Distribution and size composition of the arctic lamprey Lethenteron camtschaticum in the North Pacific

Results of the long-term study of the spatial and vertical distribution of the parasitic anadromous Arctic lamprey Lethenteron camtschaticum (Tilesius, 1811) (Petromyzontidae) in the North Pacific and data on its size composition are given. This species is most frequent in the northwestern Sea of Japan and the western Bering Sea. The maximum concentrations are noted in waters of southern Primorye, southwestern Sakhalin, the northwestern part of the Sea of Okhotsk, and the northern part of the Bering Sea, which is probably explained by the increased number of its victims, Pacific salmon. Near the bottom, Pacific lampreys are extremely few and are primarily encountered at depths less that 400 m, and in the Pelagic zone, in the 100-m layer. The catches have contained Arctic lampreys having a total length of 15–79 cm. The lampreys of several size groups in the catches may indicate that L. camtschaticum spends not less than four years in the sea. No relationship has been found between the body length and the capture depth. Analyzed are the relationships between the body length and weight and the body length and the condition factor. The seasonal dynamics of these indices are considered.     

Resonances in the three-body problem with equal masses

Numerical simulations of near-resonant motions occurring in planar rotating systems of three bodies with equal masses are presented for the cases of prograde and retrograde motions of the inner and outer pairs. The ratios n: m of the initial periods of these pairs are within 1 ≤ m ≤ n ≤ 7. It is shown that, as a rule, retrograde are more stable than prograde motions. The k loop structures oriented inwards for prograde and outwards for retrograde motions are revealed. Empirical relations between k and n are found for the main resonances n: 1 and n: 2.     

Search for periodic orbits in the general three-body problem

An original method for searching for regions of initial conditions giving rise to close to periodic orbits is proposed in the framework of the general three-body problem with equal masses and zero angular momentum. Until recently, three stable periodic orbits were known: the Schubart orbit for the rectilinear problem, the Broucke orbit for the isosceles problem, and the Moore eight-figure orbit. Recent studies have also found new periodic orbits for this problem. The proposed method minimizes a functional that calculates the sum of squared differences between the initial and current coordinates and the velocities of the bodies. The search is applied to short-period orbits with periodsT < 10τ, where τ is the mean crossing time for the components of the triple system. Twenty one regions of initial conditions, each corresponding to a particular periodic orbit, have been found in the current study. A criterion for the reliability of the results is that the initial conditions for the previously known stable periodic orbits are located inside the regions found. The trajectories of the bodies with the corresponding initial conditions are presented. The dynamics and geometry of the orbits constructed are described.     

Trajectories of bodies in zones of rapidly decaying triple systems

The general three-body problem with equal masses and zero initial velocities is considered. Zones in which the triple systems decay over short times T < 10T _cr are distinguished in the domain of the initial conditions, where T _cr is the mean crossing time for a component of the triple system. These zones form distinct families of structures. Properties of the trajectories of bodies within these structures are described. The structures often display a layered character, with each layer corresponding to triple systems in which a particular body departs during the decay. These layers alternate with zones in which the decay does not occur on such short time scales, and the bodies are flung outward without this leading to a departure, or undergo simple interactions. In the zones of rapid decay, the departure of one of the bodies occurs after one or a few triple encounters between the components.     

Apsidal Motion in Detached Binary Stars: Comparison of Theory and Observations

A list of 62 detached binaries having reliable data on the rotation of the line of apsides is considered. Theoretical estimates of the rate of apsidal motion are obtained. These estimates are compared with observational data. It is shown that cases in which the theoretical estimate exceeds the observed value are several times more frequent than cases in which the theoretical value is lower than the observed one. This discrepancy increases when systems with more reliable observational data are considered.     

Approach-ejection correlation in the general three-body problem

The relations between parameters of triple approaches and the lengths of subsequent ejections are analyzed for the general three-body problem with components of equal masses and zero initial velocities. A statistically significant correlation is shown to exist between the closeness of approaches and the lengths of subsequent ejections: closer approaches generally result in longer ejections. We have found several systems that evolve to a temporary quasi-stable chain-like configuration.     

The region of stable motions around a periodic eight-like orbit in the general three-body problem

We investigate the neighborhood of the periodic eight-like orbit found by Moore (1993) and Chenciner and Montgomery (2000). One-, two-, and three-dimensional scans in body coordinates, velocities, and masses were constructed. We found the regions of initial conditions in which the maximum mutual separation did not exceed 5 distance units during 2000 time units (about 300 periods of the initial solution). Larger deviations from the periodic solution lead to distant body ejections and escapes. The identified regions of finite motions are complex in structure. In some sections, these are simple-connected manifolds, while in other sections, stability zones alternate with escape zones. We estimated the fractal dimensions of the stability regions in three-dimensional scans: it typically ranges from 2 to 3. In some cases, we found transitions between motions along the figure of eight in its neighborhood and motions in the vicinity of a periodic Broucke orbit in the isosceles three-body problem.     

Restriction of motions in wide pairs in the Galactic field

The motions of the components of wide binary stars in the solar neighborhood in the regular Galactic gravitational field on time scales ～10¹⁰ yr have been studied numerically. The regions of restricted motions of the components in wide pairs have been found depending on the initial conditions: the magnitude of the relative velocity of the components, their mutual distance, and the inclination of the relative velocity vector to the Galactic plane. The size of the main part of the region of restricted motions is approximately equal to the tidal radius. Profound changes in the eccentricity of the binary orbit occur at inclinations close to 90°, which can lead to close approaches of the stars with a pericenter distance less than 1 AU. In the case of retrograde motions (the binary rotates in a direction opposite to the Galactic rotation), there is a region of restricted motions extending at least to 10 pc. Examples of the trajectories of relative motion of the stars and the change in osculating orbital elements are given for systems with restricted motions.     

Optimization of the transfer trajectory of a low-thrust spacecraft for research of Jupiter using an Earth gravity-assist maneuver

The paper analyzes the possibility of the use of a gravity-assist maneuver for flight to Jupiter. The advantage of the Earth gravity-assist maneuver in comparison with the direct transfer in terms of reduction of amount of energy required per transfer is considered. Quantitative and qualitative evaluations of two transfer profiles are given.