Restricted four-body problem. The case of a central configuration: Libration points and their stability

We consider the problem of the motion of a zero-mass body in the vicinity of a system of three gravitating bodies forming a central configuration.We study the case where two gravitating bodies of equal mass lie on the same straight line and rotate around the central body with the same angular velocity. Equations for calculating the equilibrium positions in this system have been derived. The stability of the equilibrium points for a system of three gravitating bodies is investigated. We show that, as in the case of libration points for two bodies, the collinear points are unstable; for the triangular points, there exists a ratio of the mass of the central body to the masses of the extreme bodies, 11.720349, at which stability is observed.     

Method for studying the spatial-temporal structure of wave-like disturbances in the ionosphere

The method for studying the spatial-temporal structure and propagation characteristics of traveling ionospheric disturbances, using the spectral and cross-correlation analysis of electron density disturbances at different altitudes, obtained with the incoherent scatter radar and vertical sounding ionosonde, is considered. Different algorithms for detecting traveling ionospheric disturbances and calculating the total vector of the disturbance propagation velocity are presented. The results of the method application have been considered in detail, using September 11, 2005, as an example.     

The Hypothesis of Additional Acceleration in the Motion of Comet Harrington–Abell from Jupiter

By processing 494 observations of Comet Harrington–Abell, we obtained a unified system of elements that includes its turn around the Sun during which it closely approached Jupiter to a minimum distance of 0.037 AU in 1974. A study of the cometary orbit before and after the approach showed that, probably, at the approach of the comet to Jupiter, apart from the well-known gravitational perturbations, its motion was affected by an additional force. An improvement of the cometary orbit by assuming that an additional acceleration inversely proportional to the square of the distance to Jupiter exists in its motion yielded the following values: (4.57 ± 0.42) × 10^–10 and (–7.20 ± 0.42) × 10^–10 AU day^–2 for the radial and transversal acceleration components, respectively. As a plausible explanation of the changes in the cometary orbit, we additionally considered a model based on the hypothesis of partial disintegration of the cometary nucleus. The parameter that characterizes the instant displacement of the center of inertia along the jovicentric radius vector was estimated to be –1.83 ± 0.75 km. Based on a unified numerical theory of cometary motion, we determined the nongravitational parameters using Marsden's model for two periods: A ₁ = (11.68 ± 1.74) × 10^–10 AU day^–2, A ₂ = (0.53 ± 0.0357) × 10^–10 AU day^–2 for 1975–1999 and A ₁ = (5.92 ± 5.86) × 10^–10 AU day^–2, A ₂ = (0.08 ± 0.028) × 10^–10 AU day^–2 for 1955–1969, under the assumption that the nongravitational acceleration changed at the approach of the comet to Jupiter.     

Definition of a generalized diabatic circulation based on a variational approach

Diabatic-circulation diagnostics with the use of the distributions of heating rates and potential temperature requires that, in each particular case, a special and ambiguously defined correction to the stream function be introduced to turn a globally averaged vertical velocity to zero at any isobaric level. Up to now, the physical nature of this correction has been little explained and it has been usually written in a form that has not been substantiated to a sufficient extent. In this paper, this correction and its uncertainty are related to the eddy term, which is usually neglected in the concept of diabatic velocities. The decomposition of wave fluxes into advective and diffusion components is not unique. As a result, one can formulate a variational problem of minimizing the diffusion component of the wave flux and, thus, the problem of finding advective velocities, which involve the maximum of eddy-induced advection. A unique solution of this problem is obtained, and the relation of the solution to the “standard” diabatic circulation is studied. It is shown that, in the approximation of quasi-horizontal isentropes, the generalized diabatic stream function is identical with the “standard“ stream function. This result partially justifies the correction that is commonly used in calculations of the diabatic circulation.     

Extreme Storm Surges in the Gulf of Finland: Frequency-Spectral Properties and the Influence of Low-Frequency Sea Level Oscillations

Oceanology - An analysis of hourly tide gauge observation data yields time-frequency estimates of storm surges in the Gulf of Finland. Spectral analysis of long-term series made it possible to...     

Estimation of the Nucleus Size of Comet Shoemaker-Levy 9 under the Assumption of Its Step-by-Step Disintegration

The orbital dynamics of comet Shoemaker-Levy 9 was considered. The size of the nucleus before its disintegration was estimated using positional observations of individual fragments of the comet and taking into account the time when the fragment falls on Jupiter were observed. The center of inertia of the parent body was assumed to coincide with the center of fragment H at the moment of disintegration. The diameter of the parent body was estimated under different assumptions about the moments of disintegration. Thus, if the nucleus of the comet was disintegrated at the moment when fragment H was passing the perijovion, the diameter of the nucleus is equal to 1.39 km; if the nucleus was disintegrated two hours before the perijovion passage, the estimate of the nucleus diameter must be increased up to 9.03 km. The period of revolution of the comet nucleus was estimated assuming that the comet rotated about the axis perpendicular to its orbital plane. The calculations allowed us to assume that fragmentation of the nucleus began approximately an hour before the comet passed the perijovion and the diameter of the parent nucleus was about 4 km.     

Comparison of the electron density variations measured with instruments of the ISZF SO RAN radar complex under the conditions of different geomagnetic disturbance

The variations in the electron density measured with the incoherent scatter radar, DPS-4 digisonde, and FMCW ionosonde are compared in this work. The main regularities in differences are explained by the effect of different-scale ionospheric irregularities. Considerable morning gradients of electron density result in that ionosondes give increased values as compared to the incoherent scatter radar data. Electron density disturbances measured with different instruments can be of correlated and uncorrelated character. Uncorrelated disturbances are explained by intense medium-scale ionospheric irregularities. Correlated disturbances are caused by large-scale irregularities. Observation of such disturbances can be used to determine the velocity and direction of a disturbance.