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1.
The equations for the variation of the osculating elements of a satellite moving in an axi-symmetric gravitational field are integrated to yield the complete first-order perturbations for the elements of the orbit. The expressions obtained include the effects produced by the second to eighth spherical harmonics. The orbital elements are presented in the most general form of summations by means of Hansen coefficients. Due to their general forms it is a simple matter to estimate the perturbations of any higher harmonic by simply increasing the index of summation. Finally, this paper gives the respective general expressions for the secular perturbations of the orbital elements. The formulae presented should be useful for the reductions of Earth-satellite observations and geopotential studies based on them.List of Symbols semi-major axis - C jk n (, ) cosine functions of and - e eccentricity of the orbit - f acceleration vector of perturbing force - f sin2t - i inclination of the orbit - J n coefficients in the potential expansion - M mean anomaly - n mean motion - p semi-latus rectum of the orbit - R, S, andW components of the perturbing acceleration - r radius-vector of satellite - r magnitude ofr - S jk n (, ) sine functions of and - T time of perigee passage - u argument of latitude - U gravitational potential - true anomaly - V perturbing potential - G(M++m) (gravitational constant times the sum of the masses of Earth and satellite) - n,k coefficients ofR component of disturbing acceleration (funtions off) - n,k coefficients ofS andW components of disturbing acceleration (functions off) - mean anomaly at timet=0 - X 0 n,m zero-order Hansen coefficients - argument of perigee - right ascension of the ascending node  相似文献   

2.
Using the see-saw mechanism and estimation of the hypothetical mass of the electron neutrinom e we find the hypothetical mass of muon neutrinom µ and hypothetical mass of the tau neutrinom .  相似文献   

3.
Durney  Bernard R. 《Solar physics》2001,202(2):201-228
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4.
We present here a very simple model that could explain the relatively high eccentricities and inclinations observed in the minor planet belt. This model is based upon the sweeping of the secular resonances 6 and 16 through the belt due to the gravitational effect of the dissipation of a primitive solar nebula. The sweeping of the 16 secular resonance (responsible for the high inclinations) is very sensitive to the density profile of the nebula. For the model to work we need a density profile proportional to –k with between 1.0 and 1.5.  相似文献   

5.
Einstein's equations of general relativity are solved in terms of gravitational potential derivatives, withT equal to mass and/or field energy such thatT 0 outside a body. The line element equation then describes the variance of test particle internal geometrical structure and time-rate due to work done in a field, not the space-time curvature. Specific properties of gravitational fields and bodies come from this new solution: (a) The gravitational field consists of electromagnetic spin 2 gravitons which produce the gravitational force through the magnetic vector. (b) The gravitational mass is the Newtonian mass, not the relativistic mass, of a moving body. (c) An action principle exists in gravitation theory. (d) Attractive gravity exists between matter and antimatter. (e) Unification with quantum physics appears possible.  相似文献   

6.
We review theoretical and numerical results obtained for secular resonant motion in the asteroidal belt. William's theory (1969) yields the locations of the principal secular resonances 5, 6, and 16 in the asteroidal belt. Theories by Nakai and Kinoshita (1985) and by Yoshikawa (1987) allow us to model the basic features of orbital evolution at the secular resonances 16 and 6, respectively. No theory is available for the secular resonance v5. Numerical experiments by Froeschlé and Scholl yield quantitative and new qualitative results for orbital evolutions at the three principal secular resonances 5, 6, and 16. These experiments indicate possible chaotic motion due to overlapping resonances. A secular resonance may overlap with another secular resonance or with a mean motion resonance. The role of the secular resonances as possible sources of meteorites is discussed.  相似文献   

7.
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   

8.
We consider the system of neutrino-antineutrino – plasma taking into account theirweak Fermi interaction, when the density of neutrinos andthe plasma particles are rather high and their collective interactionplays a vital role. New fluid instabilities driven by strong neutrino flux in aplasma are observed. It is shown that a bunch of neutrinos, drifting witha constant velocity across a homogeneous plasma, can also induce emission oflower energy neutrinos due to scattering, i.e. the decay of a heavy neutrinoH into a heavy and a light neutrino L(HHL) in a plasma. Furthermore we find thatthe neutrino production in stars does not lead in general to energy lossesfrom the neutron stars.  相似文献   

