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1.
In this paper, general model analysis of the form c i i () for the fractional loss of lightf() exhibited by a close binary system will be considered in the sense of the least-squares criterion. A general recursive method will be established for constructing the normal equations for the most useful functions i (), and an economical storage of the method on a digital computer, with its computational steps, will also be given. Moreover, a full recursive computational algorithm for the least-squares approximation will also be established. By means of this algorithm, all the solution vectors, the variance for different orders of fit and the corresponding variance-covariance matrix could be computed once and for all and, moreover, recursively. The economical storage of the algorithm and its computational steps will be given. Finally, some of the practical difficulties encountered in the application of the least-squares criterion will be analysed, and some techniques for detecting and controlling these difficulties are also given. Numerical examples on the Algol system using a Fourier cosine series of the form c i cos [(j - 1) /] will be given for illustration.  相似文献   

2.
It is shown that, to any change of variables:q i=qi(r, t) (i=1,..., n; =1,...,n+m; mn) increasing the number of variables, it is possible to associate a Mathieu's transformation and conversely. The results are applied to the theory of the osculating plane of motion.
Resumé On montre qu'à toute transformation:q i=qi(r, t)(i=1,..., n; =1,...,n+m; mn) augmentant le nombre de variables, on peut associer une transformation de Mathieu et réciproquement. Les résultats sont appliqués à la théorie du plan osculateur du mouvement.
  相似文献   

3.
Some weak unidentified solar photospheric lines in the wavelength range: (3400–3465) Å may be due to PH lines of the (0, 0) band of the PH(A 3 i - X 3 -)system. These faint PH molecular lines have resulted an excitation temperature of the order of 4500 K. Using experimental lifetime data for PH in the A 3 i state, an absorption oscillator strength f 00 = 0.0075 is derived for the 3410 Å band of the PH (A 3 i - X 3 -)system. Accurate line positions, oscillator strength and transition probability for the 4.4 fundamental rotation-vibration band of the PH molecule are obtained. A comparison of positions of some lines of the 4.4 band with those obtained on new tracings of high resolution solar spectra shows many coincidences with weak solar lines.  相似文献   

4.
Using the flux-transport equation in the absence of sources, we study the relation between a highly peaked polar magnetic field and the poleward meridional flow that concentrates it. If the maximum flow speed m greatly exceeds the effective diffusion speed /R, then the field has a quasi-equilibrium configuration in which the poleward convection of flux via meridional flow approximately balances the equatorward spreading via supergranular diffusion. In this case, the flow speed () and the magnetic field B() are related by the steady-state approximation () (/R)B()/B() over a wide range of colatitudes from the poles to midlatitudes. In particular, a general flow profile of the form sin p cos q which peaks near the equator (q p) will correspond to a cos n magnetic field at high latitudes only if p = 1 and m = n /R. Recent measurements of n 8 and 600 km2 s–1 would then give m 7 m s–1.  相似文献   

5.
The coefficients of correlation between spectroscopic data published by Yamashita (1967) and others for carbon stars and the statistical population indices calculated for these stars at the Toru Observatory are calculated (Table II). The intensity estimates of Cai 4227 Å, Nai D lines, the C13/C12 ratio, then=n(Li/Ca) index, as well as CN and probably C2 bands are higher in population I carbon stars. The CH(G) band and probably hydrogen (H, H, H) lines as well as Baii 4554 and 4934 Å lines are stronger in population II carbon stars. The photoelectric colour indices, corrected for interstellar reddening do not show significant population effects. They can be used as spectral type equivalents. For a population criterion the CH/CN intensity ratio is proposed.  相似文献   

6.
We prove existence and multiplicity of T-periodic solutions (for any given T) for the N-body problem in m (any m 2) where one of the bodies has mass equal to 1 and the others have masses 2,..., N , small. We find solutions such that the body of mass 1 moves close to x = 0 while the body of mass i moves close to one of the circular solutions of the two body problem of period T/k i, where ki is any odd number. No relation has to be satisfied by k 2,...,k N.  相似文献   

7.
The simplest, conventional, and original form of the circular restricted problem of three bodies is briefly described in sidereal and synodic systems using dimensional and non-dimensional variables. This dynamical system is generalized to n2 primary bodies (from n=2) with masses Mi, 1in, interacting with arbitrary force laws (instead of only gravitational forces). The number of bodies of small mass mMi not perturbing the primaries is increased from =1 to 1 where 1 and the minor bodies are allowed to interact with one another under arbitrary force laws. While the minor bodies (m) do not affect the motions of the primaries (Mi), the primaries influence the motions of the minor bodies with arbitrary force laws.For the case where n=2, 1, and only gravitational forces act on the system, an integral of the system is derived. It is shown that the energy integral of the general problem of N bodies and the Jacobian integral of the classical restricted problem of three bodies are limiting cases of this integral. The role of the integral in bounding the motion of the minor bodies is discussed. Several applications of this system are given.  相似文献   

