Accounting for the viscosity of the fluid core in the problem of the physical libration of the moon

A two-component theoretical model of the physical libration of the Moon in longitude is constructed with account taken of the viscosity of the core. In the new version, a hydrodynamic problem of motion of a fluid filling a solid rotating shell is solved. It is found that surfaces of equal angular velocity are spherical, and a velocity field of the fluid core of the Moon is described by elementary functions. A distribution of the internal pressure in the core is found. An angular momentum exchange between the fluid core and solid mantle is described by a third-order differential equation with a right-hand side. The roots of a characteristic equation are studied and the stability of rotation is proved. A libration angle as a function of time is found using the derived solution of the differential equation. Limiting cases of infinitely large and infinitely small viscosity are considered and an effect of lag of a libration phase from a phase of action of an external moment of forces is ascertained. This makes it possible to estimate the viscosity and sizes of the lunar fluid core from data of observations.     

Viewing the Shadow of the Black Hole at the Galactic Center

Nine of the most important estimators known for the two-point correlation function are compared using a predetermined, rigorous criterion. The indicators were extracted from over 500 subsamples of the Virgo Hubble volume simulation cluster catalog. The "real" correlation function was determined from the full survey in a 3000 h(-1) Mpc periodic cube. The estimators were ranked by the cumulative probability of returning a value within a certain tolerance of the real correlation function. This criterion takes into account bias and variance, and it is independent of the possibly non-Gaussian nature of the error statistics. As a result, for astrophysical applications, a clear recommendation has emerged: the Landy & Szalay estimator, in its original or grid version (Szapudi & Szalay), is preferred in comparison with the other indicators examined, with a performance almost indistinguishable from the Hamilton estimator.     

On the model of the accumulation of the moon compatible with the data on the composition and the age of lunar rocks

It is suggested that the overall early melting of the lunar surface is not necessary for the explanation of facts and that the structure of highlands is more complicated than a solidified anorthositic ‘plot’. The early heating of the interior of the Moon up to 1000K is really needed for the subsequent thermal history with the maximum melting 3.5 × 10⁹ yr ago, to give the observed ages for mare basalts. This may be considered as an indication that the Moon during the accumulation retained a portion of its gravitational energy converted into heat, which may occur only at rapid processes. A rapid (t < 10³ yr) accretion of the Moon from the circumterrestrial swarm of small particles would give necessary temperature, but it is not compatible with the characteristic time 10⁸ yr of the replenishment of this swarm which is the same as the time-scale of the accumulation of the Earth. It is shown that there were conditions in the circumterrestial swarm for the formation at a first stage of a few large protomoons. Their number and position is evaluated from the simple formal laws of the growth of satellites in the vicinity of a planet. Such ‘systems’ of protomoons are compared with the observed multiple systems, and the conclusion is reached that there could have been not more than 2–3 large protomoons with the Earth. The tidal evolution of protomoon orbits was short not only for the present value of the tidal phase-lag but also for a considerably smaller value. The coalescence of protomoons into a single Moon had to occur before the formation of the observed relief on the Moon. If we accept the age 3.9 × 10⁹ yr for the excavation of the Imbrium basin and ascribe the latter to the impact of an Earth satellite, this collision had to be roughly at 30R, whereR is the radius of the Earth, because the Moon at that time had to be somewhere at this distance. Therefore, the protomoons had to be orbiting inside 20–25R, and their coalescence had to occur more than 4.0x10⁹ yr ago. The energy release at coalescence is equivalent to several hundred degrees and even 1000 K. The process is very rapid (of the order of one hour). Therefore, the model is valid for the initial conditions of the Moon.     

Third Integral and the Dynamics of the Galaxy in the Neighborhood of the Sun

Observational data on the dynamics of stars in the neighborhood of the sun indicate the existence of a third integral besides the integrals of the angular momentum and energy. The Poincaré integral is proposed as a third integral. The consequences of this assumption are derived and compared with available astrophysical data.     

