A vector field approach to calculating gravitational forces

Abstract

Calculation of gravitational forces is essential for many fundamental measurements, such as determining the gravitational constant or investigating violations of the inverse square law. These calculations, even with modern computational power, are slow and tedious. Improved calculation efficiency allows an experimentalist to easily check the effect of possible systematic biases and to ease the process of instrument design. Many gravitational measurements are expanded in terms of multipole moments for efficient calculations, however for many experimental geometries these do not converge, leaving awkward sextuple integrals. In this work we introduce a modified approach to the calculation which reduces the force between a point mass and any arbitrary object to a sum of single integrals. The force between any two objects can then be calculated as a quadruple rather than a sextuple integral.