ABSTRACT

This chapter deals with power moment problem in celestial mechanics, and examines a physical system or a body or an object of known total finite mass m < ∞. It shows how to determine how the mass m is spatially distributed across the body. Specifically, assuming that the investigated system possesses K constituents, each of which has the elementary mass mk(1 = k = K), the chapter shows how to find out how these mass points are distributed by preserving total mass m. The concern here is to use the simplest arguments to arrive straight to the main point of emergence of the moment problem for determining the distribution of mk in the studied system. For this purpose, the chapter simplifies the analysis by further assuming that the examined object has rotational symmetry.