8.
Some peculiarities in the behaviour of a model self-gravitating system described by hydrodynamical equations and isothermal equation of state connected with the presence of thermodynamical fluctuations in real systems were investigated in numerical experiment. The values of density and velocity , , respectively, were computed by numerical code perturbed on each time-step and in each computational cell by random values , for modeling such fluctuations. Perturbed values i = i + i ,v i = i + v i were used to initiate the next step of computations. This procedure is equivalent to an introduction into original hydrodynamical equations of Langevin sources which are random functions. It is shown that these small fluctuations (= v =0,2 =v 2 = 10–8) grow many times in marginally-stable state.  相似文献   

9.
The electrical conductivity of the lunar interior has been determined from magnetic field step transients measured on the lunar dark side. The simplest model which best fits the data is a spherically symmetric three layer model having a nonconducting outer crust of radial thickness 0.03R moon; an intermediate layer of thicknessR0.37R moon, with electrical conductivity 1 3.5 × 10–4 mhos/m; and an inner core of radiusR 2 0.6R m with conductivity 2 10–2 mhos/m. Temperatures calculated from these conductivities in the three regions for an example of an olivine Moon are as follows: crust, < 440 K; intermediate layer, 890 K; and core, 1240 K. The whole-moon relative permeability has been calculated from the measurements to be/ 0 = 1.03 ± 0.13. Remanent magnetic fields at the landing sites are 38 ± 3 at Apollo 12, 43 ± 6 and 103 ± 5 at two Apollo 14 sites separated by 1.1 km, and 6 ± 4 at the Apollo 15 site. Measurements show that the 38 remanent field at the Apollo 12 site is compressed to 54 by a solar wind pressure increase of 7 × 10–8 dynes/cm2.National Research Council Postdoctoral Associate.  相似文献   

10.
This work contains a transformation of Hill-Brown differential equations for the coordinates of the satellite to a type which can be integrated in a literal form using an analytical programming language. The differential equation for the parallax of the satellite is also established. Its use facilitates the computation of Hill's periodic intermediary orbit of the satellite and provides a good check for the expansion of the coordinates and frequencies. The knowledge of the expansion of the parallax facilitates the formation of differential equations for terms with a given characteristic. These differential equations are put into a form which favors the solution by means of iteration on the computer. As in the classical theory we obtain the expansions of the coordinates and of the parallax in the form of trigonometric series in four arguments and in powers of the constants of integration. We expand the differential operators into series in squares of the constants of integration. Only the terms of order zero in these expansions are employed in the integration of the differential equations. The remaining terms are responsible for producing the cross-effects between the perturbations of different order. By applying the averaging operator to the right sides of the differential equations we deduce the expansion of the frequencies in powers of squares of the constants of integration.Basic Notations f the gravitational constant - E the mass of the planet - M the mass of the satellite - t dynamical time - x, y, z planetocentric coordinates of the satellite - u x+y–1 - s x–y–1 - the planetocentric distance of the satellite - w 1/ - 0 the variational part of - w 0 the variational part ofw, - n the mean daily sidereal motion of the satellite - a the mean semi-major axis of the satellite defined by means of the Kepler relation:a 3 n 2=f(E+M) - a the mean semi-major axis defined as the constant factor attached to the variational solution - e the constant of the eccentricity of the satellite - the sine of one half the orbital inclination of the satellite relative to the orbit of the sun - c(n–n) the anomalistic frequency of the satellite - c 0 the part ofc independent frome,e, and - g(n–n) the draconitic frequency of the satellite, - g 0 the part ofg independent frome,e, and - exp (n–n)t–1 - D d/d - e the eccentricity of the solar planetocentric orbit - a the semi-major axis of the solar orbit - n the mean daily motion of the sun in its orbit around the planet - m n/(n–n) - a/a-the parallactic factor - the disturbing function  相似文献   

11.
Heinz Neckel 《Solar physics》1996,167(1-2):9-23
The limb-darkening data published by Neckel and Labs (1994) (5th-order polynomials P 5(), = cos ) are used to represent the limb darkening by the functions L n(), proposed first by Kourganoff (1949a). When plotted against wavelength, the coefficients of these functions show a rather low scatter and appear to be linear functions of either –1 or #x2212;5.  相似文献   

