Exact Finitely Expanded Gravity Anomaly of Uniform Thin Polygonal Sheets

Standard closed form anomaly formulae for polyhedral targets exhibit numerical instability. Under finite floating point precision, the accuracy of the computed anomaly increasingly degrades with increasing target distance. The instability may with advantage be studied from the anomaly of a thin polygonal sheet, as the polyhedral formulae represent a superposition of sheet formulae. We derive an exact finite expansion of the thin sheet formula, corresponding to a point source term plus perturbation. This form exhibits the required absolute numerical stability. The result suggests generalization to absolutely stable polyhedral anomaly formulae.