Dynamic status of the wide multiple system α Centauri + Proxima

We study the dynamics of a wide multiple system α Centauri + Proxima. The total energy of the system was estimated according to the available observational data on masses, coordinates, proper motions, and radial velocities of its components. To account for the effect of the observational data errors on the result, we have implemented the Monte Carlo method. From N = 10⁶ statistical tests we show that with the probability of about 90% the motion is hyperbolic, i.e., α Cen AB and Proxima will after a while diverge from each other by a considerable distance. We also perform numerical modeling of dynamic evolution of the wide pair α Cen AB + Proxima in the regular field of the Galaxy. The trajectory of relative motion is constructed. The components diverge from each other by a distance of 20 pc over the time scale of about 200 Myr. The critical parameter for determining the dynamic status of the system is the radial velocity of the C component (Proxima), known with an error of 200 ms^?1. For a reliable determination of the nature of motions in the system, we have to decrease the radial velocity error by at least an order of magnitude.     

Abundances of elements of the palladium group in the atmospheres of evolved stars. II. Ruthenium

Principal Astronomical Observatory, Ukrainian Acadey of Sciences. Translated from Astrofizika, Vol. 32, No. 2, pp. 231–234, March–April, 1990     

The Lyapunov exponents in the dynamics of triple star systems

The dynamics of weakly heirarchical triple stars with equal masses are considered. Full spectra of the Lyapunov exponents are found via numerical integration of the orbits, for various initial configurations of the systemin the planar problem and with initial conditions in the vicinity of the 2 : 1 resonance (i.e., with the initial ratios of the periods of the outer and inner binaries being close to 2 : 1). Dependences between the Lyapunov time and the disruption time of the systemare constructed for initial conditions near and far from resonance. The character of these relationships is different near and far from resonance, corresponding to two kinds of Hamiltonian intermittency. The trajectories “stick” to the regular component in phase space near resonance, while this effect is not dominant far from resonance. Analysis of the distributions of the disruption times of the triple systems for initial conditions near and far from resonance confirm these conclusions.     

Stability regions in the vicinity of a periodic Ducati orbit

One- and two-dimensional sections of the region of initial conditions in the vicinity of a periodic Ducati orbit have been studied in detail in the plane equal-mass three-body problem. A continuous stability region generated by the periodic Ducati orbit has been revealed. In addition, a number of other stability regions that are probably related to stable hierarchical triple systems have been found. Several specific trajectories from the stability regions and in the boundary zones are analyzed.     

The orbital dust torus as an enveloping surface of a family of trajectories of isotropically ejected particles

Meteorite impacts onto a small satellite lead to the ejection of a regolith mass, which is much greater than the impactor mass, into cosmic space. Assume that an isotropic ejection with velocities smaller than the maximum possible velocity b took place at the time moment t ₀. Since the orbital periods are unequal, the particle trajectories will densely fill a certain domain D. The same domain will be filled after an explosion of an artificial satellite moving in a high orbit. One to three months later, the node and pericenter longitudes will be distributed over the entire circle and the domain D will become a body of revolution, a topological solid torus. We examine the domain of possible particle motion and its boundary S immediately after the impact event (an unperturbed case) and the same domain under the assumption that the initial longitudes of nodes and pericenters were already a result of considerable changes (a perturbed case). In both cases, we managed to construct the domain D and its boundary S analytically: parametric equations containing only relatively simple functions were obtained for S. The basic topologic and differential-geometric properties of S were studied completely.     

Atmospheric circulation epochs and climate changes

The atmospheric circulation studies allow climate changes to be diagnosed and forecasted. Variations in occurrence frequencies of the atmospheric circulation forms W, E, and C (by the Vangengeim classification) and Z, M ₁, and M ₂ (by the Girs classification), which characterize climatic conditions in most of the Northern Hemisphere, are analyzed over a period of more than 100 years. It is shown that the occurrence frequency of the forms W, C, and M ₁ continually decreased, while that of the forms E and Z increased, which indicates a significant change in atmospheric circulation in the Northern Hemisphere during the last century. The occurrence frequency of the forms C and Z demonstrates specific features at inter-decade time scales. Correlations are found between accumulated sums of anomalies of occurrence frequencies of the atmospheric circulation forms C, (W + E), Z, and (M ₁ + M ₂) and inter-decade variations of the Earth’s rotation. The causes of these relationships are discussed along with possibilities of their use for diagnosis of climatic variations in the Northern Hemisphere.     

Analysis of regions of stability in the vicinity of a new periodic S orbit in the three-body problem

The vicinity of a periodic S orbit in the three-body problem with bodies of equal mass is investigated. It is shown that there exists a region of stable motions that preserve the form of the initial periodic orbit. Various sections describing this region are considered. Some specific trajectories from the region of stability and near the boundary of this region are analyzed. Several other regions of stability that are apparently associated with other periodic orbits have also been identified.     

Investigation of karst ice caves with the aid of remote sensing techniques

Considered are some results of radio sensing conducted for the Kheetei karst ice cave in Zabaikalskii region. The cave roof was investigated by the active and passive radar techniques and infrared imaging. Revealed were sources of heat, air flows and the dislocation of rocks along the fissure under the hoar-frost layer. This technique may be used in regular measurements in order to study both changes in conditions of hollow subterranean formations and thermal processes in the environment.     

Dynamical stability of the quadruple systems HD 68255/6/7 and HD 76644

We analyze the dynamical stability of the hierarchical quadruple systems HD 68255/6/7 and HD 76644 via numerical integration of the equations of motion of the four-body problem, with a chainlike regularization of close stellar interactions. The observational errors were taken into account using Monte Carlo simulations, assuming that they possessed a Gaussian distribution. HD 68255/6/7 is probably stable, while HD 76644 is unstable with a probability exceeding 0.97 and with a disruption time of no more than 10⁵ years. The influence of the observational errors and possible scenarios for the formation of unstable multiple stars are discussed.     

Motion in the field of a rotationally symmetric potential: Exact use of an approximate equation for the derivative of the field of directions along the normal to a trajectory

The previously derived equation (Agekyan 1974) for the derivative ?f/?n of the field of directions along the normal to a trajectory is approximate, because differentiating along the normal takes the point out of the orbit and changes the third integral of motion. However, on the envelope of the trajectory, i.e., on the contour of an orbit or a fold, ?f/?n undergoes a discontinuity of the second kind. Many authors have used this property to find points of the contours of orbits and folds. Although the integrable equation is approximate, the envelope points are determined accurately.