12.
General theory of electrical conductivity of a multicomponent mixture of degenerate fermions in a magnetic fieldB, developed in the preceding article (this volume), is applied to a matter in neutron star interiors at densities 0, where 0 = 2.8×1014 g cm–3 is the standard nuclear matter density. A model of free-particle mixture ofn, p, e is used, with account for appearance of –-hyperons at > c , where c 40. The electric resistivities along and acrossB, and , and the Hall resistivity H are calculated and fitted by simple analytical formulae at c and > c for the cases of normal or superfluid neutrons provided other particles are normal. Charge transport alongB is produced by electrons, due to their Coulombic collisions with other charged particles; is independent ofB and almost independent of the neutron superfluidity. Charge transport acrossB at largeB may be essentially determined by other charged particles. If c , one has = [1 + (B/B 0)2] for the normal neutrons, and for the superfluid neutrons, while H = B/B e for both cases. HereB e 109 T 8 2 G,B 01011 T 8 2 G, andT 8 is temperature in units of 108 K. Accordingly for the normal neutrons atBB 0, the transverse resistivity suffers an enhancement, 1/4 1. When 50 andB varies from 0 toBB p 1013 T 8 2 G, increases by a factor of about 103–104 and H changes sign. WhenBB p , remains constant for the superfluid neutrons, and H B 2 for the normal neutrons, while H B for any neutron state. Strong dependence of resistivity onB, T, and may affect evolution of magnetic fields in neutron star cores. In particular, the enhancement of at highB may noticeably speed up the Ohmic decay of those electric currents which are perpendicular toB.  相似文献   

13.
I give an interpretation of a result of Simpsonet al. (1988) on the variation with kinetic energyT i of the mean pathlengthX m (T i ) of the galactic cosmic rays (CGRs) in the range 0.1T i 10.0 GeV nucl–1. I argue that the data onX m (T i ) may be interpreted in terms of a model of GCR diffusion on the one-dimensional Alfvén-wave turbulence, having a cutoff in the spectrum at frequencies h , where h is the proton gyrofrequency. The cutoff results in changing of the character of variation of the GCR diffusion coefficientD(T i )T a in the rangeT i 1 GeV nucl–1 towards some more complicated variation at 0.1T i 1.0 GeV nucl–1 due to the peculiarities of the pitch-angle scattering at 900.  相似文献   

14.
Of the 7500 stars cited in the Catalog of starlight polarization, those which satisfy the condition P obs % and A V 0m.5 are selected. It is presumed that the selected stars (n=216) have circularly polarized light.  相似文献   

15.
, (DM) (RM). , DM RM N e = n e ds. M e = n e H cos ds ; . Lerche (1970a, b) , DM RM N e M e . .  相似文献   

16.
Zusammenfassung Es wird gezeigt, daß die unter der Einwirkung einer Momentenimpulsserie entstehende Bewegung eines rotierenden Flugkörpers mit Nutationsdämpfung sich vollständig einem regelmäßigen Polygon entnehmen läßt, das durch das Trägheitsmomentenverhältnis, den Integralwert eines Einzelimpulses, den Drall und eine die Dämpfung charakterisierende KonstanteK 0 bestimmt ist.Die Bewegung setzt sich aus logarithmischen Spiralen zusammen, derenn-ten Anfangsradius man erhält, indem man den Teilungspunkt des im VerhältnisK 0:1 geteilten (n–1)-ten Radius mit der (n+1)-ten Polygonecke verbindet.Es wird bewiesen, daß das Konstruktionsnetz zu einem im äußeren Polygon liegenden ähnlichen inneren Polygon konvergiert, das gegenüber ersterem gedreht ist.Einfache Beziehungen zur Bewegungsbestimmung mit dem Polygonschema werden für Pulsfrequenzen angegeben, die ganzzahlige Vielfache oder Bruchteile der Spinfrequenz sind.
It is shown that the motion of a spinning body with nutation damping due to a series of torque pulses can be completely derived from a regular polygon determined by the ratio of inertias, the integral of one pulse, the momentum and a constantK 0 characterizing damping.The motion is composed of spirals thenth initial radius of which is obtained by connecting the dividing point of the (n–1)th radius with the (n+1)th polygon corner. Each dividing point divides the respective radius in the ratioK 0:1. The net of construction lines converges into an inner polygon turned against the outer one and having the same shape.Simple rules are shown for the application of the scheme on pulse frequencies which are multiples or fractions of spin frequency.
Symbole 1-2-3 Achsen des flugkörperfesten Koordinatensystems - a,b,c Hilfsgrößen zur Bestimmung der Iterationsgrößen - E i i-te Polygonecke - H Drall des Flugkörpers - K i Verhältnis deri-ten Drehzeigerlängen zu Beginn und am Ende eines Impulses - M Iterationsmatrix - Integralwert des Momentenimpulses - P 0 Äußeres Polygon - P 1 Spitze des Drehzeigersr 00e - P Drehpunkt des Drehzeigersr 00 - P Konvergierendes Polygon - P i Teilungspunkt des [i–1]-ten Zeigers - r 0i Drehzeiger aufgrund desi-ten Impulses allein - r 0ia Zeigerr 0i in Anfangslage - r 0ie Zeigerr 0i in Endlage - r i i-ter Summenzeiger - r ia Zeigerr i in Anfangslage - r ie Zeigerr i in Endlage - T Dauer einer Flugkörperumdrehung - t,t, Zeitargumente - x-y-z Achsen eines raumfesten Koordinatensystems - x i ,y i Iterationskoordinaten - n Phase desn-ten Radius gegenüber der anliegenden Polygonseite - Drehung des inneren Polygons gegenüber dem äußeren - Abklingkonstante - Phasenänderung des Drehzeigers innerhalb einer Flugkörperumdrehung - 0 Anteil der über 2 hinausgehenden Phasenänderung des Drehzeigers - 3 Trägheitsmoment um die Spinachse - 12 Trägheitsmoment um die Querachsen - Zahl der Ecken des Konstruktionspolygons - 1,2 Eigenwerte der Iterationsmatrix - Zahl der vollen Umläufe des Konstruktionspolygons - Fortbewegungsachse des Drallvektors - 0 Ausgangsphasenwinkel - i Phasenlage desi-ten Summenzeigers - x, y Drehwinkel nach Einzelimpuls fürt - , Funktionen der Iterationsgrößen - , Drehwinkel umx-bzw.y-Achse - Drehgeschwindigkeit der Spinachse um den Drallvektor - Fiktive Größen bei Pulsfrequenzen kleiner als Spinfrequenz - Fiktive Größen bei Pulsfrequenzen größer als Spinfrequenz  相似文献   