On the analogy between the zebra patterns in radio emission from the sun and the crab pulsar

We investigate the close analogy between the solar radio emission with a quasi-harmonic spectrum structure and one of the microwave emission components of the Crab pulsar in the form of the so-called zebra pattern. The radio emission mechanism of this component can be provided by instability at double plasma resonance and can be realized in extraordinary (for a radio pulsar) conditions, namely in a nonrelativistic plasma with a relatively weak magnetic field. We point out possible models of the emission source in the form of a magnetic trap or a neutral current sheet with a transverse magnetic field localized in the corotating region of the pulsar magnetosphere far from the neutron star surface.     

On the determination of the north direction of the sun's image

For a perfectly aligned Coudé heliograph the north direction of Sun's image in the image plane of the heliograph changes linearly with the hour angle of the Sun or in a common heliograph it is constant. But if the alignment is not perfect and there are instrumental errors the angle between the north direction of the Sun's image and a direction fixed in the image plane is a complicated function of the hour angle of the Sun. In this paper we derive this dependence.     

Dynamical equation for the degree of ionization of the cosmic substratum before the formation of the galaxy

We discuss the variable degree of ionizationx of a hydrogen-helium plasma in the early Universe for a quasi-static expansion in thermal equilibrium. The final equation for the degree of ionization can be reduced to a polynomial of fourth order inx with known coefficients depending on the temperature. Restricting to a pure hydrogen-plasma applied to the recombination era, where the main ionization effects are due to photo-electric and collisional processes, we study the dynamical evolution of the degree of ionization for nonstatic and nonequilibrium situations. The calculation can be reduced to a pure quadrature. In the linear case, we also calculate the rate of ionization.     

Protostars and the origin of the angular momentum of the solar system

Protostars in a group exert gravitational tidal torques on an aspherical nebula located in the group. The net torque transfers angular momentum from the orbital motions of the stars to rotation of the nebula. A relation can be derived between the parameters describing the protostars and the final angular momentum of the nebula. While the parameters concerned are uncertain, a conservative choice results in a value for the angular momentum equal to about 1/3 of that of the present solar system. This suggests that if the Sun formed in a group, tidal interactions with other protostars may account for a significant part of the angular momentum of the solar system.     

Automation of the Filament Tracking in the Framework of the HELIO Project

We present a new method to automatically track filaments over the solar disk. The filaments are first detected on Meudon Spectroheliograph Hα images of the Sun, applying the technique developed by Fuller, Aboudarham, and Bentley (Solar Phys. 227, 61, 2005). This technique combines cleaning processes, image segmentation based on region growing, and morphological parameter extraction, including the determination of filament skeletons. The coordinates of the skeleton pixels, given in a heliocentric system, are then converted to a more appropriate reference frame that follows the rotation of the Sun surface. In such a frame, a co-rotating filament is always located around the same position, and its skeletons (extracted from each image) are thus spatially close, forming a group of adjacent features. In a third step, the shape of each skeleton is compared with its neighbours using a curve-matching algorithm. This step will permit us to define the probability [P] that two close filaments in the co-rotating frame are actually the same one observed on two different images. At the end, the pairs of features, for which the corresponding probability is greater than a threshold value, are associated using tracking identification indices. On a representative sample of filaments, the good agreement between automated and manual tracking confirms the reliability of the technique to be applied on large data sets. This code is already used in the framework of the Heliophysics Integrated Observatory (HELIO) to populate a catalogue dedicated to solar and heliospheric features (HFC). An extension of this method to other filament observations, and possibly sunspots, faculae, and coronal-holes tracking, can also be envisaged.     

The use of the distribution of the orbital energy to investigate the evolution of the Perseid meteoroid stream

Numerical integration of a meteor stream over a long period is a very time consuming process, especially if a number of different models have to be investigated. In this paper we demonstrate that using the distribution of orbital energy as a vector in a Markov process can be a useful tool and that meaningful results can be obtained with far less computation than is normally required.     

