Limits on the changes in the gravitational constant from nucleosynthesis

Due to the recent all-sky, high-precision measurement of microwave background anisotropies by WMAP, a value for baryon-to-photon ratio η was obtained. At the WMAP value for η, the ⁴HE abundance was predicted. In this article we use a simple semi-analytical method with ⁴He predicted and measured values to place a limit on the variation of the gravitational constant G. We find using a conservative range for the measured values for Y _p , that ΔG/G is constrained between −0.26 and 0.15. If we assume a monotonic power law time dependence G∼t ^−β then β values is constrained between −0.008 and 0.0038, which translate into . This compares well with results obtained by others using full numerical analysis.      

A procedure of selection of meteors from major streams for determination of mean orbits

A procedure of selection of meteoroids from major streams is suggested and applied to the IAU Lund photographic database modified by a check for internal consistency among orbital elements (3411 orbits). Limits for choice of stream members were defined by break points on the plots of the cumulative numberN _C vs. the Southworth-HawkinsD discriminant. For the break points were considered the points from which the dependenceN _C vs.D changes to a quasi-linear one, and with the increasingD, N _C changes only moderately. Except for the Taurids which desire a separate analysis, theN _C vs.D diagrams are presented for the following major meteoroid streams: Quadrantids, Lyrids, Aquarids, Capricornids, N and S Aquarids, Perseids, Orionids, Leonids and Geminids. The mean orbits, velocities and radiants of the streams are derived and compared with the osculating orbits of their parent bodies. The limitingD _B was found to be a function of the number of the stream membersN _CB. Omitting the exceptionally concentrated Geminids, the relation is in the formD _B = 0.058 *ln(N _CB) – 0.04.     

On the number of central configurations in the N-body problem

Central configurations are critical points of the potential function of the n-body problem restricted to the topological sphere where the moment of inertia is equal to constant. For a given set of positive masses m ₁,..., m _n we denote by N(m ₁, ..., m _n, k) the number of central configurations' of the n-body problem in ^k modulus dilatations and rotations. If m _{n 1},..., m _n, k) is finite, then we give a bound of N(m ₁,..., m _n, k) which only depends of n and k.     

Analytical theory of a lunar artificial satellite with third body perturbations

We present here the first numerical results of our analytical theory of an artificial satellite of the Moon. The perturbation method used is the Lie Transform for averaging the Hamiltonian of the problem, in canonical variables: short-period terms (linked to l, the mean anomaly) are eliminated first. We achieved a quite complete averaged model with the main four perturbations, which are: the synchronous rotation of the Moon (rate ), the oblateness J ₂ of the Moon, the triaxiality C ₂₂ of the Moon ( ) and the major third body effect of the Earth (ELP2000). The solution is developed in powers of small factors linked to these perturbations up to second-order; the initial perturbations being sorted ( is first-order while the others are second-order). The results are obtained in a closed form, without any series developments in eccentricity nor inclination, so the solution apply for a wide range of values. Numerical integrations are performed in order to validate our analytical theory. The effect of each perturbation is presented progressively and separately as far as possible, in order to achieve a better understanding of the underlying mechanisms. We also highlight the important fact that it is necessary to adapt the initial conditions from averaged to osculating values in order to validate our averaged model dedicated to mission analysis purposes.     

The Non-Linear Stability of L4 in the Restricted Three-Body Problem when the Bigger Primary is a Triaxial Rigid Body

The non-linear stability of L ₄ in the restricted three-body problem has been studied when the bigger primary is a triaxial rigid body with its equatorial plane coincident with the plane of motion. It is found that L ₄ is stable in the range of linear stability except for three mass ratios:

Why are spicules absent over plages and long under coronal holes?

One-dimensional hydrodynamic simulations are performed in order to examine the influence of initial atmospheric structures on the dynamics of spicules. This is an extended version of our previous spicule theory: spicules are produced by the shock wave (MHD slow mode shock) which originates from a bright point appearance (sudden pressure increase) at the network in the photosphere or in the low chromosphere. Simulation results well reproduce the observational facts that spicules are absent over plages and long under coronal holes. The physical reason is that the growth of a shock wave during its propagation through the chromosphere is small in plage regions and large in coronal hole regions, since the growth of a shock is determined by the density ratio ( _{h 0}/ _c ) between the bright point and the corona. An empirical formula H _max ( _{h 0}/ _c )^0.46 is obtained, where H _max is the maximum height of spicules above the transition region. The cross-section of the vertical magnetic flux tube is assumed to be constant in the numerical simulations.     

