Nonsingular charged analogues of Schwarzschild’s interior solution

The problem of finding nonsingular charged analogue of Schwarzschild’s interior solutions has been reduced to that of finding a monotonically decreasing function f. The models are discussed in generality by imposing reality condition on f. It is shown that the physical solutions are possible only for surface density to central density ratio greater than or equal to 2/3 i.e. $\frac{\rho_{a}}{\rho_{0}}\ge2/3$ . The unphysical nature of solutions with linear equation state has been proved. A generalization procedure has been utilized to generalize solutions by Guilfoyle (1999). Recently found solutions by Gupta and Kumar (2005a, 2005b, 2005c) are generalized by taking particular form of f and seen to have higher mass and more stable. The maximum mass is found to be 1.59482 M _Θ . The models have been found to be stable once the physical requirements are established due to mass to radius less than 4/9, total charge to total mass ratio less than 1 and redshift quite low.     

The effect of the Earth’s oblateness on the Moon’s physical libration in latitude

The Moon’s physical libration in latitude generated by gravitational forces caused by the Earth’s oblateness has been examined by a vector analytical method. Libration oscillations are described by a close set of five linear inhomogeneous differential equations, the dispersion equation has five roots, one of which is zero. A complete solution is obtained. It is revealed that the Earth’s oblateness: a) has little effect on the instantaneous axis of Moon’s rotation, but causes an oscillatory rotation of the body of the Moon with an amplitude of 0.072″ and pulsation period of 16.88 Julian years; b) causes small nutations of poles of the orbit and of the ecliptic along tight spirals, which occupy a disk with a cut in a center and with radius of 0.072″. Perturbations caused by the spherical Earth generate: a) physical librations in latitude with an amplitude of 34.275″; b) nutational motion for centers of small spiral nutations of orbit (ecliptic) pole over ellipses with semi-major axes of 113.850″ (85.158″) and the first pole rotates round the second one along a circle with radius of 28.691″; c) nutation of the Moon’s celestial pole over an ellipse with a semi-major axis of 45.04″ and with an axes ratio of about 0.004 with a period of T = 27.212 days. The principal ellipse’s axis is directed tangentially with respect to the precession circumference, along which the celestial pole moves nonuniformly nearly in one dimension. In contrast to the accepted concept, the latitude does not change while the Moon’s poles of rotation move. The dynamical reason for the inclination of the Moon’s mean equator with respect to the ecliptic is oblateness of the body of the Moon.     

Out-of-plane equilibrium points and their stability in the Robe’s problem with oblateness and triaxiality

This paper examines the existence and stability of the out-of-plane equilibrium points of a third body of infinitesimal mass when the equations of motion are written in the three dimensional form under the set up of the Robe’s circular restricted three-body problem, in which the hydrostatic equilibrium figure of the first primary is an oblate spheroid and the second one is a triaxial rigid body under the full buoyancy force of the fluid. The existence of the out of orbital plane equilibrium points lying on the xz-plane is noticed. These points are however unstable in the linear sense.     

Asymmetric periodic solutions of the averaged Hill problem with allowance for a planet’s oblateness

We consider asymmetric periodic solutions of the double-averaged Hill problem by taking into account oblateness of the central planet. They are generated by steady-state solutions, which are stable in the linear approximation and correspond to satellite orbits orthogonal to the line of intersection of the planet’s equatorial plane with the orbital plane of a disturbing point. For two model systems [(Sun+Moon)-Earth-satellite] and [Sun-Uranus-satellite], these periodic solutions are numerically continued from a small vicinity of the equilibrium position. The results are illustrated by projecting the solutions onto the (pericenter argument-eccentricity) and (longitude-inclination) planes.     

