New Approaches on the Theory of Planetary Sciences: Applications of Non-Classical Equations of Mathematical Physics for Plasma Models of Jupiter’s Magnetosphere

Abstract

In this paper, considered non-classical equations of mathematical physics are applied in the fields of astronomy and astrophysics in the case of plasma models of Jupiter’s magnetosphere. It is known that non-classical equations of mathematical physics have applications in gas dynamics, aerodynamics, hydrodynamics, and magneto-hydrodynamics. According to comparisons and observation results of Pioner-10, 11, and Voyager 1-2, considered mathematical models of Jupiter’s magnetosphere, which is cold plasma, as searches of Jupiter’s Io. At first, the mathematical justification of the physical process of Io concerning plasma was described by a non-classical equation of the Keldysh type. For this reason, using MHD equations for the derivation of the model equations of cold plasma and hot plasma on Jupiter’s magnetosphere. In the region tail of Jupiter given analyses of basic model equations of the Jupiter magnetosphere for the equilibrium between magnetic force, pressure gradient, and centrifugal force in the presence of plasma rotations. Additionally, based on the basic theoretical and observational results, the role of the Alfven Mach number with a constant Euler potential parameter in the region tail of Jupiter’s magnetosphere proves the justification of the steady magneto-hydrodynamic equilibrium. As agreed previously in the results of observation Voyager 1,2. Therefore, in the magnetosphere, Jupiter’s hot and cold plasma describe the same class equation of Keldysh-Tricomi types. In this case, the exact solution is obtained by integrals, which are first expressed as analytical formulas. Theoretical aspects of the model hot and cold plasma on the tail magnetosphere contain concepts of reconnection, which connects lost mass from Jupiter’s Io. Such an effect reconnection coronal problem as Parker’s also occurs by lost temperature and energy dissipation. Lorentz force, supported by means of solar wind, changes cold plasma to hot plasma in cases where a magnetic disk acts as a balancing mechanical equilibrium to retain cold-hot plasma. For motivation, both mathematical and physical, we used some figures, a table, and an appendix. Note that considered approaches to the theory of planetary sciences at first time applicable for Jupiter.