Stability of the multiple star system ι UMa (ADS 7114)     

A. V. Mel’nikov  V. V. Orlov  I. I. Shevchenko 《Astronomy Reports》2014,58(9):640-649

The physical and orbital parameters of the quadruple star system ι UMa (HD 76644 = ADS 7114) were determined earlier, when it was concluded based on modeling the system’s dynamics and applying theoretical stability criteria that the system was probably unstable. Here the stability of the ι UMa system is studied by calculating the Lyapunov characteristic exponents for representative sets of parameters and initial conditions. The conclusions on the system’s stability (or instability) based on various stability criteria and the calculated Lyapunov exponents are compared. The instability of the system as a whole is confirmed rigorously based on massive computations of the Lyapunov exponents. This system appears to be the only known multiple system whose instability has been rigorously established. The Lyapunov time-disruption time statistical relations are constructed, which show that the Hamiltonian intermittency of the second kind dominates. Typical disruption times are shorter than 1000 years, and the Lyapunov times are shorter than 100 years.  相似文献   

The multiple system ADS 9626: A quadruple star or an encounter of two binaries?     

O. V. Kiyaeva  R. Ya. Zhuchkov  E. V. Malogolovets  V. V. Orlov  A. V. Glukhova  Yu. Yu. Balega  I. F. Bikmaev 《Astronomy Reports》2014,58(11):835-848

The parameters of the quadruple system ADS 9626 (µ Boo) are analyzed. The system consists of two double stars: the Aa pair with an angular separation of ρ = 0.08″ and the BC pair with an angular separation of ρ = 2.2″, separated by ρ = 107″ and having the same parallaxes and proper motions. Position observations with the Pulkovo 26″ refractor have yielded from direct astrometric measurements the difference in the apparent magnitudes and the component-mass ratio for the BC subsystem: Δm = 0.59 ± 0.06, M(B)/M(C) = 1.18 ± 0.02. Spectroscopy with the Russian-Turkish 1.5-m telescope has yielded the radial velocities and physical parameters of the Aa, B, and C components. Speckle-interferometric observations with the 6-m telescope of the Special Astrophysical Observatory have provided the first measurements of the magnitude difference in the close Aa subsystem: Δm = 0.46 ± 0.03 (λ = 5500 Å) and Δm = 0.41 ± 0.03 (λ = 8000 Å). The new observations are consistent with the known orbits, which were used to find the radial velocities for the centers of mass of the inner subsystems. Themotion of the outer pair, Aa-BC, is studied using the apparent motion parameters (AMP) method. It is not possible to derive an elliptical orbit for this pair; the elements of a hyperbolic orbit have been estimated. The difference of the heavy-element abundances for the Aa and BC subsystems of 0.5 dex confirms that these pairs have a different origin. This suggests that we are observing here a close encounter of two binary stars.  相似文献   

Disintegration process of hierarchical triple systems II: non-small mass third body orbiting equal-mass binary     

M. M. Saito  K. Tanikawa  V. V. Orlov 《Celestial Mechanics and Dynamical Astronomy》2013,116(1):1-10

The stability limit of coplanar hierarchical triple systems is numerically studied. Systems we investigated consist of two equal mass bodies initially on a circular orbit and third body with various masses, which at the maximum are equal to the mass of the binary. In order to estimate the stability limit, we use an empirically-found fact that the system is quasi-periodic if the initial eccentricity of the outer binary is less than some critical value, otherwise the third body eventually escapes. We make an analytical expression for the stability limit in terms of the ratio of the orbital radii and find that the expression improves the previous criteria. The resultant expression also suggests that the ratio of the orbital radii rapidly approaches to a certain value (e.g. $\sim $ 2, in an initially circular outer binary) as the mass of the third-body tends to zero.  相似文献   

Disintegration process of hierarchical triple systems. I. Small-mass planet orbiting equal-mass binary     

M. M. Saito  K. Tanikawa  V. V. Orlov 《Celestial Mechanics and Dynamical Astronomy》2012,112(3):235-251

The stability of hierarchical triple system is studied in the case of an extrasolar planet or a brown dwarf orbiting a pair of main sequence stars. The evolution of triple system is well modelled by random walk (RW) diffusion, particularly in the cases where the third body is small and tracing an orbit with a large eccentricity. A RW model neglects the fact that there are many periodic orbits accompanied by stability islands, and hence inherently overestimates the instability of the system. The present work is motivated by the hope to clarify how far the RW model is applicable. Escape time and the surface section technique are used to analyse the outcome of numerical integrations. The analysis shows that the RW-like model explains escape of the third body if the initial configuration is directly outside of the KAM tori. A small gap exists in (q ₂/a ₁, e ₂)-plane between locations of the stability limit curves based on our numerical study and on RW-model (the former is shifted by –1.4 in q ₂/a ₁ direction from the latter).  相似文献   

Dynamics of groups of galaxies in different models of gravitation     

O. B. Beketov  V. V. Orlov 《Astrophysics》2012,55(1):21-33

A series of numerical experiments is carried out to simulate the dynamical evolution of groups of galaxies in different models of gravitation. The simulation results are compared with observations of the Local Group and of the CenA/M83 and M81/M82 galactic groups. It is found that the LCDM model and the MOND (Modified Newtonian Dynamics) model are in substantially better agreement with the observations than the other two models examined here. The dispersion in the velocities relative to Hubble’s law in these models is small, but the MOND model yields slightly elevated values. For initial conditions close to virial equilibrium, the mean square deviations in the velocities of the galaxies are ~30 km/s, in agreement with observational estimates.  相似文献   