Motion in a modified Chermnykh’s restricted three-body problem with oblateness

In this paper, the restricted problem of three bodies is generalized to include a case when the passively gravitating test particle is an oblate spheroid under effect of small perturbations in the Coriolis and centrifugal forces when the first primary is a source of radiation and the second one an oblate spheroid, coupled with the influence of the gravitational potential from the belt. The equilibrium points are found and it is seen that, in addition to the usual three collinear equilibrium points, there appear two new ones due to the potential from the belt and the mass ratio. Two triangular equilibrium points exist. These equilibria are affected by radiation of the first primary, small perturbation in the centrifugal force, oblateness of both the test particle and second primary and the effect arising from the mass of the belt. The linear stability of the equilibrium points is explored and the stability outcome of the collinear equilibrium points remains unstable. In the case of the triangular points, motion is stable with respect to some conditions which depend on the critical mass parameter; influenced by the small perturbations, radiating effect of the first primary, oblateness of the test body and second primary and the gravitational potential from the belt. The effects of each of the imposed free parameters are analyzed. The potential from the belt and small perturbation in the Coriolis force are stabilizing parameters while radiation, small perturbation in the centrifugal force and oblateness reduce the stable regions. The overall effect is that the region of stable motion increases under the combine action of these parameters. We have also found the frequencies of the long and short periodic motion around stable triangular points. Illustrative numerical exploration is rendered in the Sun–Jupiter and Sun–Earth systems where we show that in reality, for some values of the system parameters, the additional equilibrium points do not in general exist even when there is a belt to interact with.     

Peculiarities of the variations in the coordinates of the Earth’s pole

The appearance of features with cusp points on the diagrams of changes in the coordinates of the Earth’s instantaneous pole (polhodes) is considered as the result of mapping onto the plane of its displacement over the surface during the Earth’s rotational-translational motion. The results of qualitative and quantitative analyses of the data on the coordinates of the Earth’s instantaneous pole are discussed. The basic principles of the theory of Whitney singularities and their application for explaining the bifurcations of the equilibrium positions for the Zeeman catastrophe machine (Arnold 1990) are used in the analyses.     

Changes in the activity of Jupiter’s hemispheres

Solar-induced changes in the reflective properties of the visible disk of Jupiter mostly depend on variations in the Earth’s jovimagnetic latitude. Since the orbit of Jupiter is eccentric (the eccentricity is e = 0.04845) and the planet passes perihelion at the time close to the summer solstice, the atmosphere receives 21% more solar energy in the northern hemisphere than in the southern one. According to the results of our studies, the ratio of the brightness values for the northern and southern tropical and temperate zones is a clear indicator of photometric activity of the processes in the atmosphere of Jupiter. From the analysis of the observational data for the period from 1962 to 2017, the cyclicity in changes of the activity factor of the hemispheres of the planet with a period of 11.87 years was found. This suggests that the atmosphere of Jupiter experiences seasonal restructuring.     

Ambartsumian’s methods in the theory of radiative transfer

The purpose of this article is to provide some insight into Ambartsumian’s methods in the theory of radiative transfer, their applications, and further development. Two of these methods are emphasized--the invariance principle and the method of addition of layers, proposed by Ambartsumian in the 1940’s. The difference between these methods and the classical approach for solving radiative transfer problems is discussed. We discuss only a small portion of the subsequent work by others that we believe reveals, in a more intuitive way, the essence and significance of Ambartsumian’s methods and their efficiency for applications. Thus, for example, a separate section is devoted to applications of the Lagrangian formalism to radiative transfer and it is shown that the invariance principle is a special case of a more general variational principle that reflects an invariance with respect to translational transformation of the optical depth. Our discussion of the method of addition of layers points out its generality and the major role it has played in the later creation of such methods as Bellman’s invariant imbedding method and the method for solving radiative transfer problems in inhomogeneous media. The latter method has yielded a number of new analytic results. The concluding section is a brief summary of Ambartsumian’s results in the nonlinear theory of radiative transfer, where he was a pioneer in the study of the class of multilevel problems. This article also sets out to demonstrate the place and role of Ambartsumian’s methods in the theory of radiative transfer, which, to a great extent, set the path along which this theory developed for many years to come. Translated from Astrofizika, Vol. 52, No. 1, pp. 5–27 (February 2009).     

On the Dynamical Foundations of the Lidov–Kozai Theory

The Lidov–Kozai theory developed by each of the authors independently in 1961–1962 is based on qualitative methods of studying the evolution of orbits for the satellite version of the restricted three-body problem (Hill’s problem). At present, this theory is in demand in various fields of science: in the field of planetary research within the Solar system, the field of exoplanetary systems, and the field of high-energy physics in interstellar and intergalactic space. This has prompted me to popularize the ideas that underlie the Lidov–Kozai theory based on the experience of using this theory as an efficient tool for solving various problems related to the study of the secular evolution of the orbits of artificial planetary satellites under the influence of external gravitational perturbations with allowance made for the perturbations due to the polar planetary oblateness.     

