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1.
The masses of the particles of the baryon octet have been calculated using the theory of the origin of mass described in a former paper (Hoyle, 1990, referred to here as Paper A). The results are:
Particle  相似文献   

2.
Semi-relativistic calculations are performed for the photoionization of Fe X (an important coronal ion) from its ground state 3s23p $^{5}(^{2}P^{0}_{3/2})$ and the first two excited states 3s23p $^{5}(^{2}P^{0}_{1/2})$ and 3s3p $^{6}(^{2}S_{1/2})$ using the Breit?CPauli R-matrix method. A lowest 41 state eigenfunction expansion for Fe XI is employed to ensure an extensive treatment of auto ionizing resonances that affect the effective cross-sections. In the present calculations, we have considered all the important physical effects like channel coupling, exchange and short range correlation. The present calculations using the lowest 41 target levels of Fe XI in the LSJ coupling scheme are reported and we expect that the present results should enable more accurate modelling of the emission spectrum of highly excited plasma from the optical to the far UV region.  相似文献   

3.
In a previous paper (Stellmacher, 1981, hereafter mentioned as Paper I), we have given an algorithm for the construction of periodic orbits in a rotating frame, for satellites around an oblate planet. In the present paper, we apply this theory to the Mimas-Tethys case; we obtain the following results:
  1. Without resonance, it is possible to find a rotating system in which the solution is a periodic one. The angular velocity of this rotating frame is calculated as function of the masses of the two satellites.
  2. Including the resonant terms and assuming an exact commensurability of the implied frequencies, we demonstrate that the condition for periodic solutions in the rotating system as defined in (a) is: the initial position of the satellites at conjunction lies on an axis defined by (Ω1+Ω2)/2 or (Ω1+Ω2)/2 + π/2;Ω1 and Ω2 are the longitudes of the ascending nodes of the satellite's orbits. The solution still is a periodic one, thus all the conjunction occur in either axis.
  3. In the Mimas Tethys case there is only approximately commensurability between these frequencies. The two satellites are considered as oscillators whose amplitudes and phases are functions of time. The equation of the libration can be established; we find the usual form, but for each satellite the generating solution is a periodic solution (as defined in Paper I), but not a Keplerian one. It follows a determination of the masses which slightly differs from that given by Kozai (1957), when the same values of the observed quantities are used for calculations.
  4. The equation of the libration is: $$\ddot z + n_1^2 h^2 \sin z + n_1 q\dot z\sin z = 0$$
  相似文献   

4.
In Paper I (Hu, 1982), we discussed the the influence of fluctuation fields on the force-free field for the case of conventional turbulence and demonstrated the general relationships. In the present paper, by using the approach of local expansion, the equation of average force-free field is obtained as (1+b)?×B 0=(α#x002B;a)B 0#x002B;a (1)×B 0#x002B;K. The average coefficientsa,a (1),b, andK show the influence of the fluctuation fields in small scale on the configurations of magnetic field in large scale. As the average magnetic field is no longer parallel to the average electric current, the average configurations of force-free fields are more general and complex than the usual ones. From the view point of physics, the energy and momentum of the turbulent structures should have influence on the equilibrium of the average fields. Several examples are discussed, and they show the basic features of the fluctuation fields and the influence of fluctuation fields on the average configurations of magnetic fields. The astrophysical environments are often in the turbulent state, the results of the present paper may be applied to the turbulent plasma where the magnetic field is strong.  相似文献   

5.
We continue the investigation of the dynamics of retrograde resonances initiated in Morais and Giuppone (Mon Notices R Astron Soc 424:52–64, doi:10.1111/j.1365-2966.2012.21151.x, 2012). After deriving a procedure to deduce the retrograde resonance terms from the standard expansion of the three-dimensional disturbing function, we concentrate on the planar problem and construct surfaces of section that explore phase-space in the vicinity of the main retrograde resonances (2/ $-$ 1, 1/ $-$ 1 and 1/ $-$ 2). In the case of the 1/ $-$ 1 resonance for which the standard expansion is not adequate to describe the dynamics, we develop a semi-analytic model based on numerical averaging of the unexpanded disturbing function, and show that the predicted libration modes are in agreement with the behavior seen in the surfaces of section.  相似文献   

