Linear stability of the triangular equilibrium points in the photogravitational elliptic restricted problem,II

The linear stability of the triangular equilibrium points in the photogravitational elliptic restricted three-body problem is examined and the stability regions are determined in the space of the parameters of mass, eccentricity, and radiation pressure, in the case of equal radiation factors of the two primaries. The full range of values of the common radiation factor is explored, from the gravitational caseq ₁ =q ₂ =q = 1 down to the critical value ofq = 1/8 at which the triangular equilibria disappear by coalescing on the rotating axis of the primaries. It is found that radiation pressure exerts a significant influence on the stability regions. For certain intervals of radiation values these regions become qualitatively different from the gravitational case as well as the solar system case considered in Paper I. There exist values of the common radiation factor, in the range considered, for which the triangular equilibrium points are stable for the entire range of mass distribution among the primaries and for large eccentricities of their orbits.     

Dust particle in the solar gravitational and electromagnetic fields

The action of the solar electromagnetic radiation (in the form of the Poynting-Robertson effect) on the motion of interplanetary dust particle in the gravitational field of the Sun is discussed from the theoretical point of view. Results are presented to all orders inv/c (c - speed of light,v -orbital velocity of the particle) - general relativistic formula is presented.     

Stochastic scattering and other contributions to the Sun's wake in the local hydrogen cloud

Gas streaming through the solar system experiences both destructive and scattering processes, the latter primarily in collisional interactions with the solar wind protons. The scattering interactions can be important in filling the downstream wake. They may effectively increase the velocity dispersion and also cause discrete orbit changes.The downstream intensity moment is here evaluated analytically for particles suffering a single, discrete collision, and compared with the moment from a thermal velocity dispersion (both in the absence of a central force field). The elastic scattering collisions of protons in H-gas lead to a contribution to theL backscatter from the wake equivalent to an initial thermal velocity of about 1 km s^–1, giving an intensity for cool gas of the order of 10R. This exceeds the contribution due to focussing in the solar gravitational field if the radiation pressure is not less than 0.8 of the gravitational attraction.     

Multiwavelength focusing with the Sun as gravitational lens

The light deviation caused by the gravitational potential in the vicinity of the sun could be used as a means of focussing radiation that cannot be focussed easily otherwise. The gravitational lens formed by the sun is not stigmatic, but does have the advantage of being achromatic and acts identically on all types of mass-less radiations. For a source at infinity, its geometrical characteristics present a “caustic” line starting at 550 astronomical units (UA) downstream from the sun. In a plane perpendicular to that caustic line, images of distant objects are formed.The perturbations by the solar corona plasma will significantly blur electromagnetic radiation for wavelengths longer than those of the IR domain. At shorter wavelengths, for example the γ domain, the focussing process could lead to 10⁸ amplification factors. In order to reach the regions where images are formed, long distance space missions are necessary. Once launched, missions of this type would be dedicated to a single field. Some possible targets are considered, such as Sagitarius A observed in X and γ rays.In this paper we study the point spread function (PSF) of the sun as a gravitational lens. Taking into account perturbations by the planets, the non sphericity of the sun and coronal plasma index, we derive limits within which such observations could be possible.     

Timing noise and glitches

One of the most remarkable properties of radio pulsars is their rotational stability which allows many uses as clocks, For instance they enable us to determine the shapes and sizes of binary orbits, to study general relativistic effects in strong gravitational fields, to demonstrate the existance of gravitational radiation from binary systems, to permit the detection of extra solar planets, and also to put limits on the long period gravitational wave background. However, some display timing imperfections which tell us about the insides of neutron stars. This review describes the basic physics of slowdown and how period instabilities seem to be related to the rate of slowdown and the presence of internal superfluid liquid. Careful studies of glitches and the subsequent rotational behaviour of the pulsars can provide valuable information on the internal structure of neutron stars.     

