On the existence of neutral directions of the normal gravity field

Abstract

A neutral direction of a gravity field is a direction along which the components of the gravity vector remain locally unchanged. A neutral point is a point at which there exists a neutral direction. This research will focus on the neutral directions for the normal gravity vector. The necessary condition for the existence of neutral directions at an arbitrary point P above the ellipsoid is that the determinant of the Eötvös matrix must be equal to zero. The slopes of these directions depend on the value of the principal curvatures and the curvature of the plumbline. In all cases the neutral directions lie on the meridian plane at point P. An interesting case is when the vertical gradient of normal gravity is equal to zero. Finally in the last two paragraphs we show that neutral points are not isolated in the three dimensional space and give a numerical example for the case of a spherical gravity field.