6.
We have investigated how the gradients of temperature and expansion velocities will change the emergent profiles from an extended medium in spherical symmetry. Variation of the source function and expansion velocities are assumed. The following variations of temperature are employed:
  1. T(r) ; T0 (isothermal case)
  2. T(r) ; T0(r/r0)1/2
  3. T(r) ; T0(r/r0)-1
  4. T(r) ; T0(r/r0)-2
  5. T(r) ; T0(r/r0)-3
The profiles calculated present an interesting feature of broadening.  相似文献   

7.
The new analysis of radar observations of inner planets for the time span 1964–1989 is described. The residuals show that Mercury topography is an important source of systematic errors which have not been taken into account up to now. The longitudinal and latitudinal variations of heights of Mercury surface were found and an approximate map of equatorial zone |?|≤120° was constructed. Including three values characterizing global nonsphericity of Mercury surface into the set of parameters under determination allowed to improve essentially all estimates. In particular, the variability of the gravitational constantG was evaluated: $$\dot G/G = (0.47 \pm 0.47) \times 10^{ - 11} yr^{ - 1} $$ . The correction to Mercury perihelion motion: $$\Delta \dot \pi = - 0''.017 \pm 0''.052 cy^{ - 1} $$ and linear combination of the parameters of PPN formalism: $$\upsilon = (2 + 2\gamma - \beta )/3 = 0.9995 \pm 0.0013$$ were determined; they are in a good agreement with General Relativity predictions. The obtained values Δ.π and ν correspond to the negligible solar oblateness, the estimate of solar quadrupole moment being: $$J_2 = ( - 0.13 \pm 0.41) \times 10^{ - 6} $$ .  相似文献   

8.
It is now recognised that the traditional method of calculating the LSR fails. We find an improved estimate of the LSR by making use of the larger and more accurate database provided by XHIP and repeating our preferred analysis from Francis and Anderson (New Astron 14:615–629, 2009a). We confirm an unexpected high value of $U_0$ by calculating the mean for stars with orbits sufficiently inclined to the galactic plane that they do not participate in bulk streaming motions. Our best estimate of the solar motion with respect to the LSR $(U_0, V_0, W_0) = (14.1\, \pm \, 1.1, 14.6\, \pm \, 0.4, 6.9\, \pm \, 0.1)$ km s $^{-1}$ .  相似文献   

9.
The planar problem of three bodies is described by means of Murnaghan's symmetric variables (the sidesa j of the triangle and an ignorable angle), which directly allow for the elimination of the nodes. Then Lemaitre's regularized variables \(\alpha _j = \sqrt {(\alpha ^2 - \alpha _j )}\) , where \(\alpha ^2 = \tfrac{1}{2}(a_1 + a_2 + a_3 )\) , as well as their canonically conjugated momenta are introduced. By finally applying McGehee's scaling transformation \(\alpha _j = r^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \tilde \alpha _j\) , wherer 2 is the moment of inertia a system of 7 differential equations (with 2 first integrals) for the 5-dimensional triple collision manifold \(T\) is obtained. Moreover, the zero angular momentum solutions form a 4-dimensional invariant submanifold \(N \subset T\) represented by 6 differential equations with polynomial right-hand sides. The manifold \(N\) is of the topological typeS 2×S 2 with 12 points removed, and it contains all 5 restpoint (each one in 8 copies). The flow on \(T\) is gradient-like with a Lyapounov function stationary in the 40 restpoints. These variables are well suited for numerical studies of planar triple collision.  相似文献   

10.
We present our photometric observations of an early B supergiant with an infrared excess, the protoplanetary object LSIV-12°111, and the previously suspected variable star NSV 24971. We confirm its photometric variability. During two observing seasons (2000–2001), the star exhibited rapid irregular light variations with amplitudes $\Delta V \sim 0\mathop .\limits^m 3$ , $\Delta B \sim 0\mathop .\limits^m 3$ , and $\Delta U \sim 0\mathop .\limits^m 4$ and a time scale of ～1d. There is no correlation between the colors and magnitudes of the star. The variability patterns of LSIV-12°111 and two other hot post-AGB stars, V886 Her and V1853 Cyg, are shown to be similar.  相似文献   

