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On the probabilistic model of the Kordylewski cosmic dust cloudsтезисы доклада
- Авторы: Salnikova T.V., Stepanov S.Ya, Shuvalova A.I.
- Сборник: The Seventh Moscow Solar System Symposium (7M-S3)
- Тезисы
- Год издания: 2016
- Место издания: Российская Академия Наук Москва
- Первая страница: 103
- Последняя страница: 103
- Аннотация: The Seventh Moscow Solar System Symposium (7M-S3) Moscow 2016 On the probabilistic model of the Kordylewski cosmic dust clouds Salnikova T.V.1, Stepanov S.Ya.2, Shuvalova A.I.3, 1,3 Lomonosov Moscow State University, GSP-1, Leninskie Gory, 119991, Russia; 2 Dorodnicyn Computing Center, FRC CSC RAS, Vavilov st. 40, 119333, Russia. Con- tact: tatiana.salnikova@gmail.com Introduction: Within the mathematical model of Kordylewski clouds, the probability of formation of dust clouds in the vicinity of triangular libration points of the Earth–Moon system taking into account pertur︎bation from the Sun is investigated. In the perturbed problem, Lyapunov stable triangular libration points become unstable. However, the Polish astronomer K. Kordylewski observed and photographed cosmic dust clouds near the libration point L5. It might be sup︎posed that Kordylewski observed clouds in the vicinity of periodic motion that were in the line of sight of the triangular libration points at the time of observation. Problem setting: The problem of determining the phase︎ space distribution function for the system of the non︎ interacting dust particles for the mathematical model of cosmic dust Kordylewski clouds—clusters of the non︎interacting dust particles in the vicinity of the triangular libration points of the Earth–Moon–Particle system taking into account perturbation from the Sun was considered. Let us consider an ensemble of particles with the same mass and the same probability density distribu︎tion functions in the vicinity of the Lagrangian libra︎tion points. If there is no interaction between the par︎ticles, the ensemble is statistically equivalent to the test particle P(x, y, u, v) with the mass mP and the distribu︎tion function ρ(x, y, u, v, t) is described by the Liou︎ville equation. It is a homogeneous linear partial differential equation of the first order. Its solution is constant along the characteristics, the equations of which coincide with the equations of motion of the particle. The probabilistic model of formation of the concentrations of cosmic particles based on integration of the Liouville equation for the probability density distribution function was in qualitative agreement with the known observed clusters of Trojan asteroids in the unperturbed Sun-Jupiter- Asteroid system. In the circular restricted three︎ body Earth–Moon– Particle problem, when we consider the periodical per︎turbation of the Sun, each of the Lagrangian libration points is captured by the two periodical stable orbits. Stability of the periodic solution implies that, in the case of small deviations of coordinates and velocities from periodic motion, we should see an ensemble of particles, moving in the vicinity of this periodic motion. In order to estimate the probability of formation of cos︎mic dust clouds, the Liouville equation is considered, which gives us the time evolution of the phase ︎space distribution function for the system of the non︎interact︎ing dust particles. The numerical integration of the Liouville equation in the vicinity of a periodic solution shows an increase in the density at the current position of the point on a periodic trajectory. Hence, in this model the numerical analysis shows the probability of formation of dust clouds. Conclusion: The results based on integration of the Liouville equation are in a good agreement with the parameters of the Kordylewski cloud that were shown by the Poincaré map for the equation of motion of the particle. The probabilistic model con︎firmed the findings of the existence and observation condition of Kordylewski clouds.
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