Current problems of dynamics of moons of planets and binary asteroids based on observations

The general approach to studying the dynamics of moons of planets and asteroids consists in developing more and more accurate models of motion based on observational data. Not only the necessary ephemerides, but also some physical parameters of planets and moons are obtained this way. It is demonstrated in the present study that progress in this field is driven not only by the increase in accuracy of observations. The accuracy of ephemerides may be increased by expanding the observation time interval. Several problems arise on the way toward this goal. Some of them become apparent only when the procedure of observational data processing and use is examined in detail. The method used to derive astrometric data by processing the results of photometric observations of mutual occultations and eclipses of planetary moons is explained below. The primary contribution to the error of astrometric results is produced by the unaccounted noise level in photometric readings and the inaccuracy of received values of the albedo of moons. It is demonstrated that the current methods do not allow one to eliminate the noise completely. Extensive additional photometric measurements should be performed at different angles of rotation of moons and in different spectral bands of the visible wavelength range in order to obtain correct values of the albedo of moons. Many new distant moons of the major planets have been discovered in the early 21st century. However, the observations of these moons are scarce and were performed over short time intervals; as a result, some of the moons were lost. The necessity of further observations of these Solar System bodies is pointed out in the present study. Insufficient knowledge of asteroid masses is an obstacle to improving the accuracy of the ephemerides of Mars. The basic method for determining the masses of large asteroids consists in analyzing their influence on the motion of Mars, the Earth, and spacecraft. The masses of more than 100 large asteroids were determined this way. One of the principal techniques for Earth-based measurement of the masses of asteroids involves astrometric observations of binary asteroids. The determination of relative coordinates is made rather difficult by the apparent proximity of components. The success of these efforts depends on the availability of instrumentation and the expertise of observers skilled in adaptive optics and speckle interferometry. Collaboration between different research teams and observers is absolutely necessary.     

Inhibitory effects of divalent metal ions on liver microsomal 7-ethoxyresorufin O-deethylase (EROD) activity of leaping mullet

The purpose of the present study was to elucidate in vitro effects of Hg(2+), Zn(2+), Ni(2+) and Cd(2+) on cytochrome P4501A1 (CYP1A1) dependent EROD activities in leaping mullet liver microsomes. Fish captured from the most polluted part of Izmir Bay, had highly elevated EROD activities, and induced CYP1A1 protein levels as determined by Western blotting. Although all of the metal ions caused inhibition of the initial velocity of the reaction, Hg(2+) and Cd(2+) exhibited much higher inhibitory effect at lower concentrations and they were evidently more potent inhibitors than others. The inhibitor concentration giving 50% inhibition (IC(50) values) of Zn(2+), Ni(2+), Cd(2+) and Hg(2+) of initial EROD activity were 107, 16, 1.3 and 0.15 micromolar, respectively. Glutathione (GSH) at 0.5 mM final concentration, completely reversed Ni(2+) and Cd(2+) inhibition of EROD activity indicating the protective action of GSH.     

Quasi-Tangency Points on the Orbits of a Small Body and a Planet at the Low-Velocity Encounter

We propose a method for selecting a low-velocity encounter of a small body with a planet from the evolution of the orbital elements. Polar orbital coordinates of the quasi-tangency point on the orbit of a small body are determined. Rectangular heliocentric coordinates of the quasi-tangency point on the orbit of a planet are determined. An algorithm to search for low-velocity encounters in the evolution of the orbital elements of small bodies is described. The low-velocity encounter of comet 39P/Oterma with Jupiter is considered as an example.     

On the expansion of the secular part of the perturbing function of mutual attraction in the satellite systems of planets

We propose a special representation for the secular part of the perturbing function describing the mutual attraction of satellites. In contrast to the known representations, it has a single analytical form for any ratio between the semimajor axes of the perturbed and perturbing satellites. The resulting expression is a partial sum of a power series with respect to the small eccentricities and planet-equatorial inclinations of the satellites’ orbits. This sum includes terms up to and including the fourth degree with respect to these small parameters. The proposed expansion is compared with one of the known expansions for the secular part of the perturbing function.     

