Optimization of the geometry for dipole-dipole and dipole-monopole experiments, using the gravitational interaction between a point-source and a finite cylinder

Summary

The torsion balance has been used frequently in the search for weak gravitational-like forces. A major problem in the design of these experiments is the optimization of the geometry of the cylindrical masses that have been used. Starting from the formula for simple Newtonian gravitational interaction, the general formulae for treating both «dipole-dipole» and «dipole-monopole» interactions for cylindrically shaped bodies are derived. These formulae are used to optimize the shape of both the attracting and balance masses. The interaction forces are derived using only 3D integration—rather than the usual 6D integration carried out over the volumes of both interacting bodies. This has resulted in considerably reduced computational time, and thereby the attainment of high accuracy in the optimization.