17.
We analyze the hypothesis of quantization in bands for the angular momenta of binary systems and for the maount of actionA c in stable and pulsating stars. This parameter isA c=Mv eff R eff, where the effective velocity corresponds to the kinetic energy in the stellar interior and the effective radius corresponds to the potential energyGM 2/R eff. Analogous parameters can be defined for a pulsating star withm=M where is the rate of the massm participating in the oscillation to the total massM andv osc,R osc the effective velocity and oscillation radius.From an elementary dimensional analysis one has thetA c (energy x time) (period)1/3 independently ifA c corresponds to the angular momentum in a binary system, or to the oscillation in a pulsating star or the inner energy and its time-scaleP eff in a stable star.From evolving stellar models one has that P effP eff(solar)1.22 hr a near-invariant for the Main Sequence and for the range of masses 0.6M <M<1.6M .With this one can give scalesn k=kn 1 withk integers andn 1=(P/P 1)1/3 withP 1=P eff1.22 hr. In these scales proportional toA c, one sees that the periods in binary and pulsating stars are clustered in discrete unitsn 1,n 2,n 3, etc.This can be seen in pulsating Scuti, Cephei, RR Lyrae, W Virginis, Cephei, semi-regular variables, and Miras and in binary stars as cataclysmic binaries, W Ursa Majoris, Algols, and Lyrae with the corresponding subgroups in all these materials. Phase functions (n k) in RR Lyrae and Cephei are also associated with discrete levelsn k.the suggested scenario is that the potential energies and the amounts of actionE p(t), Ac(t) are indeed time-dependent, but the stars remain more time in determinated most proble states. The Main Sequence itself is an example of this. These most probable states in binary systems, or pulsating or stable stars, must be associated with velocities sub-multiplesc/ F , given by the velocity of light and the fine structure constant.Additional tests for such a hypothesis are suggested when the sufficient amount of observational data are available. They can made with oscillation velocities in pulsating stars and velocity differences of pairs of galaxies.  相似文献   

18.
In the last four years we have carried out a number of studies on the radiative and collisional processes in theA 2 i state of CN. Many of these of interest to those studying planetary atmospheres, comets and solar spectra are summarized in this paper. Data for CNA 2 i fluorescence lifetimes and quenching rates, and collisional energy transfer between CNA 2 i andX 2+ are reported. Detailed comparisons and a discussion of the results may be found in several already published papers.  相似文献   

19.
An approximate analytical method of solving the polytropic equilibrium equations, first developed by Seidov and Kuzakhmedov (1978), has been extended and generalized to equilibrium configurations of axisymmetric systems in rigid rotation, with polytropic index,n =n p + n , nearn p =0, 1, and 5. Though the details of the method depend on the value ofn p , acceptable results are obtained for | n | 0.5 to describe slowly rotating configurations in the range 0n1.5, 4.5n5. In the limit of rotational equilibrium configurations, when the distorsion may be large enough, a satisfactory approximation holds only in the range 0n, 1n1.5, 4.5n5.  相似文献   

20.
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.  相似文献   

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