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1.
While solutions for bounded orbits about oblate spheroidal planets have been presented before, similar solutions for unbounded motion are scarce. This paper develops solutions for unbounded motion in the equatorial plane of an oblate spheroidal planet, while taking into account only the J 2 harmonic in the gravitational potential. Two cases are distinguished: A pseudo-parabolic motion, obtained for zero total specific energy, and a pseudo-hyperbolic motion, characterized by positive total specific energy. The solutions to the equations of motion are expressed using elliptic integrals. The pseudo-parabolic motion unveils a new orbit, termed herein the fish orbit, which has not been observed thus far in the perturbed two-body problem. The pseudo-hyperbolic solutions show that significant differences exist between the Keplerian flyby and the flyby performed under the the J 2 zonal harmonic. Numerical simulations are used to quantify these differences.  相似文献   

2.
The three-dimensional periodic solutions originating at the equilibrium points of Hill's limiting case of the Restricted Three Body Problem, are studied. Fourth-order parametric expansions by the Lindstedt-Poincaré method are constructed for them. The two equilibrium points of the problem give rise to two exactly symmetrical families of three-dimensional periodic solutions. The familyHL 2v e originating at L2 is continued numerically and is found to extend to infinity. The family originating at L1 behaves in exactly the same way and is not presented. All orbits of the two families are unstable.  相似文献   

3.
A.T. Young 《Icarus》1973,18(4):564-582
Water solutions of sulfuric acid, containing about 75% H2SO4 by weight, have a refractive index within 0.01 of the values deduced from polarimetric observations of the Venus clouds. These solutions remain liquid at the cloud temperature, thus explaining the spherical shape of the cloud particles (droplets). The equilibrium vapor pressure of water above such solutions is 0.01 that of liquid water or ice, which accounts for the observed dryness of the cloud region. Furthermore, H2SO4 solutions of such concentration have spectra very similar to Venus in the 8–13 μm region; in particular, they explain the 11.2 μm band. Cold sulfuric acid solutions also seem consistent with Venus spectra in the 3–4 μm region. The amount of acid required to make the visible clouds is quite small, and is consistent with both the cosmic abundance of sulfur and the degree of out-gassing of the planet indicated by known atmospheric constituents. Sulfuric acid occurs naturally in volcanic gases, along with known constituents of the Venus atmosphere such as CO2, HCl, and HF ; it is produced at high temperature by reactions between these gases and common sulfate rocks. The great stability and low vapor pressure of H2SO4 and its water solutions explain the lack of other sulfur compounds in the atmosphere of Venus—a lack that is otherwise puzzling.Sulfuric acid precipitation may explain some peculiarities in Venera and Mariner data. Because sulfuric acid solutions are in good agreement with the Venus data, and because no other material that has been proposed is even consistent with the polarimetric and spectroscopic data, H2SO4 must be considered the most probable constituent of the Venus clouds.  相似文献   

4.
The paper presents a variety of classes of interior solutions of Einstein–Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid with well behaved nature. These classes of solutions describe perfect fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the center. The outmarch of pressure, density, pressure–density ratio and the adiabatic speed of sound is monotonically decreasing for these solutions. Keeping in view of well behaved nature of these solutions, two new classes of solutions are being studied extensively. Moreover, these classes of solutions give us wide range of constant K for which the solutions are well behaved hence, suitable for modeling of super dense star. For solution (I1) the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ b =2×1014 g/cm3 corresponding to K=1.19 and X=0.20, the maximum mass of the star comes out to be 2.5M Θ with linear dimension 25.29 Km and central redshift 0.2802. It has been observed that with the increase of charge parameter K, the mass of the star also increases. For n=4,5,6,7, the charged solutions are well behaved with their neutral counterparts however, for n=1,2,3, the charged solution are well behaved but their neutral counterparts are not well behaved.  相似文献   

5.
In a binary system with both bodies being luminous, the inner collinear equilibrium pointL 1 becomes stable for values of the mass ratio and radiation pressure parameters in a certain region. The kind of periodic motions aroundL 1 is examined in this case. Second-order parametric expansions are given and the families of periodic orbits generated fromL 1 are numerically determined for several sets of values of the parameters. Short- and long-period solutions are identified showing a similarity in the character of periodicity with that aroundL 4. It is also found that the finite periodic solutions in the vicinity ofL 1 are stable.  相似文献   

6.
It is shown that the recently presented Brans-Dicke-Bianchi type-VII h perfect fluid solutions by Guzmán (1989) are nothing but the solutions given already by us in our previous paper (Lorenz-Petzold, 1984).  相似文献   

