Gravitational–tidal evolution of planetary subsystems of the Sun

Abstract

The results of some of our work and new research in which the motion of celestial bodies is considered to be subject to dissipative interactions is generalized in this article. In a number of problems the interaction of celestial bodies according to the law of universal gravitation is supplemented by a dissipative force. In the framework of this model, the evolution processes are studied, stationary configurations of an n-body systems are found, and their stability is investigated. In other problems the model of the axisymmetric celestial body that consists of a solid core and a viscoelastic mantle is considered. In such a model, the dissipation of energy under deformations is taken into account. The tidal evolution of a planet rotational motion is analysed in detail. Also phase portraits are constructed and an qualitative analysis of the global evolution of the dynamic characteristics of the Sun’s planetary subsystems is presented on the basis of averaged evolution equations.