Newtonian dynamics of systems of extended bodies

Abstract

A consistent method for the description of the Newtonian dynamics of a bounded system composed of a number of perfect-fluid bodies of finite dimensions, with arbitrary internal structure and internal motions is presented. It is explored under what conditions the dynamical equations for such a system become formally the same as the corresponding ones valid for a system of point-masses. For this purpose a consistent and complete dynamical description of each one of the bodies of the system is simultaneously developed. The relative accuracy with which the dynamical equations describing bounded systems of point masses and bounded perfect-fluid bodies apply to systems of extended bodies, and the time-scale over which the application of these equations becomes doubtful are explicitly derived. Generally these two quantities depend on three ratios. From these ratios the first one depending on the internal structure and internal motions of each body represents its own contribution. The second, which is intimately related to the space density of the system, represents the contribution of the system as a whole. Finally, the third one being always a power of the ratio of the linear dimensions of the bodies over their mutual distances represents the interaction between each body and the system. In most of the cases of astrophysical interest the relative accuracies are small numbers, while the time scales are always much larger than the typical Keplerian orbital period of the corresponding system.