7.
We present a consistent method to construct some new Bianchi type-VI0 and type-VIh perfect fluid solutions from known solutions. The corresponding seed solutions are due to Collins (1971).  相似文献   

8.
New solutions of the equations of the bimetric scalar-tensor theory of gravitation for neutron stars are found. In these solutions the scalar field is constant, φ = φφ, while the metric space-time tensor is determined by the equations of the general theory of relativity. The problem was to find a background metric corresponding to φφ. Solutions with a variable φ were studied earlier [M. R. Avakian, L. Sh. Grigorian, and A. A. Saharian, Astrofizika, 35, 121 (1991)] and are determined by the dimensionless parameter ζ of the theory. Differences between solutions with constant and variable ? are considerable for ¦ζ¦ ≤ 1.  相似文献   

9.
We derive some new exact 7-dimensional cosmological solutions |R⊗ I ⊗N, whereN = I, II, VI0, VII0, VIII and IX are the various 3-dimensional Bianchi models. The solutions given are higher-dimensional generalizations of the mixmaster cosmologies. There is a strong influence of the extra spacesN, which results in a fundamental change of the 3-dimensional cosmology.  相似文献   

10.
Special analytical solutions are determined for restricted, coplanar, four-body equal mass problems, including the Caledonian problem, where the masses Mi = M for i = 1,2,3,4. Most of these solutions are shown to reduce to the Lagrange solutions of the Copenhagen problem of three bodies by reducing two of the masses (mi = m for i = 1,2) in the four-body equal mass problem to zero while maintaining their equality of mass. In so doing, families of special solutions to the four-body problem are shown to exist for any value of the mass ratio μ = m/M.  相似文献   

11.
In this problem, one of the primaries of mass \(m^{*}_{1}\) is a rigid spherical shell filled with a homogeneous incompressible fluid of density ρ 1. The smaller primary of mass m 2 is an oblate body outside the shell. The third and the fourth bodies (of mass m 3 and m 4 respectively) are small solid spheres of density ρ 3 and ρ 4 respectively inside the shell, with the assumption that the mass and the radius of the third and the fourth body are infinitesimal. We assume that m 2 is describing a circle around \(m^{*}_{1}\) . The masses m 3 and m 4 mutually attract each other, do not influence the motions of \(m^{*}_{1}\) and m 2 but are influenced by them. We also assume that masses m 3 and m 4 are moving in the plane of motion of mass m 2. In the paper, equilibrium solutions of m 3 and m 4 and their linear stability are analyzed. There are two collinear equilibrium solutions for the system. The non collinear equilibrium solutions exist only when ρ 3=ρ 4. There exist an infinite number of non collinear equilibrium solutions of the system, provided they lie inside the spherical shell. In a system where the primaries are considered as earth-moon and m 3,m 4 as submarines, the collinear equilibrium solutions thus obtained are unstable for the mass parameters μ,μ 3,μ 4 and oblateness factor A. In this particular case there are no non-collinear equilibrium solutions of the system.  相似文献   

12.
The return-flux sunspot model is generalized by including azimuthal magnetic field B Φ . The basic equation is obtained and numerical solutions are compared with the analogous solutions for the Schlüter-Temesvary sunspot theory for two cases: B Φ ～ B r and B Φ ～ rB r . The solutions demonstrate that the twisting of the sunspot magnetic field decreases with height. Our models confirm Yun's early statement: the azimuthal field only slightly influences sunspot structure.  相似文献   

13.
We discuss the Brans-Dicke-Bianchi type-VIIh field equations. Exact solutions are given for the vacuum case as well as for the stiff matter case. The derived solutions are the generalizations of the GRT-solutions first given by Doroshkevichet al. (1973) and Lukash (1974a). In addition we present a new BDT-stiff matter solution which has no analogy in the GRT.  相似文献   

14.
The Stokes components of He i D3 emission in two quiescent prominences, using full spectral profile measurements, are analyzed to derive vector magnetic fields. Two independently developed schemes, based on the Hanle effect, are used for interpretation. They involve solutions of the statistical equilibrium equations for the He i D3 multiplet, including the effect of coherency and full level crossing, which predict the magnetic field dependence of the observed polarization. Derived magnetic field vector solutions for each pair of linear polarization Stokes profiles corresponding to an observational point in the prominence are, intrinsically, not uniquely determined, and a set of possible solutions is usually obtained. However, mutual consistency of these solutions with those independently predicted by the form of the circular polarized component, allow, in almost all cases, rejection of all solutions of a set except one symmetrical pair. Of such a pair, a unique solution can be determined with a high confidence level by reference to independent potential field information. Field vectors are found usually to be close to horizontal and normal to the prominence surface, but extreme exceptions are found. Field values range from 6 G to 60 G. The derived vectorfield configurations and their magnitudes are briefly discussed relative to these prominences and to different quiescent prominence models.The National Center for Atmospheric Research is sponsored by the National Science Foundation.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.  相似文献   