9.
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   

10.
The accuracy of the approximate replacement of the frequency meanj() of the total intensityJ () byJ c+a{J 0()–J c} by Geovenelli, whereJ c is the total intensity at the continuum,J 0() is that at the line center anda is independent of depth, is studied. Numerical calculations for strong solar lines show very high values of the residual intensities. A slight change in the approximation is then suggested to get a result quite consistent with observational and existing calculated data.  相似文献   

11.
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   

12.
Absolute wavelengths for Fraunhofer lines are compared with laboratory measurements for several atomic and molecular spectra. The wavelength differences are shown to be consistent with the proposal that the deeper layers of the photosphere are in convective motion: e -3 km/sec for log 0> -1.0. Convective motions in the outer layers (log0< - 1.0) are shown to be very small. Wavelength shifts of Fraunhofer lines formed in these outer layers are in good quantitative agreement with the predictions of the General Theory of Relativity.  相似文献   

13.
Cold plus hot (neutrino) dark matter models are studied and compared with the tilted cold dark matter models (which have a non-Zel'dovich initial density perturbation spectrum). For the hybrid dark matter models, a simpler treatment for the relativistic neutrinos is presented. The numerical results of this treatment are shown to be in good agreement with those given by other authors. Comparing the theoretical and the observational results of the quadrupole fluctuations of the cosmic background radiation and the large-scale velocity field of galaxies, the hybrid dark matter models require a fraction of neutrino density 0.3, a fraction of cold dark matter c 0.7 and a number of massive neutrino speciesN = 1 for the case of Hubble's constantH 0 = 50 km s–1 Mpc–1. The distribution of comoving number density of quasars at high redshifts is studied using the Press-Schechter theory. The calculations show that the hybrid dark matter model ( c 0.7, 0.3) and the tilted CDM model withn = 0.7 0.8 both account for the observed quasar abundance at high redshift.  相似文献   

14.
Free convection effects on MHD flow past a semi infinite porous flat plate is studied when the time dependent suction velocity changes in step function form. The solution of the problem is obtained in closed form for the fluid with unit Prandtl number. It is observed that for both cooling and heating of the plate the suction velocity enhances the velocity field. The heat transfer is higher with increase in suction velocity.Notations B intensity of magnetic field - G Grashof number - H magnetic field parameter,H=(M+1/4) 1/2–1/2 - M magnetic field parameter - N u Nusselt number - P Prandtl number of the fluid - r suction parameter - T temperature of the fluid - T w temperature of the plate - T temperature of the fluid at infinity - t time - t non-dimensional time - u velocity of the fluid parallel to the plate - u non-dimensional velocity - U velocity of the free stream - suction velocity - 1 suction velocity att0 - 2 suction velocity att>0 - x,y coordinate axes parallel and normal to the plate, respectively - y non-dimensional distance normal to the plate - coefficient of volume expansion - thermal diffusivity - kinematic viscosity - electric conductivity of the fluid - density of the fluid - non-dimensional temperature of the fluid - shear stress at the plate - non dimensional shear stress - erf error function - erfc complementary error function  相似文献   

15.
On the basis of the solutions obtained in the previous paper, the changes in the scenario of the standard model of the Big Bang are found. The chaos degree (constrainst on fluctuation spectra) is obtained, which could be still preserved by the initially completely chaotic Universe at the time of light elements nucleosynthesist es. The time boundaries of hadron and lepton eras and the time the electron neutrinos and neutrons become frozen in reactions of weak interaction may be shifted up to 1.4 times. The corresponding temperatures may shift off from the standard ones 0.88 times if the mean-square level of fluctuations is close to unity. If the density of the energy of fluctuations concentrated in the short-wave region of the spectrum is less than 1.5 – , the nucleosynthesis leads to a helium abundance coinciding with the observe one. If at the timet es the maximum of the spectral density of the energy is in the long-wave region, that is max ct es the level of the chaos during the period of nucleosynthesis is restricted to 1.76 (where |C K |2 d3 K,C K is Fourier component of the amplitude of metric fluctuations). In particular, the protogalactic vortical disturbances with a wide spectrum 4 × 103 -1( = K/K, = /crit) are compatible with the observed helium abundance.  相似文献   

