Poynting–Robertson effect in non-singular gravitational potential

We use a non-singular potential that appears in the literature under the influence of which the Poynting-Robertson effect is studied. For that, dust particles originating within the asteroid belt are used, in circular and elliptic orbits, and expressions for the semimajor axis as a function of time are obtained. The derived expressions are written in terms of the two basic dust particle parameters, namely the density and the diameter. In both cases, we obtain expressions for the time that the dust particles take to reach the orbit of Earth under the action of the non-singular potential and solar radiation. For the non-singular potential, dust particles of diameter 10⁻³ m in circular and elliptical orbits require times of the order of 4.058×10⁷ and 2.823×10⁷ y to reach the orbit of the Earth respectively. Finally, the derived expressions and numerical results are compared with those of the Newtonian potential.     

Radiative recombination in some ions of astrophysical interest

Radiative recombination coefficients for some quadruply and quintuply ionized atoms, present in the Sun and its atmosphere, are investigated in the temperature range 10–10⁴ K by using the method of detailed balance. Simple expressions are given for a quick estimation.     

Some weak interaction processes in highly evolved stars

Some weak interaction processes which are important in stars whose central temperatures and densities exceed 10^9°K and 10⁶ gm/cm³ are discussed. Simple analytic expressions for reaction rates which are convenient for computer studies of the late stages of stellar evolution are given.Of the National Bureau of Standards and University of Colorado.     

ON THE POSSIBLE NUMBER AND MASS OF FRAGMENTS FROM PUŁTUSK METEORITE SHOWER, 1868

The earlier efforts to approximate the total number and mass of fragments from Pu?tusk meteorite shower 1868 have been found unsatisfactory With the use of the field data of Samsonowicz and the sorting equation after Frost, differential expressions approximating the mass and number of fragments are derived. These expressions numerically integrated over the elliptical strewnfield area lead to the estimates ～ 1.8 times 10⁵ and ～ 2 times 10⁶ g for the total number and mass of fragments respectively. The meaning of the obtained results is discussed.     

Autoionization rate coefficients for some ions of astrophysical interest

Autoionization rate coefficients for some quadruply and quintuply ionized atoms have been computed in the temperature range 10⁵–10⁸ K. Typical temperature dependence has been found and simple expressions are given for their quick estimation.     

On the equivalence of expressions for inverting the 3-dimensional zodiacal light brightness integral

In the research notes of this Journal, both Schuerman (1979, henceforth Paper I) and Buitrago (1979, henceforth Paper II) independently derived expressions for the general¹, mathematical inversion of the zodiacal light brightness integral. In this communication, it is shown that the expressions are equivalent, differing only in the choice of reference systems.     

Computer-developed construction of analytic expressions for the coordinates and partial derivatives of Jupiter's Galilean satellites

In his effort to develop series expressions for the coordinates of the Galilean satellites accurate to one are second (Jovicentric), R. A. Sampson was forceda priori to adopt certain numerical values for several constants imbedded in his theory. His final numerical values for the series expressions are not amenable to adjustment of the constants of integration nor of physical constants which affect the motion of the satellites. A method which utilizes computer-based algebraic manipulation software has been developed to reconstruct Sampson's theory, to remove existing errors, to introduce neglected effects and to provide analytical expressions for the coordinates as well as for the partial derivatives with respect to orbital parameters, Jupiter and satellite masses, Jupiter's oblateness (J ₂,J ₄) and Jupiter's pole and period of rotation. The computer-based manipulations enable one to perform, for example, the approximately 10⁸ multiplications required in calculating some perturbations (and their partial derivatives) of Satellite II by Satellite III with ease, and provide algebraic expressions which can readily be adjusted to generate theories corresponding to revised constants of integration and physical parameters.     

The Fokfer-Planck equapions for magnetic monopoles and charged particles

We investigate the Fokker-Planck equations (non-relativistic case) for the interaction between magnetic monopoles and charged particles. We find that, the collision integral in this case is also logarithmically divergent, showing that the main effect is still produced by far encounters. We give, for thermal equilibrium, expressions for the three relaxation times. Compared with the well-known expressions for charged particles, these are generally amplified by a factor (light velocity/thermal velocity)², showing that, under ordinary conditions, the interaction between monopoles and charged particles is negligible but that, under certain astrophysical conditions, it is not. In the latter case, the MHD equations must be modified accordingly and the modified equations are given.     