15.
Special solutions of the planar rectilinear elliptic restricted 3-body problem are investigated for the limiting case e=1. Numerical integration is performed for primaries of equal masses. Starting values which define circular orbit solutions lead to bounded solutions if the initial radius a0 is larger than 3.74 in units of the primaries' semimajor axis a. A comparison with the Eulerian two-fixedcentre problem is presented in order to understand qualitatively the characteristic features of bounded orbits and the transition to escape orbits.  相似文献   

16.
Exact Bianchi type-VI0 cosmological solutions to Einstein's equations are presented in vacuum and for stiff-matter in the normal gauge for Lyra's geometry and in scalar-tensor theories developed by Saez and Ballester (1985) and Lau and Prokhovnik (1986). Also cosmological solutions are obtained for pure massive strings (p-strings) and for pure geometric strings. The dynamical behaviour of the models have been discussed.  相似文献   

17.
We present three new categories of exact and spherically symmetric Solutions with finite central parameters of the general relativistic field equations. Two well behaved solutions in curvature coordinates first category are being studied extensively. These solutions describe perfect fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing for these solutions. Keeping in view of well behaved nature of these solutions, one of the solution (I1) is studied extensively. The solution (I1) gives us wide range of Schwarzschild parameter u (0.138≤u≤0.263), for which the solution is well behaved hence, suitable for modeling of Neutron star. For this solution the mass of Neutron star is maximized with all degree of suitability and by assuming the surface density ρ b =2×1014 g/cm3. Corresponding to u=0.263, the maximum mass of Neutron star comes out to be 3.369 M Θ with linear dimension 37.77 km and central and surface redshifts are 4.858 and 0.4524 respectively. We also study some well known regular solutions (T-4, D-1, D-2, H, A, P) of Einstein’s field equations in curvature coordinates with the feature of constant adiabatic sound speed. We have chosen those values of Schwarzschild parameter u for which, these solutions describe perfect fluid balls realistic equations of state. However, except (P) solution, all these solutions have monotonically non-decreasing feature of adiabatic sound speed. Hence (P) solution is having a well behaved model for uniform radial motion of sound. Keeping in view of well behaved nature of the solution for this feature and assuming the surface density; ρ b =2×1014 g/cm3, the maximum mass of Neutron star comes out to be 1.34 M Θ with linear dimension 28.74 km. Corresponding central and surface redshifts are 1.002 and 0.1752 respectively.  相似文献   

18.
Two new classes of solutions with constant observed proper and rest mass densities are described. Unlike the well-known solution of constant coordinate mass density, these solutions pertain to realistic physical situations. For these solutions, the various relevant parameters, viz. the redshifts (dP/d)0 and binding coefficients have been calculated.  相似文献   

19.
Asymptotic motion near the collinear equilibrium points of the photogravitational restricted three-body problem is considered. In particular, non-symmetric homoclinic solutions are numerically explored. These orbits are connected with periodic ones. We have computed numerically the families containing these orbits and have found that they terminate at both ends by asymptotically approaching simple periodic solutions belonging to the Lyapunov family emanating from L3.  相似文献   

20.
The secular variations of the orbital elements of principal planets are calculated by means of classical Lagrange's method. The terms of the second order with respect to mass, introduced by Hill (1897) and Brouwer and van Woerkom (1950), have been taken into account as well. The best contemporary values of planetary masses and mean elements (Bretagnon, 1982) served as the starting data set for this calculation. Considerable differences with respect to previous solutions of the same type (Brouwer and van Woerkom, 1950: Sharaf and Boudnikova, 1967) were found in the coefficientsA 55,A 56, andA 66 of the system of equations of variation of elements and in the roots (frequencies)r 5 andr 6. Results are compared with some higher order/higher degree solutions and their accuracy discussed. It is confirmed that the solutions like that of Brouwer and van Woerkom, although not being completely inferior to all higher order/higher degree ones, can be considered as the first approximation only. Hence, they should be replaced by more accurate ones (Duriez, 1979: Bretagnon, 1984: Laskar, 1984) in the future applications.  相似文献   

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