Halley's comet is typical of all short period comets, taken together with the assumption that the average sizes of long and short period comets are approximately equal, leads to an increase in the total mass of comets in the solar system by almost two orders of magnitude. If gravitational ejection from the Uranus - Neptune zone during the later phases of planet formation is indeed responsible for the classical Oort cloud between 10⁴–10¹⁵ AU, then the mass of comets in this transplanetary region during cosmogonie times has to exceed the combined masses of Uranus and Neptune by over an order of magnitude. Furthermore, if the recent arguments for as many as 10¹⁴ comets in an inner Oort cloud between ~40– 10⁴AU are valid, then the total mass of comets in the solar system approaches 2% of a solar mass.     

Some peculiarities in the Asteroidal Belt

The analysis of the fine structure of the Asteroidal Belt evidenciates a group of asteroids next to the resonance 4/9 with Jupiter. In this group and in other groups associated to the Hirayama families there are indications that their orbital parameters can be represented by quantum numbers as defined here and in two of our previous works. Together with this the distribution of the eccentricities and inclinations of the orbital planes of short period comets and diverse type of asteroids indicates that they can be classified as objects with e > sin i and objects with e > sin i with a limit e = sin i which determinates geometrical properties of the orbits related with discrete states in the solar system. This study lets open the possibility of following studies in order to confirm the quantum characteristics of the Asteroidal Belt being these characteristics common to all the solar system and depending of the same fundamental constant of action per mass unit H ₀ = 1/2 ₀ × T ₀ (potential × time) because only a small part of all the available data in the Asteroid Belt is used here.     

The skin friction in the unsteady free-convection flow past an accelerated plate

In this paper the unsteady laminar free-convection flow of a viscous incompressible fluid, past an accelerated infinite vertical porous plate subjected to a constant suction (or injection) in considered. Numerical results for the skin-friction on the plate are obtained for the class of accelerated motions whose velocity is of the formU ₀ t ⁿ wheret is time,U ₀ a constant, andn is a positive integer. The skin friction tends to zero with increasingt when the Grashof number Gr=², the Prandtl number =1,n=0, and >0 which corresponds to suction.On leave of absence from the Department of Mathematics, University of Dhaka, Bangladesh.On leave from absence from the Department of Mathematics, University of Dar-es-Salaam, Tanzania.     

Magnetic reconnection in a high-temperature plasma of solar flares

A simple self-consistent model of a high-temperature turbulent current sheet (HTCS) is considered. The anomalous character of plasma conductivity in a sheet is assumed to be due to gradient instabilities. The possibility of a low threshold of their excitation is demonstrated by an example of temperature-drift instability.Application of the HTCS model to the hot or main phase of a solar flare is discussed. The model consistently explains many observed properties of this phase.     

Spectrophotometric study of Be stars

A large sample of Be stars has been studied spectrophotometrically in the visible region. The continuum energy distribution data for 23 Be stars included in the list of Harmanecet al. (1983) are presented and discussed in the wavelength range 3200 Å–8000 Å. For 15 Be stars the observations reported in the present work are new. By comparing the observed continua with models, the effective temperatures of these stars have been estimated. It is found that, in general, Be stars have lower effective temperature than the corresponding normal B stars. The present study shows that the early-Be stars (B0–B5) possess near-ultraviolet and near-infrared excess emissions more frequently than the late-Be stars (B5–B9). The seven new Be stars are detected to show pole-on characteristics.     

Nuclear reactions on accreting neutron star surface

The production of X-rays and gamma-rays in bursts is believed to be due to the rapid burning of matter accreted onto a neutron star surface from its companion, most probably a giant star. The accreted matter consists mainly of hydrogen and helium and a very small amount of heavy elements. Due to the infall of matter, the temperature at the bottom layers is raised to a value of the order of 10⁸ K. The neutron star surface density is>10⁷ g cm^–3. As hydrogen burning is a slow process under any temperature and density conditions, we consider the helium-burning reactions as the source of gamma-rays in the neutron star surface. Under high-density conditions the ordinary laboratory reaction rates should become modified. At high-density conditions, the strong screening effect due to the polarising cloud of electrons around the ions become important and enhances the reaction rates considerably. The helium-burning reactions are calculated under such conditions. The abundances of helium-burning products such as¹²C, 1¹⁶O, and²⁰Ne, etc., are computed. Under high-density and temperature conditions carbon is found to be more abundant than oxygen. Neon is completely absent in almost all the relevant physical conditions in which a strong screening effect is operative. It is suggested that explosive burning of accreted helium of 10^–13 M will account for the observed energy of gamm-ray burst.     

About the problem of motion of n gyrostats: I. The first integrals

In this paper, the problem of the motion of n gyrostats in a central field, with relative momenta _k ^r (k=1, 2, ..., n) functions of the time, is considered.In these conditions, the existence of the linear and angular momentum integrals is established.Moreover, a sufficient condition for the existence of the Jacobi's Integral is given. This study generalizes the results given by Duboshin for n rigid bodies.     

Further analysis of temperature and emission measure during the decay phase of solar flares derived from soft X-ray light curves

The light curves of soft X-ray lines, observed by the Flat Crystal Spectrometer on Solar Maximum Mission during eight solar flares are modeled to determine the plasma temperature and emission measure as functions of time using the method first presented by Bornmann (1985, Paper I), but modified to include a ² search routine. With this modification the technique becomes more general, more accurate, and applicable throughout the gradual phase of the flare. The model reproduces the light curves of the soft X-ray lines throughout these flares. Model fits were repeated for each flare using five different sets of published line emissivity calculations. The emissivities of Mewe and Gronenschild (1981) consistenly gave the best fits to the observed light curves for each flare.