The influence of a turbulent region on the flux of auroral electrons

The influence of low-frequency electrostatic turbulence on the flux of precipitating magnetospheric electrons is analyzed in the framework of the quasilinear kinetic equation. It is shown that an electron population in a turbulent region, with an electric field parallel to the ambient magnetic field, can be separated into two parts by introducing a pitch angle dependent runaway velocity v_r(θ). Lower energy electrons with parallel velocity v_∥ < v_r are effectively scattered by plasma waves, so that they remain in the main population and are subjected to an anomalous transport equation. A distribution function f ∞ v^?4 (or the particle flux vs energy J ∞ E^?1) is established in this velocity range. Faster electrons with v_∥ ? v_r are freely accelerated by a parallel electric field, so that they contribute directly to hot electron fluxes which are observed at ionospheric altitudes. New expressions are derived for the magnetic-field aligned current and the electron energy flux implied by this model. These expressions agree well with empirical relations observed in auroral inverted-V structures.     

Empirical limb effect curves for the FeI lines λ5250 and λ5576

The center to limb variation of solar spectral line positions, or limb effect, has been measured for the two neutral iron lines at 5250.2 Å and 5576.1 Å. Both limb effect curves show a disk-center reversal of 40–60 ms^–1 and the 5576 data also exhibit a possible second reversal at the limb. The limb effect curves are best described by polynomial expressions rather than by traditional power law expressions.Visiting Student, Kitt Peak National Observatory, operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The interaction of matter and radiation in a hot-model universe

In this paper we continue the investigation initiated by Weymann as to the reason why the spectrum of the residual radiation deviates from a Planck curve. We shall consider the distortions of the spectrum resulting from radiation during the recombination of a primeval plasma. Analytical expressions are obtained for the deviation from an equilibrium spectrum due to Compton scattering by hot electrons. On the basis of the observational data it is concluded that a period of neutral hydrogen in the evolution of the universe is unavoidable. It is shown that any injection of energy att>10¹⁰ sec (red shiftz<10⁵) leads to deviation from an equilibrium spectrum.Translated by Peter Foukal.     

Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis

In this paper of the series, elliptic expansions in terms of the sectorial variables θ _j ⁽ⁱ⁾ introduced in Paper IV (Sharaf, 1982) to regularise highly oscillating perturbation force of some orbital systems will be explored for the first four categories. For each of the elliptic expansions belonging to a category, literal analytical expressions for the coefficients of its trigonometric series representation are established. Moreover, some recurrence formulae satisfied by these coefficients are also established to facilitate their computations, numerical results are included to provide test examples for constructing computational algorithms.     

Hydrogen atom in intense magnetic field

The structure of a hydrogen atom situated in an intense magnetic field is investigated. Three approaches are employed. An elementary Bohr picture establishes a crucial magnetic field strength,H _a ?5×10⁹G. Fields in excess ofH _a are intense in that they are able to modify the characteristic atomic scales of length and binding energy. A second approach solves the Schrödinger equation by a combination of variational methods and perturbation theory. It yields analytic expressions for the wave functions and energy eigenvalues. A third approach determines the energy eigenvalues by reducing the Schrödinger equation to a one-dimensional wave equation, which is then solved numerically. Energy eigenvalues are tabulated for field strengths of 2×10¹⁰G and 2×10¹² G. It is found that at 2×10¹² G the lowest energy eigenvalue is changed from ?13.6 eV to about ?180 eV in agreement with previous variational computations.     

