Vector integral representations in gravimetry

In the theory of gravitation, usually a potential function is introduced to describe the gravity field. This has the advantage that Green’s integral representations of potential theory can be used in a straight-forward manner. However, the introduction of a scalar potential also has some disadvantages. Although the potential can be associated with the work done when moving around a point mass in a gravitational field, it still is a somewhat artificial quantity that cannot directly and unambiguously be measured. This is in contrast with the gravitational field strength. In the present paper we investigate the possibility of avoiding the introduction of a gravitational potential and concentrate on the gravitational field vector itself. In that case, appropriate vector integral representations of the Green type have to be derived for the gravitational field. It turns out that these vector integral representations are also suited for describing the gravity field of the earth.