Properties of Newtonian Potentials at Points of Free Space

Abstract

So far, we have studied potentials arising from given distributions of matter. But in many problems, the distribution is not known, and the potential must be determined by means of other data. Thus in higher geodesy, very little is known of the distribution of the masses except at the surface. But the forces can be measured on the surface, and from these the potential can be determined, approximately, at least. In order to solve problems given in terms of data other than the distribution of acting matter, we need more information on the properties of potentials. We first consider such properties at points exterior to the regions occupied by the distributions. Such points are called points of free Space.