Gravitational Radiation of Relativistic <Emphasis Type="Italic">n</Emphasis> = 1 Polytropes

The gravitational radiation of n = 1 polytropes undergoing quasiradial pulsations is examined. The intensity of the gravitational radiation and the gravitational wave amplitudes are calculated for polytropic models of white dwarfs and neutron stars when the energy of rotation of the object serves as the source of the radiated energy. Calculations of h₀ show that objects with a polytropic equation of state can describe the expected gravitational radiation from white dwarfs and neutron stars. The gravitational radiation of polytropic models of galactic nuclei and quasars is also examined. These objects can create a high enough background of gravitational radiation at frequencies of 10^-8–10^-11 Hz for gravitational wave detectors operating in this frequency range. __________ Translated from Astrofizika, Vol. 48, No. 4, pp. 603–612 (November 2005).     

A diffraction limit on the gravitational lens effect

The focussing of gravitational radiation by the interior and exterior gravitational field of a Newtonian gravitational lens is considered. A graphical method for determining the caustic structure of a Newtonian gravitational lens is presented and the caustic structure of a solar type gravitational lens is discussed. Estimates of the amplitude magnification in the caustic region indicate that waves with frequencies less than a critical cutoff frequency ω _c are not amplified significantly. For a lens of massM this cutoff frequency is ω _c ≈(10^-1πM)^-1; for the Sun ω _c ≈10⁴s^-1. Work supported in part by National Science Foundation Grant PHY78-05368.     

Equilibrium points and zero velocity surfaces in the restricted four-body problem with solar wind drag

We have analyzed the motion of an infinitesimal mass in the restricted four-body problem with solar wind drag. It is assumed that the forces which govern the motion are mutual gravitational attractions of the primaries, radiation pressure force and solar wind drag. We have derived the equations of motion and found the Jacobi integral, zero velocity surfaces, and particular solutions of the system. It is found that three collinear points are real when the radiation factor 0<β<0.1 whereas only one real point is obtained when 0.125<β<0.2. The stability property of the system is examined with the help of Poincaré surface of section (PSS) and Lyapunov characteristic exponents (LCEs). It is found that in presence of drag forces LCE is negative for a specific initial condition, hence the corresponding trajectory is regular whereas regular islands in the PSS are expanded.     

Dynamics and gravitational waveforms in spinning compact eccentric binaries

The effects of eccentricity on the Hamiltonian dynamics of post-Newtonian spinning compact binaries and gravitational radiation from eccentric orbits are discussed. The simulation results of scans for chaos show that the eccentricity has a great effect on the dynamics without considering dissipation due to gravitational radiation. Moreover, both the dynamics behavior and the orbital eccentricity jointly modulate the gravitational waveforms, and the spin–spin coupling effect play an important role during the gravitational radiation of inspiral and coalescence. Moreover, the imprint of characteristic of the original system can be deduced from the time-domain and frequency-domain waveforms.     

Role of “Core” and “Halo” solar electrons in ionization of the interstellar medium

The probability of the interstellar wind atoms (H and He) to survive ionization by solar wind electrons is presented. For the first time a dual temperature electron distribution is used to model the effects of “core” (10 eV) and “halo” (60 eV) solar electrons on the probabilities. Survival probability distributions as a function of helicocentric distance were calculated for variations in the electron temperature, solar radiation force, and the interstellar wind flow velocity. These probabilities are important in determining the radial density distributions of the interstellar atoms. It has been found that the interstellar wind has a distinctively higher probability of surviving “halo” rather than “core” electron ionization only at heliocentric distances, ρ, smaller than about 0.5 a.u. For distances larger than 0.5 a.u., the probabilities of surviving “halo” electrons are close to the probabilities of surviving “core” electrons. Also, the probabilities for both “core” and “halo” electrons are relatively insensitive to changes in u_∞ (interstellar wind velocity at infinity), μ (the solar ratio of radiation to gravitational force) and α (a model parameter for solar electron temperature) for ρ > 0.5. For distances smaller than that, the sensitivity increases significantly.     

Formation flying solar-sail gravity tractors in displaced orbit for towing near-Earth asteroids

Several methods of asteroid deflection have been proposed in literature and the gravitational tractor is a new method using gravitational coupling for near-Earth object orbit modification. One weak point of gravitational tractor is that the deflection capability is limited by the mass and propellant of the spacecraft. To enhance the deflection capability, formation flying solar sail gravitational tractor is proposed and its deflection capability is compared with that of a single solar sail gravitational tractor. The results show that the orbital deflection can be greatly increased by increasing the number of the sails. The formation flying solar sail gravitational tractor requires several sails to evolve on a small displaced orbit above the asteroid. Therefore, a proper control should be applied to guarantee that the gravitational tractor is stable and free of collisions. Two control strategies are investigated in this paper: a loose formation flying realized by a simple controller with only thrust modulation and a tight formation realized by the sliding-mode controller and equilibrium shaping method. The merits of the loose and tight formations are the simplicity and robustness of their controllers, respectively.     