Kuiper Belt structure as a reflection of the migration process of a planet

One of the main particular features of the structure of the Kuiper Belt is that it contains clusters of objects of small orbital eccentricity and inclination (“cold population”). In order to solve the problem of the origin of the objects, we considered the process of the gravitational interaction of a comparatively small-mass planet with a planetesimal disk. We found that one particular property of the process is that the planet changes its direction of migration. The interaction with the planet results in the transportation of a considerable portion of planetesimals from the inner zone out to the Kuiper Belt. After such a transition of the objects, the planet returns to the inner regions of the planetesimal disk. Numerical simulations show that the reversible migration of a planet of a mass similar to that of the Earth can explain the main properties of the Kuiper Belt’s cold population orbit distribution.     

Minor elements in carbonaceous sediments of the Baltic Sea

According to the geochemical analysis, the carbonaceous sediments of the Baltic Sea??s deep basins containing 3?C5% C_org are enriched with some metals such as Cu, Mo, Ni, Pb, Zn, V, and U as compared with the shallow-water facies of the Bay of Finland. These metals are also concentrated (against the background values in the clayey rocks) in ancient carbonaceous shales, where the average Cu and V contents are slightly higher and that of Mo, Pb, and Zn lower than in the deepwater carbonaceous sediments of the Baltic Sea. In addition, the carbonaceous sediments of the last basin are enriched, although less notably than the ancient shales, with Ag, As, Bi, and Cd. These data confirm the previous assumptions that the carbonaceous sediments accumulating now in seas and oceans may be considered as recent analogs of ancient metalliferous shales.     

A method of symplectic integrations with adaptive time-steps for individual Hamiltonians in the planetary <Emphasis Type="Italic">N</Emphasis>-body problem

A new algorithm is developed for long-term integrations of the N-body problem. The method uses symplectic integrations of the Hamiltonian equations of motion for each body. This allows one to employ individual adaptive time-steps in computations. The efficiency of this technique is demonstrated by several tests performed for typical problems of Solar System dynamics.     

Study of dynamical processes at the final stages of planetary system formation: Resonance motion of giant planets

According to current observational data, planets of many exoplanetary systems have resonant motion. The formation of resonance configurations is studied within a unified model of planetary migration. Planets in the observed systems 24 Sex, HD 37124, HD 73526, HD 82943, HD 128311, HD 160691, Kepler 9, NN Ser, which are moving in the 2: 1 resonance, could have been captured into this resonance due to both the Type I and II migration with a wide range of parameters. The migration conditions are defined for the formation of HD 45364 and HD 200964 that are in the 3: 2 and 4: 3 first-order resonances, correspondingly. The results obtained for HD 200964 show that planets can be captured in the first-order resonances, when the outer-to-inner orbital period ratios for the planets are less than 3: 2, only if Type I migration rates are large, and the mass of at least one planet is substantially less than the modern masses of the observed giant planets. The formation of the HD 102272, HD 108874, HD 181433 and HD 202206 systems with planets in high-order resonances is considered. The capture into these resonances can be realized with very slow Type II migration. Possible bounds for migration parameters are considered. In particular, it has been found that the capture of HD 108874 into the 4: 1 resonance is possible only if the angle between the plane of planetary orbits and the plane of sky is appreciably less than 90°, i.e., the planetary masses are a few times larger than the minimum values. The capture of HD 202206 into the 5: 1 resonance is possible at low migration rates; however, another mechanism is required to explain the high observed eccentricity of the inner planet (for example, strong gravitational interaction between the planets). Resonant configurations can be disrupted due to the interaction between planets and remaining fragments of the planetesimal disk as, for example, may occur in the three-planet system 47 UMa. The specific orbital features observed for this system are explained.