GPS-Based On-Board Orbit Determination of a Satellite Using Extended H ∞ Filtering Algorithms

In this paper the extended H filtering algorithms for the design of the GPS-based on-board autonomous navigation system for a low earth orbit (LEO) satellite are introduced. The dynamic process models for the estimation of position, velocity and acceleration from the GPS measurements are established. The nominal orbit of the small LEO satellite is determined by using the 7th–8th order Runge—Kutta algorithms. Three filtering approaches are applied to smooth the orbit solutions, respectively, based upon the simulated GPS pseudo range observables using the Satellite Navigation Tool Box. The simulation shows that the observed orbit errors obtained by using the extended H filtering algorithms can be reduced to a lower level than the observed orbit errors in the sense of RMS within 12 h of tracking time by using the H filtering algorithms and the extended Kalman filtering algorithms under the appropriately designed parameters. Based upon the position errors predicted by the three filtering algorithms after the last observation, we find that the extended H filtering algorithm provides the least position errors of the user satellite.This revised version was published online in October 2005 with corrections to the Cover Date.     

The Phase Space Structure Around L4 in the Restricted Three-Body Problem

The phase space structure around L ₄ in the restricted three-body problem is investigated. The connection between the long period family emanating from L ₄ and the very complex structure of the stability region is shown by using the method of Poincarés surface of section. The zero initial velocity stability region around L ₄ is determined by using a method based on the calculation of finite-time Lyapunov characteristic numbers. It is shown that the boundary of the stability region in the configuration space is formed by orbits suffering slow chaotic diffusion.     

Grain formation in the expanding gas flow around cool luminous stars

We studied grain formation process and flow structure around cool luminous mass-loss stars. The nucleation and growth theory of Yamamoto and Hasegawa was extended to the case of expanding gas flow.The envelope was assumed to be steady, spherically symmetric, in thermal and radiative equilibrium, optically thin, and driven by radiation pressure on grains. For oxygen rich stars, Mg-silicate was found to be the first condensate which can drive the gas effectively. The following stellar parameters were chosen; stellar massM _*=1M , effective temperatureT _*=3000K, stellar luminosityL _* from 7.5×10³ to 2.0×10⁴ L , and mass-loss rate |M| from 1.0×10^–6 to 1.0×10^–4 M yr^–1.Main results of calculations are as follows; (1) grain condensation temperatureT _c9801080 K; (2) total gas pressure at the condensation pointP _t6×10^–116×10^–9 atm; (3) scale parameterA _c10³6×10⁴; and (4) final grain sizer _f=400Å1m. For the smaller |M| or the largerL _*, these values are the smaller. We recognized two types of flow solutions (1) Dust driven flow for large |M|, which reaches the sonic point near the condensation point; and (2) Modified Parker flow for small |M| for which grain sizer _f is almost independent of |M|.A comparison with observational results ofL _* and gas terminal velocityV suggests that Mg-silicate grains are of submicron size, which are effective for interstellar extinction in visible and infrared. Fe-grains condense in the rarefied outflow with a size probably smaller than 100Å, which may contribute for interstellar ultraviolet extinction. The envelope has three-layer structure inner dense region with small outflow velocity, grain formation layer and outer rarefied region with fast outflow velocity.No flow solutions exist forM _* greater than a critical stellar massM _*cr for a given stellar luminosityL _* and mass-loss rate |M|.For example, critical stellar massM _*cr=1.8M forL _*=10⁴ L ,T _*=3000 K, and |M|=10^-5 M yr^-1.     

