Investigation of the Influence of the Field of Co-Rotation on the Possibility of the Long-Term Orbital Existence of Submicron Particles in the Plasma-Sphere of the Earth

The problems of the dynamics of fine-dispersed particles in near-Earth space (NES) are actively considered for more than 30 years in connection with the problem of manmade pollution of near space by manmade micro-particles (MP). At the same time, the main attention is paid to the determination of the characteristics of man-made MP and the conditions for their injection into NES, capable of long-term holding in near-Earth space. As a result of the conducted researches it was established that the large orbital existence times in the NES can have fairly large particles with dimensions of the order of 1-100μm. At the same time, the fundamental possibility of prolonged holding of manmade particles of submicron sizes in the vicinity of the Earth was questionable, since, as shown by numerical simulation data on the dynamics of particles with dimensions of the order of 0.11μm in the NES, the orbital lifetimes of MPs of the indicated sizes, as a rule, when injected at high altitudes by a disturbing effect of the solar pressure force [1,2] and in low Earth orbits by the residual gas resistance of the upper atmosphere [3,4]. For the first time studies of the dynamics of smaller particles with dimensions less than 0.1μm were carried out by us in [5,6]. Received in [5,6] the results of numerical modeling of the motion of these particles in the Earth’s plasma-sphere showed that, in contrast to the previously considered submicron particles with dimensions of the order of 0.1-1μm, particles with dimensions less than 0.1μm (on the order of tens of nm) under certain conditions as a result of disturbing effects on their the movement in the NES of the Lorentz force acting on the electric charge accumulating on the MP from the magnetic and electric fields of near-Earth space is able to be held for a long time in the near-Earth space and may be, therefore, an important factor of manmade pollution of near space. In connection with the foregoing, it became necessary to carry out fundamental theoretical studies of the conditions for the “capture” of submicron particles in the vicinity of the Earth, including, on the basis of the application of appropriate analytical methods. In the work [7], we showed that under certain model assumptions about the number, nature, and method of determining perturbing forces acting on MP, the problem of the dynamics of submicron particles in the plasma-sphere admits a canonical formulation in the form of a Hamiltonian system of equations. In this case a basis for an analytic study of the properties of motion are methods of the qualitative theory of Hamiltonian systems developed in the papers of Kolmogorova AN, Arnold VI and Moser J (the so-called KAM-theory) [8,9]. Using well-known methods of KAM-theory, we in [10,11] proved that in the Earth’s plasma-sphere, the weakly elliptic orbits of micro-particles with dimensions on the order of tens of nm and a quasi-equilibrium charge retain their shape. However, in the model used in [10,11], we did not take into account the electric field of co-rotation. In this paper the influence of the electric field of co-rotation on the possibility of prolonged holding of these micro-particles is considered with the help of analytical and numerical methods.