On the stabilization of the collinear libration points of the restricted circular three-body problem

The possibility of stabilizing the collinear libration points of the circular restricted three-body problem by using an additional jet acceleration (constant in magnitude) is investigated. Three stabilization laws are considered when the jet acceleration is either directed continuously to one of the primariesm ₁,m ₂ or is parallel to the line joining them. The solution of the problem formulated is based on the method of the driving forces structure analysis created by W. Thomson and P. Tait. It is shown that none of the stabilization laws mentioned ensures the existence of the isolated minimum of changed potential energy, and therefore the secular stability of the collinear libration points is impossible. In the 3rd and 4th paragraphs the possibility of a gyroscopic stabilization of these points is considered. It is shown that the gyroscopic stabilization of the external libration points is possible only when jet acceleration is either directed to the distant mass or is parallel to the line joining the primaries. The necessary and sufficient conditions of the gyroscopic stabilization are given. It is also shown that the internal libration points cannot be stabilized by any of the laws considered. For the Earth-Moon system the numerical data of time-existence of the satellite in the vicinity of the libration point situated near the Moon are given.     

Regional features of atmospheric manifestations of tropical cyclones according to ground-based GPS network data

Using statistically significant data, we show that the GPS observation method is efficient for revealing the response of the upper atmosphere to global synoptic processes with the help of correlation techniques.     

On the collinear libration points in the photo-gravitational three-body problem

The existence of the three-parametric family of the collinear-libration points in the photo-gravitational three-body problem (differing from the classical one by the addition to the gravitational field the light repulsion force-field) is proved. The number and situation of these points are determined with respect to the system parameters. Their stability to a first approximation is investigated. It is shown that oppositly to the classical problem the internal collinear libration-points may be stable in some domain of parameter-space.     

Equatorial ionosphere: IRI and NeQuick modeling vs. radio tomographic imaging

The outputs of the IRI-2001 and NeQuick ionospheric models are compared with radio tomographic (RT) images of the ionosphere near the crest of the equatorial anomaly (EA) between Manila and Shanghai (about 850 cross sections overall). The values of the slant total electron content measured in an RT experiment as opposed to the corresponding values derived from the IRI-2001 and NeQuick models are analyzed. A comparison of model cross sections and ionosonde measurements revealed discrepancies in the critical frequencies of the ionospheric F2 layer, which were the strongest in the region of high spatial gradients close to the crest of the EA. The specific features of the dynamics of the EA are discussed based on the results of the models and radio tomography. Our analysis has shown that the IRI-2001 and NeQuick models mainly reproduce the “plasma fountain effect” but are incapable of recognizing the stable structural features of the EA observed on RT reconstructions, for example, the daytime orientation of the mature core of the EA parallel to geomagnetic field lines. A method to correct the IRI-2001 and NeQuick models in the vicinity of the EA crest is suggested.     

A ring of traveling ionospheric disturbances around Moscow megapolis

Doklady Earth Sciences - According to interferometric data of radio waves from GPS satellites, which are received in Moscow region on the stations of the Moscow Navigation-Geodesic Support Network...     

Modeling of vertical sounding ionograms for nonmonotonous ionospheric layers

The problem of radiosignal reflection from a plane layered isotropic ionosphere has been considered. The vertical sounding ionograms for ionospheric layers with a complicated structure have been modeled. It has been demonstrated that the structure of reflected signals depends on the degree of ionospheric irregularities. Diffuse reflection of radiosignals, caused by the vertical irregularity of the ionosphere, has been detected.     

On the stability of Laplace's solutions of the unrestricted three body problem

The instability criterion of a nonlinear mechanical system neutral to the first approximation is formulated for the internal resonance case which is characterized by the existence of commensurabilities between the frequencies of the system.The criterion derived is used for determining the regions of instability of Laplace's constant triangular solutions of the unrestricted three-body problem. It is shown that in the region where necessary Routh-Joukovsky's stability conditions are satisfied there may exist eight resonanceunstable sets of the masses of the three bodies. These sets may be mechanically interpreted as follows: in the case of resonance instability the barycentre of the equilateral triangle formed by the three bodies is located on one of the eight circles constructed in the geometrical centre of this triangle.     

To the problem of satellite's perturbed motion under the influence of solar radiation pressure

A possibility of developing the analytical theory of perturbed motion for a balloon-satellite influenced by solar radiation pressure force is analysed here on the basis of the limit case modification of the two fixed centers problem whose force-field is a superposition of the Newtonian central field and a homogeneous one. Such an approach enables us in the intermediate orbit already to take into account the effect of a constant force, all coordinates of a satellite being expressed as functions of some monotonically increasing variable by means of inversion of elliptic quadratures. The relations between canonical constants of the intermediate orbit and a quasikeplerian elements coinciding in the absence of solar radiation pressure with keplerian ones are derived. The numerical results and illustrating the perturbations in the radius-vector of the intermediate orbit of a balloon-satellite of the Echo-I type are given.

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On the stability of triangular libration points of the photogravitational restricted circular three-body problem

This paper considers the restricted circular three-body problem with respect to the radiation repulsion force acting upon a particle on the part of one of the main bodies (the Sun). The characteristic of the family of stationary particular solutions of the problem (libration points) representing the relative equilibrium positions in a rotating Cartesian system is given. On the basis of the KAM theory with the help of a computer a nonlinear analysis of the triangular libration points stability for the planar case is carried out. These libration points are proved to be strictly stable by Liapunov practically in the whole area of fulfilling the necessary stability conditions. Instability is discovered at the resonant curve of the third order and at the greater part of the resonant curve of the fourth order. The plotted results of the investigation allowed us to draw a conclusion about the Liapunov stability of the triangular libration points in a problem with respect to the radiation pressure for all the planets of the Solar system.