16.
We develop simple accurate methods of calculating ideal MHD instability eigenvalues for infinitely-long cylindrical tubes, with twist functionT(r)=B /rB z . A complete theoretical treatment is presented for force-free magnetic equilibria with arbitraryT(r), and detailed semi-analytic results for the kink instability are given for the particular case of a power-law twistT(r)=r , where the index is non-negative. Our results show that the most rapidly growing and energetic instabilities occur in the Gold-Hoyle =0 field, with the instability progressively weakening with increasing . However, the maximum force eigenvalue is always small, so that even in the Gold-Hoyle case (where =O(10–2) in dimensionless units) only a small proportion of the available magnetic energy can be released in the linear phase. Our results also confirm that the linear pinch (=) is remarkably weak (=O(10–3)) yet relatively resistant to line-tying! It is shown that the weakness of the force eigenvalue implies that the influence of uniform gas pressure on stability is negligible. Implications for the energy-release mechanism in solar flares are discussed.  相似文献   

17.
The estimates of the population of excited vibrational states of the CO2 molecule and of the rate of radiative cooling of the atmosphere in the 15-m CO2 band are given for the nighttime mesosphere and thermosphere of Mars. For the first time, these estimates are made (1) with allowance for the overlap of lines in the 15-m band; (2) for a wide set of vibrational states of seven isotopes of the CO2 molecule, which was used earlier in the solution of a similar terrestrial problem; and (3) using the rate constant for quenching of the CO2(0110) state in collisions with oxygen atoms, which has been recently measured for low temperatures by Khvorostovskaya et al. (2002). The main results are as follows. 1. The approximation of isolated lines provides a satisfactory accuracy of determining the radiative cooling rate and overestimates vibrational temperatures of the states of the 2 mode by no more than 3 K for the 12C16O2 molecule and by no more than 2 K for low-abundant isotopes of the CO2 molecule. 2. A reasonably high accuracy of estimating the cooling rate can be achieved by taking into account only fundamental vibrational transitions in 12C16O2, 13C16O2, 16O12C18O, and 16O12C17O molecules and the hot transitions 22 2 and 32 22 in the 12C16O2 molecule. 3. The vertical profile of the total rate of radiative cooling displays two peaks. The maximum near a height of 130 km is very sensitive to temperature and to the ratio of the mixture for oxygen in the atmosphere.  相似文献   

18.
We show that the overall densityg() of asymptotic acoustic frequencies of a star obeys a Weyl lawg() D–1, whereD is the dimensionality of the oscillating stellar configuration. For realistic stars with a finite non-zero surface sound speed,D is equal to the actual dimensionality of the star,D=3. For formal models with a vanishing sound velocity at the surface, heuristic arguments lead to a dimensionality parameterD=4.5. The empirical frequencies of Eddington's standard model are found to be consistent with the latter distribution, with reasonable agreement already occurring in the low-frequency range > i 2× fundamental radial mode. We argue that real stars obey this 3.5-power law in some finite frequency interval i << f , f being a very high frequency critically depending on the surface sound velocity, while the full asymptotic law, withD=3, holds for > f .  相似文献   

19.
An exact analysis of the effects of mass transfer on the flow of a viscous incompressible fluid past an uniformly accelerated vertical porous and non-porous plate has been presented on taking into account the free convection currents. The results are discussed with the effects of the Grashof number Gr, the modified Grashof number Sc, the Schmidt number Sc, and the suction parametera for Pr (the Prandtl number)=0.71 representating air at 20°C.Nomenclature a suction parameter - C species concentration - C species concentration at the free stream - g acceleration due gravity - Gc modified Grashof number (vg*(C –C )/U 0 3 ) - Pr Prandtl number (C p/K) - T temperature of the fluid near the plate - T dimensionless temperature near the plate ((T-T )/(T -T )) - U(t) dimensionless velocity of the plate (U/U 0) - v normal velocity component - v 0 suction/injection velocity - x, y coordinate along and normal to the plate - v kinematic viscosity (/gr) - C p specific heat at constant pressure - C w species concentration at the plate - C non-dimensional species concentration ((C-C )/(C w -C )) - Gr Grashof number (g(T w -T )/U 0 3 ) - D chemical molecular diffusivity - K thermal conductivity - Sc Schmidt number (/D) - T w temperature of the plate - T free stream temperature - t time variable - t dimensionless time (tU 0 2 /) - U 0 reference velocity - u velocity of the fluid near the plate - u non-dimensional velocity (u/U 0) - v dimensionless velocity (v/U 0) - v 0 non-dimensionalv 0 (v 0 /U0)=–at–1/2 - y dimensionless ordinate (yU 0/) - density of the fluid - coefficient of viscosity  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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