Collisional heating of interplanetary gas: Fokker-Planck treatment

Interstellar gas streaming through the solar system undergoes both elastic collisions with solar wind ions and destructive, ionizing processes. The Boltzmann equation is set up, with linear Fokker-Planck terms describing the glancing elastic collisions. Solutions combining the dynamical effects of the central force field and the diffusion in velocity space are derived, appropriate to cool gas.For the He component of the streaming gas, if initially at 100 K, the collisional heating dominates inside 2 a.u. upstream and 5 a.u. downstream. A modified formula is given for the density in the downstream wake, as enhanced by gravitational focussing. Calculations of the helium resonant radiation backscatter require substantial modification.     

Symmetries in the Optimal Control of Solar Sail Spacecraft

The theory of optimal control is applied to obtain minimum-time trajectories for solar sail spacecraft for interplanetary missions. We consider the gravitational and solar radiation forces due to the Sun. The spacecraft is modelled as a flat sail of mass m and surface area A and is treated dynamically as a point mass. Coplanar circular orbits are assumed for the planets. We obtain optimal trajectories for several interrelated problem families and develop symmetry properties that can be used to simplify the solution-finding process. For the minimum-time planet rendezvous problem we identify different solution branches resulting in multiple solutions to the associated boundary value problem. We solve the optimal control problem via an indirect method using an efficient cascaded computational scheme. The global optimizer uses a technique called Adaptive Simulated Annealing. Newton and Quasi-Newton Methods perform the terminal fine tuning of the optimization parameters.     

Monte-Carlo simulation of neutral atoms trajectories in the solar system

The Monte-Carlo simulation of the neutral interstellar atoms penetration into the solar system is considered. The ionization and charge exchange processes with due regard for the plasma interface structure as well as the gravitational force and the radiation pressure are taken into account. The Monte-Carlo scheme with splitting of atom trajectories is developed, and its high efficiency is shown against the imitation Monte-Carlo scheme. The main algorithms of the splitting scheme and the possible applications of the suggested method are described. In particular calculation of the mass, momentum and energy sources appearing in the plasma gasdynamical equations is considered. The gasdynamical approach for these terms is shown to be inconsistent with the Monte-Carlo results.     

The sodium tail of the Moon

During the few days centered about new Moon, the lunar surface is optically hidden from Earth-based observers. However, the Moon still offers an observable: an extended sodium tail. The lunar sodium tail is the escaping “hot” component of a coma-like exosphere of sodium generated by photon-stimulated desorption, solar wind sputtering and meteoroid impact. Neutral sodium atoms escaping lunar gravity experience solar radiation pressure that drives them into the anti-solar direction forming a comet-like tail. During new Moon time, the geometry of the Sun, Moon and Earth is such that the anti-sunward sodium flux is perturbed by the terrestrial gravitational field resulting in its focusing into a dense core that extends beyond the Earth. An all-sky camera situated at the El Leoncito Observatory (CASLEO) in Argentina has been successfully imaging this tail through a sodium filter at each lunation since April 2006. This paper reports on the results of the brightness of the lunar sodium tail spanning 31 lunations between April 2006 and September 2008. Brightness variability trends are compared with both sporadic and shower meteor activity, solar wind proton energy flux and solar near ultra violet (NUV) patterns for possible correlations. Results suggest minimal variability in the brightness of the observed lunar sodium tail, generally uncorrelated with any single source, yet consistent with a multi-year period of minimal solar activity and non-intense meteoric fluxes.     