A nonhydrostatic model of the global circulation of the atmosphere of venus     

I. V. Mingalev  A. V. Rodin  K. G. Orlov 《Solar System Research》2012,46(4):263-277

The mechanisms of the global circulation in the atmosphere of Venus have been studied with the use of numerical models. To calculate the heating/cooling of the atmosphere due to absorption/emission of electromagnetic radiation under initially weak and strong superrotation of the atmosphere, the complete system of gas dynamics equations in the relaxation approximation was considered. It has been shown that at sufficiently high rates of heating of the atmosphere by radiation on the day side and at sufficiently high rates of cooling on the night side, a thermal tide develops at altitudes of 40?C70 km, and its energy and impulse is transferred to the zonal superrotation of the atmosphere. Due to the interaction between the superrotation and the meridional transfer of the air mass through the polar region from the day side of the planet to the night side, near-polar vortices are formed at altitudes of 40?C70 km near the morning terminator.  相似文献   

The rectilinear three-body problem     

Victor Vladimirovich Orlov  Anna V. Petrova  Kiyotaka Tanikawa  Masaya M. Saito  Alija I. Martynova 《Celestial Mechanics and Dynamical Astronomy》2008,100(2):93-120

The rectilinear equal-mass and unequal-mass three-body problems are considered. The first part of the paper is a review that covers the following items: regularization of the equations of motion, integrable cases, triple collisions and their vicinities, escapes, periodic orbits and their stability, chaos and regularity of motions. The second part contains the results of our numerical simulations in this problem. A classification of orbits in correspondence with the following evolution scenarios is suggested: ejections, escapes, conditional escapes (long ejections), periodic orbits, quasi-stable long-lived systems in the vicinity of stable periodic orbits, and triple collisions. Homothetic solutions ending by triple collisions and their dependence on initial parameters are found. We study how the ejection length changes in response to the variation of the triple approach parameters. Regions of initial conditions are outlined in which escapes occur after a definite number of triple approaches or a definite time. In the vicinity of a stable Schubart periodic orbit, we reveal a region of initial parameters that corresponds to trajectories with finite motions. The regular and chaotic structure of the manifold of orbits is mostly defined by this periodic orbit. We have studied the phase space structure via Poincaré sections. Using these sections and symbolic dynamics, we study the fine structure of the region of initial conditions, in particular the chaotic scattering region.  相似文献   

The technique of ethnogeodemographic research     

A.Yu. Orlov 《Geography and Natural Resources》2009,30(1):73-78

The theoretical and methodological foundations of a new interdisciplinary research area, ethnogeodemography, are considered. The subject matter of ethnogeodemography is the territorial and ethnic differentiation of demographic processes in a large polyethnic region. The algorithm of ethnogeodemographic research has been developed.  相似文献   

Manifestation of gravitational tides and planetary waves in long-term variations in geophysical parameters     

B. G. Shpynev  A. V. Oinats  V. P. Lebedev  M. A. Chernigovskaya  I. I. Orlov  A. Yu. Belinskaya  O. M. Grekhov 《Geomagnetism and Aeronomy》2014,54(4):500-512

Long-term variations in the parameters of the Earth’s upper atmosphere and geophysical activity have been studied based on the current spectra. The main sources of quasiperiodic oscillations in the atmosphere (including variations in the solar radiation, geomagnetic activity, and gravity) have been considered. It was shown that the most stable quasiharmonic variations are related to tidal gravitational oscillations and Rossby planetary waves with stable spectra. These oscillatory processes substantially contribute to the dynamics of the middle and upper atmosphere and manifest themselves in ionospheric parameters.  相似文献   

The ecology, distribution, and abundance of midwater fishes of the Subarctic Pacific gyres     

R. J. Beamish  K. D. Leask  O. A. Ivanov  A. A. Balanov  A. M. Orlov  B. Sinclair 《Progress in Oceanography》1999,43(2-4)

We describe the distribution and abundance of the midwater fish community, between 200 m and 500 m, in the North Pacific. The main area of interest was the Subarctic Pacific gyres, but we include species from the Bering Sea and the Sea of Okhotsk. There were 196 species identified in each gyre, 38 of which were common to both gyres. The most abundant species belong to the family Myctophidae and the most ecologically important myctophid probably is Stenobrachius leucopsarus. This species could have a biomass of approximately 21 million tonnes (t) in the Subarctic Pacific (including the Bering Sea and Sea of Okhotsk). S. leucopsarus is a small (about 8 cm maximum length) fish that lives up to 7 years. It is prey for a variety of other fishes, birds and mammals and may migrate into the mixing layer each evening where it feeds mainly on euphausiids and copepods.The total abundance of midwater fishes appears to be large relative to total catches of other fish in the same areas. The vertical migratory behaviour of some of the residents provides a mechanism to transfer production out of the mixing layer. The movement into the surface layer by some fishes at night indicates that dynamic changes occur in the midwater community between the day and night, and the ecosystem dynamics in the surface layer are different in the day and in the night. This behaviour and the huge biomass relative to commercial species means that the dynamics of fish communities in the Subarctic Pacific are complex and need to be studied over a 24 hour period. The large biomasses may eventually attract commercial interest, thus it is important to establish international, cooperative programs now to learn more about the dynamics of these populations and the relationships with other species.  相似文献