Equilibrium Structures of Differentially Rotating Primary Components of Binary Stars

In this paper a method is proposed for computing the equilibrium structures and various other observable physical parameters of the primary components of stars in binary systems assuming that the primary is more massive than the secondary and is rotating differentially about its axis. Kippenhahn and Thomas averaging approach (1970) is used in a manner earlier used by Mohan, Saxena and Agarwal (1990) to incorporate the rotational and tidal effects in the equations of stellar structure. Explicit expressions for the distortional terms appearing in the stellar structure equations have been obtained by assuming a general law of differential rotation of the typeω² = b ₀+b ₁ s ²+b ₂ s ⁴, where ω is the angular velocity of rotation of a fluid element in the star at a distance s from the axis of rotation, and b ₀, b ₁, b ₂ are suitably chosen numerical constants. The expressions incorporate the effects of differential rotation and tidal distortions up to second order terms. The use of the proposed method has been illustrated by applying it to obtain the structures and observable parameters of certain differentially rotating primary components of the binary stars assuming the primary components to have polytropic structures. This revised version was published online in July 2006 with corrections to the Cover Date.     

Transport properties of the degenerate electron gas of neutron stars along the quantizing magnetic field

The expressions are derived for thermal and electric conductivities as well as thermopower of a degenerate relativistic electron gas in the surface layers of neutron stars along the magnetic fieldB=4×10¹¹–10¹⁴G for two scattering mechanisms of electrons, namely, for Coulomb scattering on ions in the ion-liquid regime and on high-temperature phonons in the solid regime. The results may be of use to study neutron star cooling rates, nuclear burning of the matter in the surface layers, diffusion of the magnetic field, etc.     

A new approximate solution of parallel whistler-mode dispersion equation

A new approximation of the real part of the nonrelativistic plasma dispersion function ?Z of a real argument ξ₀ is proposed: namely, $$\Re Z_A (\xi _0 ) = \frac{{2\xi _0 }}{{1 - 2\xi _0^2 }}.$$ This approximation gives the exact value for ?Z when d²?Z/dξ ₀ ² = 0 and gives the correct expressions for the first two terms of its expansion for large ξ₀. On the basis of this approximation, a new approximate expression for whistler-mode refractive index is derived for the case of wave propagation parallel to the magnetic field in a hot anisotropic and dense plasma. Under certain conditions this expression is more convenient for practical applications in magnetospheric and/or astrophysical conditions than other approximate expressions. The approximation ?Z _A was also used in deriving the approximate expression for whistler-mode instability or damping (γ), although in this case it seems to have little merit when compared with the previously used expressions for γ.     

Analytical theory of earth's artificial satellites (A.T.E.A.S.)

The problem of A.T.E.A.S. is treated, for the zonal perturbations, in its Hamiltonian form. The method consists in eliminating angular variables from the Hamiltonian function. Nearly identity canonical transformations are used, first to remove short periodic terms, second to remove long periodic terms. The general solution, up toJ ₂ ³ , is represented by the generators of the transformations and by the mean motions of averaged variables, known up toJ ₂ ⁴ . Open expressions in the eccentricity are avoided as far as possible. It permits to obtain a closed second order theory with closed third order mean motions.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

Formation mechanisms of “Negative”-intensity spots in the cosmic microwave background radiation and distant objects

We consider the formation mechanisms of “negative”-intensity spots in the radio band for various astrophysical conditions. For wavelengths λ<1.5 mm, the regions of reduced temperature (relative to the cosmic microwave background radiation, CMBR) are shown to be produced only by high-redshift objects moving at peculiar velocities. The main processes are CMBR Thomson scattering and bremsstrahlung. We show that the effect δT/T can be ～10^?5 in magnitude. We derive simple analytic expressions, which allow the redshifts, electron densities, and linear sizes of these regions to be estimated from observed spectral and spatial parameters. Additional observational methods for refining these parameters are outlined.     

URCA shells in dense stellar interiors

Thermal and vibrational energy losses due to URCA shells in stellar interiors are calculated. Analytic expressions are derived for semidegenerate, relativistic electrons. Results are given for more general cases calculated with a computer. The calculations are carried out for a large number of nuclei that may contribute to URCA energy losses in various stages of stellar evolution. An illustration is given of the cooling and vibrational damping of a white dwarf. For a central Fermi energy 5 MeV, the internal temperature of the star should be reduced to the order of 10⁶ K and the relative vibrational amplitude should be reduced to the order of 10^–5 on a time scale of 10⁹ yr. URCA shells are present, the URCA neutrino energy loss dominates in the temperature region up to about 2×10⁹ K.