Modelling the bar in the centre of the starburst galaxy M82

We present VLA A-array 21-cm atomic hydrogen (H  i ) absorption observed against the central region of the starburst galaxy M82 with an angular resolution of ∼1.3 arcsec (≃20 pc). These observations, together with MERLIN H  i absorption measurements, are compared with the molecular (CO) and ionized ([Ne  ii ]) gas distributions and are used to constrain the dynamics and structure of the ionized, neutral and molecular gas in this starburst.
A position–velocity diagram of the H  i distribution reveals an unusual 'hole' feature which, when previously observed in CO, has been interpreted as an expanding superbubble contained within a ring of gas in solid body rotation. However, we interpret this feature as a signature of a nearly edge-on barred galaxy. In addition, we note that the CO, H  i and [Ne  ii ] position–velocity diagrams reveal two main velocity gradients, and we interpret these as gas moving on x₁- and x₂-orbits within a bar potential. We find the best fit to the data to be produced using a bar potential with a flat rotation curve velocity v _b=140 km s⁻¹ and a total length of 1 kpc, a non-axisymmetry parameter q =0.9, an angular velocity of the bar Ω_b=217 km s⁻¹ arcsec⁻¹, a core radius R _c=25 pc, an inclination angle i =80° and a projected angle between the bar and the major axis of the galaxy φ '=4°. We also discuss the orientation of the disc and bar in M82.     

On the planetary acceleration and the rotation of the Earth

We have developed a cosmological model for the Earth rotation and planetary acceleration that gives a good account (data) of the Earth astronomical parameters. These data can be compared with the ones obtained using space-base telescopes. The expansion of the universe has shown to have an impact on the rotation of planets, and in particular, the Earth. The expansion of the universe causes an acceleration that is exhibited by all planets.     

On the Precursor Star of the Pulsar in the Crab Nebula

The spatial distribution of the youngest pulsars, with a characteristic age of less than 12,000 years, is considered. All the pulsars except for the pulsar in the Crab Nebula lie in groups of young OB stars. It is suggested that the precursor of the Crab pulsar was a rapidly rotating, massive OB star. The group of young massive stars from which the fast-moving star was ejected is indicated. Estimates of the age of the precursor of the Crab pulsar and of the age of the group of young stars from which it was ejected favor this hypothesis. It is concluded that the fast-moving star must have acquired a high velocity due to the dynamical evolution of the young stellar group.     

Hypothesis on the origin of the spiral structure of the galaxies

The spiral waves in a model galaxy consisting of differentially rotating and non-rotating subsystems are considered on the basis of participating phenomena. The subsystems involved represent the Populations I and II of normal spirals, respectively. The spiral waves in such a systems are unstable in the Landau sense. Due to this instability they grow up to attain finite amplitude. This growth is stopped by a non-linear effect (the quasilinear effect), the steady state with waves of finite amplitude being established. The hypothesis is proposed that these waves should be identified with the spiral structure of the galaxies.     

On the origin of the metagalaxy

An attempt is made to explain two properties of the metagalaxy: its expansion and the absence of causal connection of its distant regions during a large part of its initial history. It is postulated that the gravitating matter was born from the cosmological field, i.e., a medium with equation of statep=–.It is shown that such a postulate explains the expansion of metagalaxy and leads to a correct estimate of the entropy per baryon. The problem of causal connection can also be solved on this basis.     

On the early history of the asteroids

Among the major features of the asteroids as a group is the fact that they are small and numerous rather than being a single planet, and that they have unusually high eccentricities and inclinations. Regarding the first, this paper presents two lines of argument concerning the concept that the asteroids formed with a mass-distribution similar to what we observe today. Considerations of planet accretion are used to clarify the role of Jupiter in preventing coalescence of asteroids into a single planet. Regarding the eccentricities and inclinations, it is proposed that they were excited by secular resonances associated with the presence of Jupiter within a dissipating solar nebula.     

On the formation of the planetary system the titius-bode law

The linear density and velocity perturbations are analyzed in a differentially rotating thin gravitating disc consisting of gas and dust. For the radial behaviour of the equilibrium density and the velocity of sound we assume a power law. The zeros of these perturbations have a distance behaviour like the distances of the planets and their satellites known as the Titius-Bode rule. It is suggested, that the knots of the velocity disturbances are the places where ring like dust accumulations occur. The mechanism is the same as in the Kundt's tube, where collisions between the dust and the oscillating gas are responsible for this effect.