11.
The Ideal Resonance Problem in its normal form is defined by the Hamiltonian (1) $$F = A (y) + 2B (y) sin^2 x$$ with (2) $$A = 0(1),B = 0(\varepsilon )$$ where ? is a small parameter, andx andy a pair of canonically conjugate variables. A solution to 0(?1/2) has been obtained by Garfinkel (1966) and Jupp (1969). An extension of the solution to 0(?) is now in progress in two papers ([Garfinkel and Williams] and [Hori and Garfinkel]), using the von Zeipel and the Hori-Lie perturbation methods, respectively. In the latter method, the unperturbed motion is that of a simple pendulum. The character of the motion depends on the value of theresonance parameter α, defined by (3) $$\alpha = - A\prime /|4A\prime \prime B\prime |^{1/2} $$ forx=0. We are concerned here withdeep resonance, (4) $$\alpha< \varepsilon ^{ - 1/4} ,$$ where the classical solution with a critical divisor is not admissible. The solution of the perturbed problem would provide a theoretical framework for an attack on a problem of resonance in celestial mechanics, if the latter is reducible to the Ideal form: The process of reduction involves the following steps: (1) the ration 1/n2 of the natural frequencies of the motion generates a sequence. (5) $$n_1 /n_2 \sim \left\{ {Pi/qi} \right\},i = 1, 2 ...$$ of theconvergents of the correspondingcontinued fraction, (2) for a giveni, the class ofresonant terms is defined, and all non-resonant periodic terms are eliminated from the Hamiltonian by a canonical transformation, (3) thedominant resonant term and itscritical argument are calculated, (4) the number of degrees of freedom is reduced by unity by means of a canonical transformation that converts the critical argument into an angular variable of the new Hamiltonian, (5) the resonance parameter α (i) corresponding to the dominant term is then calculated, (6) a search for deep resonant terms is carried out by testing the condition (4) for the function α(i), (7) if there is only one deep resonant term, and if it strongly dominates the remaining periodic terms of the Hamiltonian, the problem is reducible to the Ideal form.  相似文献   

12.
Photoelectric observations of the eclipsing variable β Per, were obtained inUBV standard system, and new elements for the primary minimum were determined as $$J.D. = 2445641.5135,O - C = 0_.^d 0.009.$$ The light curves of the system were analysed using Fourier techniques in the frequency-domain. The fractional radii of both components are $$r_1 = 0.217 \pm 0.002,r_2 = 0.233 \pm 0.002andi = 85.5 \pm 0.5.$$ Absolute elements were derived and the effective temperatures are $$T_1 = 11800K,T_2 = 5140K.$$   相似文献   

13.
We obtain an approximate solution $\tilde{E}=\tilde{E}(e,M)$ of Kepler’s equation $E-e\sin (E)=M$ for any $e\in [0,1)$ and $M\in [0,\pi ]$ . Our solution is guaranteed, via Smale’s $\alpha $ -theory, to converge to the actual solution $E$ through Newton’s method at quadratic speed, i.e. the $n$ -th iteration produces a value $E_n$ such that $|E_n-E|\le (\frac{1}{2})^{2^n-1}|\tilde{E}-E|$ . The formula provided for $\tilde{E}$ is a piecewise rational function with conditions defined by polynomial inequalities, except for a small region near $e=1$ and $M=0$ , where a single cubic root is used. We also show that the root operation is unavoidable, by proving that no approximate solution can be computed in the entire region $[0,1)\times [0,\pi ]$ if only rational functions are allowed in each branch.  相似文献   