Hamiltonian Formulation and Perturbations for Dust Motion Around Cometary Nuclei

In this paper we analyze the dynamical behavior of large dust grains in the vicinity of a cometary nucleus. To this end we consider the gravitational field of the irregularly shaped body, as well as its electric and magnetic fields. Without considering the effect of gas friction and solar radiation, we find that there exist grains which are static relative to the cometary nucleus; the positions of these grains are the stable equilibria. There also exist grains in the stable periodic orbits close to the cometary nucleus. The grains in the stable equilibria or the stable periodic orbits won’t escape or impact on the surface of the cometary nucleus. The results are applicable for large charge dusts with small area-mass ratio which are near the cometary nucleus and far from the Solar. It is found that the resonant periodic orbit can be stable, and there exist stable non-resonant periodic orbits, stable resonant periodic orbits and unstable resonant periodic orbits in the potential field of cometary nuclei. The comet gravity force, solar gravity force, electric force, magnetic force, solar radiation pressure, as well as the gas drag force are all considered to analyze the order of magnitude of these forces acting on the grains with different parameters. Let the distance of the dust grain relative to the mass centre of the cometary nucleus, the charge and the mass of the dust grain vary, respectively, fix other parameters, we calculated the strengths of different forces. The motion of the dust grain depends on the area-mass ratio, the charge, and the distance relative to the comet’s mass center. For a large dust grain (> 1 mm) close to the cometary nucleus which has a small value of area-mass ratio, the comet gravity is the largest force acting on the dust grain. For a small dust grain (< 1 mm) close to the cometary nucleus with large value of area-mass ratio, both the solar radiation pressure and the comet gravity are two major forces. If the a small dust grain which is close to the cometary nucleus have the large value of charge, the magnetic force, the solar radiation pressure, and the electric force are all major forces. When the large dust grain is far away from the cometary nucleus, the solar gravity and solar radiation pressure are both major forces.     

Fluctations in the cosmic microwave background arising from low-frequency gravitational radiation

Intense low-frequency intergalactic gravitational radiation with wave lengths λ smaller than the HUBBLE distance λ_H ≌ 3000 (100/H₀) Mpc but not exceedingly small compared to λ_H. generates anisotropies in the microwave background radiation. One contribution results from the local wave field and produces mainly a quadrupole-type temperature variation on the sky. Available data on large-scale microwave fluctuations do not exclude appreciable amounts of gravitational background radiation in the Megaparsec wave band. A more sensitive test is provided by a second far-field contribution, which has a small angular scale. Its amplitude depends strongly on the ratio of the (present) rest mass density to the HUBBLE constant, if a cosmological origin of the blackbody radiation is assumed. In a low-density universe, pre-galactic COMPTON scattering of the blackbody radiation is not able to reduce the fluctuations caused by the low-frequency gravitational wave field. The recent small-scale data by PARIJSKIJ would allow only small amplitudes of gravitational waves with an energy density significantly below the critical cosmological density. On the other hand, in a high-density universe, the small angular scale fluctuation in the blackbody radiation is completely damped out, and a gravitational radiation cosmos reaching the critical density is admitted. Independent of the matter density, the data by PARIJSKIJ would confine gravitational background radiation to insignificant amplitudes if a discrete source model for the origin of the microwave background has to be assumed.     

On gravitational radiation from binary systems

We discuss gravitational radiation from a neutral mass particle within a bound orbit in the background Schwarzschild metric. We compare the power loss of gravitational radiation according to this formalism with the heuristic quadrupole radiation formula as applied to a binary system. There are evidence and compelling reasons to believe that the quadrupole formula is valid even in a fairly strong gravitational field, although its fully consistent analytical derivation is not yet known. In particular, we emphasize that the application of the quadrupole formula to the binary pulsar system PSR 1913+16 as well as other binary pulsars, which are weakly bound by gravity, is well justified.     

Gravitational radiation from differentially rotating and oscillating white dwarfs

We examine the possible emission of gravitational waves from white dwarfs undergoing self-similar oscillations driven by the energy released during relaxation of their differential rotation. Two distributions of the initial angular momentum are considered. It is assumed that 1% of the energy dissipated by a rotating white dwarf is converted into the energy of self-similar oscillations and, therefore, into gravitational radiation. The relative amplitude of the gravitational radiation from an isolated white dwarf at a distance of 50 pc is found to be less than 10⁻²⁷. The emission from the galactic population of white dwarfs may create a background which overlaps the random cosmological background of gravitational radiation for the improved decihertz detectors currently being proposed. __________ Translated from Astrofizika, Vol. 49, No. 2, pp. 231–242 (May 2006).