A gravitational eye: a method for extracting maximum information from gravitational potentials

Gravity measurements have uses in a wide range of fields including geological mapping and mine-shaft inspection. The specific application under consideration sets limits on the survey and the amount of information that can be obtained. For example, in a conventional gravity survey at the Earth’s surface a gravimeter is translated on a two-dimensional planar grid taking measurements of the vertical component of gravity. If, however, the survey points cannot be chosen so freely, for example if the gravimeter is constrained to operate in a tunnel where only a one-dimensional line of data could be taken, less information will be obtained. To address this situation, we investigate an alternative approach, in the form of an instrument which rotates around a central point measuring the gravitational potential or its radial derivative on the boundary of a sphere. The ability to record additional components of gravity by rotating the gravimeter will give more information than obtained with a single measurement traditionally taken at each point on a survey, consequently reducing ambiguities in interpretation. We term a device which measures the potential, or its radial derivatives, around the surface of a sphere a gravitational eye. In this article we explore ideas of resolution and propose a thought experiment for comparing the performance of diverse types of gravitational eye. We also discuss radial analytic continuation towards sources of gravity and the resulting resolution enhancement, before finally discussing the possibility of using cold-atom gravimetry and gradiometry to construct a gravitational eye. If realised, the gravitational eye will offer revolutionary capability enabling the maximum information to be obtained about features in all directions around it.