Polarization of ULF waves in the earth’s magnetosphere

Conditions for the realization of ULF waves with different polarization are formulated and verified with the use of observational data from the spacecrafts which performed measurements in the earth’s magnetosphere. It is shown that the conditions formulated are in good agreement with observed wave parameters.     

Linearization of the Hamiltonian in the generalized photogravitational Chermnykh’s problem

Linearization of the Hamiltonian is being performed in the generalized photogravitational Chermnykh’s problem. The normal form of the second order part of the Hamiltonian have been found. The effect of radiation pressure, gravitational potential from the belt have been examined analytically and numerically     

Aerosol in the upper layer of earth’s atmosphere

The upper atmospheric layer of Venus, Mars, Jupiter, Saturn, and earth contains an aerosol layer. The meteorites, rings, and removal of small planetary particles may be responsible for its appearance. The observations from 1979–1992 have shown that the optical aerosol thickness over the earth’s polar regions varies from τ ≈ 0.0002 to 0.1 to λ = 1 μm. The highest τ value was in 1984 and 1992 and was preceded by intense activity of the El Chichon (1982) and Pinatubo (1991) volcanoes. We have shown that increase in τ of the stratospheric aerosol may lead to decrease in ozone layer registered in the 1970s. The nature of the stratospheric aerosol (a real part of the refraction index), effective size particles r, and latitudinal variation τ remain unknown. The analysis of phase dependence of the degree of polarization is effective among the distal methods of determination of n _r and r. The observation value of intensity and degree of polarization in the visible light are caused by the optical surface properties and optical atmospheric thickness, whose values varied with latitude, longitude, and in time. Thus, it is impossible to correctly distinguish the contribution of the stratospheric aerosol. In UV-rays (λ < 300 nm), the ozone layer stops the influence of the surface and earth’s atmosphere up to height of 20–25 km. In this spectrum area, the negative factors are emission of various depolarizating gases, horizontal heterogeneity of the effective optical height of the ozone layer, and oriented particles indicated by variation of the polarization plane.     

Mach’s principle and Yukawa-like corrections to the Newtonian potential as a bound for the mean energy density of the universe

The (Newton + Yukawa)-type gravitational potential V(r)=?(γ M/r)[1+Aexp?(?r/B)](γ= the gravitational constant as measured at infinity, M= the mass of the source, A, B are constants) is considered in the framework of the Sciama linear approach to Mach’s principle. The coupling constant A of the Yukawa component is found to be related to the mass density and size of the observable (causally connected) universe.     

Properties of acoustic-gravity waves in the Earth’s polar thermosphere

The properties of acoustic-gravity waves in the polar regions of the Earth’s thermosphere have been studied. It has been shown that the change in AGW amplitudes occurs against the background of large-scale rotational movements of the medium in the polar thermosphere. The amplitudes of waves increase with AGW propagation against the motion of the medium and decrease when AGW propagate along rotation. An analytical expression for the gain coefficient of AGW perturbations is obtained; the wave’s amplification effect in the opposite wind given the characteristic parameters of the thermosphere is estimated. The results are consistent with the measurements of AGW parameters in the polar regions from the “Dynamic Explorer 2” satellite.)     

Nonlinearity in Inverse Problems of the Dynamics of Jupiter’s Outer Satellites

Solar System Research - This paper presents the results of a study of total and intrinsic nonlinearities in inverse problems of the dynamics of Jupiter’s Outer Satellites, observed on very...     

Collinear equilibrium points of Hill’s problem with radiation and oblateness and their fractal basins of attraction

We discuss the existence, location, and stability of the collinear equilibrium points of a generalized Hill problem with radiation of the primary (the Sun) and oblateness of the secondary (the planet), and present some remarkable fractals created as basins of attraction of Newton’s method applied for their computation in several cases of the parameters.     

Statistical Characteristics of Meteoroid Parameters in the Earth’s Atmosphere

Statistical characteristics of meteoroids with kinetic energy from 0.1 to 440 kt TNT are estimated based on NASA satellite observations made in 1994–2016. The distributions of the number of falling meteoroids are constructed and analyzed based on the values of their initial kinetic energy, initial velocity, initial mass, altitude, geographic coordinates of the maximum total radiated energy region, and the year of the fall. Correlation dependences “mass–initial kinetic energy,” “maximum total radiated energy region altitude–initial kinetic energy,” and “maximum total radiated energy region altitude–initial velocity (the square of the initial velocity)” are constructed.