Existence of the continuations in theN-body problem

The method of obtaining the estimates of the maximalt-interval ( _–, ₊) on which the solution of theN-body problem exists and which is such that some fixed mutual distance (e. g. ₁₂) exceeds some fixed non-negative lower bound, for allt contained in ( _–, ₊), is considered. For given masses and initial data, the increasing sequences of the numbers _k , each of which provides the estimate ₊ > _k , are constructed. It appears that if ₊ = +, then .     

Fe XXI emission line ratios as electron temperature diagnostics for the coronae of cool stars

A method for the reconstruction of the linear force-free magnetic field in a bounded domain (as a rectangular box, ) is presented here. The Dirichlet boundary-value problem for the Helmholtz equation is solved for the B _z component specified at the boundary. Chebyshev's iteration method with the optimal rearrangement of the iteration parameters sequence was used. The solution is obtained as for the positive-definite, and for the non-sign-definite difference analogue of the differential operator ² u + ² u. Specifying two scalar functions, B _x and B _y on the intersection of the lateral part of the boundary with one selected plane z = constant, and using B _z inside the , we have found B _x and B _y throughout .The algorithm was tested with the numerical procedure which gives the analytic solution B of the linear force-free field (LFFF) equations for the dipole in a half-space. The root-mean-square deviation of the analytic solution B from the calculated B does not exceed 1.0%. Boundary conditions for the B calculation were taken as given by the analytic LFFF solution B. Comparison of B with B, which was calculated by the potential non-photospheric boundary conditions, show that they differ significantly. Thus, the specification of boundary conditions at non-photospheric boundaries of the volume under consideration is of particular importance when modeling the LFFF in a bounded volume.The algorithm proposed here allows one to use the information about magnetic fields in the corona for the modeling of LFFF in a limited domain above an active region on the Sun.     

Green's theorem and Green's functions for the steady-state cosmic-ray equation of transport

Green's Theorem is developed for the spherically-symmetric steady-state cosmic-ray equation of transport in interplanetary space. By means of it the momentum distribution functionF _o(r,p), (r=heliocentric distance,p=momentum) can be determined in a regionr _arr_bwhen a source is specified throughout the region and the momentum spectrum is specified on the boundaries atr _a andr _b . Evaluation requires a knowledge of the Green's function which corresponds to the solution for monoenergetic particles released at heliocentric radiusr _o , Examples of Green's functions are given for the caser _a =0,r _b = and derived for the cases of finiter _a andr _b . The diffusion coefficient is assumed of the form = _o(p)r ^b . The treatment systematizes the development of all analytic solutions for steady-state solar and galactic cosmic-ray propagation and previous solutions form a subset of the present solutions.     

The N-gon is not a local minimum of U 2 I for N > 7

A theorem of Palmore's concerning coplanar central configurations of equal mass bodies was shown to be false for all even N 6 by Slaminka and Woerner. Using a variation of that argument I prove that Palmore's Theorem is false for all N 6.Northwestern University     

Experimental verification of gravitational interaction of bodies immersed in fluids

This article deals with the experimental verification of the generalized Newton's gravitational law, formulated by Z. Horák. According to this law, the gravitational force between two resting homogeneous bodies immersed in resting homogeneous fluids is dependent on the densities ₁, ₂ of both the bodies and densities₁,₂ of both the fluids: furthermore,F=(1–₁/ ₁)(1–₂/ ₂)F=h ₁ h ₂ F, whereF is the force between the bodies in a vacuum andh ₁,h ₂ are the density factors. The aim of the experimental verification of the law was to determine the density factors by exploring the phenomenon that is influenced by the gravitational interaction of the bodies immersed in different fluids.The dynamic torsion-balance method was applied, during which the period of swinging of the torsion pendulum in the gravitational field of two cast iron spheres in the water.The swings of the pendulum suspended on a torsion filament in a vacuum chamber were measured in three regimes: (1) without the spheres, (2) with the spheres in the air, (3) with the spheres in the water. The motion of the pendulum was scanned by a laser ray, the period of the swing was measured electronically. The density factor determined by the dynamic torsion-balance method was 0.8562±0.0035, whereas the same factor determined by direct calculation from the densities was 0.8542±0.0003. Thus, with the relative error of 0.4%, the validity of Horák's gravitational law was proved.     

