The self-attraction correction for the FG5X absolute gravity meter

The gravitational attraction of the body of a gravity meter upon its own proof mass is sometimes called the self-attraction. The self-attraction is a source of systematic error for absolute measurements of g, the acceleration of an object due to Earth's gravity. While the effect is typically small-of the order of one part per billion of the Earth's gravitational attraction-it is significant at the current level of accuracy of absolute gravity meters. In the past, a self-attraction correction for the FG5 gravity meter has been estimated by considering a rather coarse description of the instrument using simple geometrical shapes (spheres and cylinders). This paper describes a more complete calculation using a CAD-based digitized model of the newest FG5X instrument. We have also included the attraction of the co-moving drag-free chamber as well as the self-attraction of the counterweights used in the FG5X to reduce recoil. The results are also applicable to older style FG5 instruments with a fibre-optic interferometer base. The correction found with this new approach agrees with previous estimates but is now based upon a more complete and accurate model.