New Forms of the Perturbed Motion Equation

Abstract

Real celestial bodies are neither spherical nor solid. Celestial bodies are unsteady, in the process of evolution their masses, sizes, shapes and structures are changes. The paper considers a model problem proposed as an initial approximation for the problems of celestial mechanics of bodies with variable mass. Based on this model problem, perturbation theory methods are developed and new forms of the perturbed motion equation are obtained. The model problem as the problem of two bodies with variable mass in the presence of additional forces proportional to speed and mutual distance is a class of intermediate motions. This class of intermediate motions describes an aperiodic motion along a quasiconical section. In this paper, on the basis of this class of aperiodic motion over a quasiconical section, various new forms of the perturbed motion equation in the form of Newton's equations are obtained. Based on the known equations of perturbed motion for the osculating geometric elements p, e, , i, , in the form of the Newton equation, we obtained the equations of perturbed motion for the following system of osculating elements p, e, i, , , and a, e, i, , , . Oscillating variables involving a dynamic element are suitable in the general case. A system of variables, where instead of the dynamic element is introduced - the average longitude in orbit is used in the quasielliptic case . The obtained new forms of the equation of perturbed motion, in the form of Newton's equations, in various systems of osculating variables can be effectively used in the study of the dynamics of non-stationary gravitating systems.

To the dynamics of the two-body problem with variable masses in the presence of reactive forces

“…Real celestial bodies are nonstationary, their masses, sizes, shapes and structures change during evolution Eggleton (2006). In this connection, we investigated the problem of two spherical celestial bodies in the general case when the masses of the bodies change nonisotropically at different rates in the presence of reactive forces Minglibayev (2012), Minglibayev et al (2020).…”