14.
New theoretical electron-density-sensitive Fe xii emission line ratios $$R_1 = I(3s^2 3p^3 {}^4S_{3/2} - 3s3p^4 {}^4P_{5/2} )/I(3s^2 3p^3 {}^2P_{3/2} - 3s3p^4 D_{5/2} )$$ and $$R_2 = I(3s^2 3p^3 {}^2P_{3/2} - 3s3p^4 {}^2D_{5/2} )/I(3s^2 3p^3 {}^4S_{3/2} - 3s3p^2 P_{3/2} )$$ are derived using R-matrix electron impact excitation rate calculations. We have identified the Fexii \(3s^2 3p^3 {}^4S_{3/2} - 3s3p^4 {}^4P_{5/2} ,{\text{ }}3s^2 3p^3 {}^2P_{3/2} - 3s^3 3p^4 {}^2D_{5/2} ,{\text{ }}3s^2 3p^3 S_{3/2} - 3s^2 3p^3 P_{3/2} \) and \(3s^2 3p^3 {}^4S_{3/2} - 3s^2 3p^3 {}^2P_{1/2}\) transitions in an active region spectrum obtained with the Harvard S-055 spectrometer on board Skylab at wavelengths of 364.0, 382.8, 1241.7, and 1349.4 Å, respectively. Electron densities determined from the observed values of R 1 (log N e ? 11.0) and R 2(log N e ? 11.4) are significantly larger than the typical active region measurements, but are similar to those derived from some active region spectra observed with the Skylab 2082A instrument, which provides observational support for the atomic data adopted in the line ratio calculations, and also for the identification of the Fe xii transitions in the S-055 spectrum. However the observed value of R 3 = I(1349.4 Å)/I(1241.7 Å) is approximately a factor of two larger than one would expect from theory which, considering that the 1349.4 Å line lies at the edge of the S-055 wavelength coverage, may reflect errors in the instrument efficiency curve. Another possibility is that the 1349.4 Å transition is blended, probably with Si ii 1350.1 Å.  相似文献   

15.
We investigate the ‘equilibrium’ and stability of spherically-symmetric self-similar isothermal blast waves with a continuous post-shock flow velocity expanding into medium whose density varies asr ?ω ahead of the blast wave, and which are powered by a central source (a pulsar) whose power output varies with time ast ω?3. We show that:
  1. for ω<0, no physically acceptable self-similar solution exists;
  2. for ω>3, no solution exists since the mass swept up by the blast wave is infinite;
  3. ? must exceed zero in order that the blast wave expand with time, but ?<2 in order that the central source injects a finite total energy into the blast wave;
  4. for 3>ωmin(?)>ω>ωmax(?)>0, where $$\begin{gathered} \omega _{\min } (\varphi ){\text{ }} = {\text{ }}2[5{\text{ }} - {\text{ }}\varphi {\text{ }} + {\text{ }}(10{\text{ }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 )^{1/2} ]^2 [2{\text{ }} + {\text{ (10 }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 {\text{)}}^{{\text{1/2}}} ]^{ - 2} , \hfill \\ \omega _{\max } (\varphi ){\text{ }} = {\text{ }}2[5{\text{ }} - {\text{ }}\varphi {\text{ }} - {\text{ }}(10{\text{ }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 )^{1/2} ]^2 [2{\text{ }} - {\text{ (10 }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 {\text{)}}^{{\text{1/2}}} ]^{ - 2} , \hfill \\ \end{gathered} $$ two critical points exist in the flow velocity versus position plane. The physically acceptable solution must pass through the origin with zero flow speed and through the blast wave. It must also pass throughboth critical points if \(\varphi > \tfrac{5}{3}\) , while if \(\varphi< \tfrac{5}{3}\) it must by-pass both critical points. It is shown that such a solution exists but a proper connection at the lower critical point (for ?>5/3) (through whichall solutions pass with thesame slope) has not been established;
  5. for 3>ω>ωmin(?) it is shown that the two critical points of (iv) disappear. However a new pair of critical points form. The physically acceptable solution passing with zero flow velocity through the origin and also passing through the blast wave mustby-pass both of the new critical points. It is shown that the solution does indeed do so;
  6. for 3>ωmin(?)>ωmax(?)>ω it is shown that the dependence of the self-similar solution on either ω or ? is non-analytic and therefore, inferences drawn from any solutions obtained in ω>ωmax(?) (where the dependence of the solutionis analytic on ω and ?) are not valid when carried over into the domain 3>ωmin(?)>ωmax(?)>ω;
  7. all of the physically acceptable self-similar solutions obtained in 3>ω>0 are unstable to short wavelength, small amplitude but nonself-similar radial velocity perturbations near the origin, with a growth which is a power law in time;
  8. the physical self-similar solutions are globally unstable in a fully nonlinear sense to radial time-dependent flow patterns. In the limit of long times, the nonlinear growth is a power law in time for 5<ω+2?, logarithmic in time for 5>ω+2?, and the square of the logarithm in time for 5=ω+2?.
The results of (vii) and (viii) imply that the memory of the system to initial and boundary values does not decay as time progresses and so the system does not tend to a self-similar form. These results strongly suggest that the evolution of supernova remnants is not according to the self-similar form.  相似文献   