Derivation ofv μ/v μ and the spectra of neutrinos from pions and kaons produced by primary cosmic rays throughp-nucleus collisions

The muon neutrino-antineutrino flux ratios, viz.,v /v generated from the decays of charged pions and kaons in atmosphere have been derived from the latest primary spectrum and the CERN ISRpp-collision data modified forp-nucleus interactions. The dynamical method of Allkoferet al. (1978) has been used in the present investigation. The estimated result forv /v yields 1.39 and 1.70 asE0 and , respectively. The neutrino fluxes from pion- and kaon-decay spectra have been calculated. Attention has been paid on prompt neutrino spectrum calculation from the decays ofD mesons. A rough estimate on the prompt muon spectrum has been given. The calculated results have been compared with the previous available results.     

Possible mass limits for quantum double galaxies

When cosmic quantum mechanics is applied to a double galaxy, the result is mass limits in order for the two galaxies to form a quantum binary system. For a non-relativistic theory (based on the Schrödinger wave equation), the mass limits are: (m _g)_max 10¹² M and (m _g)_min 10¹⁰ M . One possible consequence appears to be a Newtonian gravitational constant that varies with cosmic time, with its value larger in the cosmic past.     

Resistive ballooning modes in line-tied coronal fields

The resistive stability of coronal loops to perturbations with short wavelength across the magnetic field is analysed, taking full account of the line tying effect due to the presence of the photosphere. The results presented are similar to those previously obtained for arcades: configurations with a pressure profile decreasing with distance from the loop axis at some point are found to be always unstable, the growth rate increasing monotonically with the wavenumber (n) and scaling approximately as (n ² D _r)^1/3 in the limit of large n.     

The effect of chemical abundance oscillations on the pulsational properties of A 5M ⊙ hydrogen-helium star

A model of a first generation intermediate star of 5M , with Z=0 has been considered. The model is at an advanced stage of its evolution and has a double shell burning. It burns helium in the inner shell, and hydrogen, via CNO cycle, in the outer shell. =(log/log) _T and _T =(log/logT) were computed allowing for the oscillations of the relative mass abundance of the reagents in nuclear reactions. Including =(log/log) _T and =(log/logT) of mean molecular weight and the effect of the oscillations of abundances due to nuclear reactions, stability was studied. Contrary to the results of the static calculations, we found that instability due to the excitation mechanism provided by the high temperature sensitivity of energy generation rate propagates up to the surface. Thus the model in question was found to be unstable against radial adiabatic pulsations, in its fundamental mode.     

On the excitation of lower levels of singlet helium in quiescent prominences

The paper deals with the excitation of the helium singlet level 2¹ P in the homogeneous and filamentary models of quiescent prominences with following parameters: the optical thickness at the limit of helium Lyman continuum _1c ^M = 0.1–100, T _e = 7000 K, n _e = 5 × 10¹⁰ cm^–3. Assuming a model He atom with seven discrete levels (1¹ S, 2³ S, 2¹ S, 2³ P, 2¹ P, 3³ D, 3¹ D) and the continuum the steady state equations for the levels 2³ S, 2¹ P and the continuum have been solved together with the radiative transfer equations for the line 584 Å and the continuum 504 Å. The variations with depth of the functions n ₂ ³ _S /n ₁ ¹ _S (₁ c), n ₂ ¹ _P /n ₁ ¹ _S (_1c ), and n ⁺ _He n _e /n ₁ ¹ S(_1c ) as well as the intensities of the triplet (D₃, 10830 Å) and singlet (16678, 20581 Å) lines have been calculated. Comparison with observations leads to the following conclusions: (1) The line intensities calculated for filamentary models of prominences agree better with observations than those for homogeneous ones. (2) The helium level 2¹ P is excited by diffuse field 584 Å being formed by recombinations and spontaneous transitions 2¹ P – 1¹ S and escaping from the prominence into the space between the filaments and to the surface. (3) Underpopulation of the singlet level 2¹ P may be explained by combination of weak excitation mechanism (recombinations and formation of the diffuse field 584 Å) and strong deexcitation mechanism (spontaneous transitions into the level 1¹ S).