16.
The fact that the energy density ρg of a static spherically symmetric gravitational field acts as a source of gravity, gives us a harmonic function \(f\left( \varphi \right) = e^{\varphi /c^2 } \) , which is determined by the nonlinear differential equation $$\nabla ^2 \varphi = 4\pi k\rho _g = - \frac{1}{{c^2 }}\left( {\nabla \varphi } \right)^2 $$ Furthermore, we formulate the infinitesimal time-interval between a couple of events measured by two different inertial observers, one in a position with potential φ-i.e., dt φ and the other in a position with potential φ=0-i.e., dt 0, as $${\text{d}}t_\varphi = f{\text{d}}t_0 .$$ When the principle of equivalence is satisfied, we obtain the well-known effect of time dilatation.  相似文献   

17.
Published photoelectric measurements over a wide wavelength range (0.36–18 µm) are used to study the continuum spectrum of the star Θ1 Ori C. The model that assumes the following three radiation sources is consistent with observations: (1) a zero-age main-sequence O7 star (object 1) of mass M 1=20M ⊙, radius R 1=7.4R ⊙, effective temperature T 2=37 000 K, and absolute bolometric magnitude $M\mathop {bol}\limits^1 = - 7\mathop .\limits^m 7$ ; (2) object 2 with M 2=15M ⊙, R 2=16.2R ⊙, T 2=4000 K, and $M\mathop {bol}\limits^2 = - 5\mathop .\limits^m 1$ ; and (3) object 3 with R 310 700 R ⊙, T 3=190 K, and $M\mathop {bol}\limits^3 = - 0\mathop .\limits^m 6$ . The visual absorption toward the system is $A_V = 0\mathop .\limits^m 95$ and obeys a normal law. The nature of objects 2 and 3 has not been elucidated. It can only be assumed that object 2 is a companion of the primary star, its spectral type is K7, and it is in the stage of gravitational contraction. Object 3 can be a cocoon star and a member of the system, but can also be a dust envelope surrounding the system as a whole.  相似文献   

18.
This short article supplements a recent paper by Dr R. Broucke on velocity-related series expansions in the two-body problem. The derivations of the Fourier and Legendre expansions of the functionsF(v), \(\sqrt {F(\upsilon )} \) and \(\sqrt {{1 \mathord{\left/ {\vphantom {1 {F(\upsilon )}}} \right. \kern-0em} {F(\upsilon )}}} \) are given, where $$F(\upsilon ) = (1 - e^2 )/(1 + 2e\cos \upsilon + e^2 ), e< 1$$ In the two-body problem,v is identified with the true anomaly,e the eccentricity andF(v) equals (an/V)2. Some interesting relations involving Legendre polynomials are also noted.  相似文献   

19.
In a previous paper, Hayliet al. (1983), two families of periodic orbits in the three-dimensional potential $$U = \frac{1}{2}(Ax^2 + By^2 + Cz^2 ) - \varepsilon xz^2 - nyz^2 $$ with \(\sqrt A :\sqrt B :\sqrt C = 6:4:3\) and ?=0.5 were described. It was found empirically that the characteristic curves of the two families intersect in the space (x0, y0, η) for |η|?0.2. This property is demonstrated in the present paper by writing explicitely the Poincaré mapping and by giving an approximation directly comparable with the numerical results obtained in Hayliet al. (1983). It is thus shown that one family bifurcates off the other.  相似文献   

20.
We constrain holographic dark energy (HDE) with time varying gravitational coupling constant in the framework of the modified Friedmann equations using cosmological data from type Ia supernovae, baryon acoustic oscillations, cosmic microwave background radiation and X-ray gas mass fraction. Applying a Markov Chain Monte Carlo (MCMC) simulation, we obtain the best fit values of the model and cosmological parameters within 1σ confidence level (CL) in a flat universe as: $\varOmega_{b}h^{2}=0.0222^{+0.0018}_{-0.0013}$ , $\varOmega_{c}h^{2}=0.1121^{+0.0110}_{-0.0079}$ , $\alpha_{G}\equiv \dot{G}/(HG) =0.1647^{+0.3547}_{-0.2971}$ and the HDE constant $c=0.9322^{+0.4569}_{-0.5447}$ . Using the best fit values, the equation of state of the dark component at the present time w d0 at 1σ CL can cross the phantom boundary w=?1.  相似文献   

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