Preparations and Electrostatic Modelling of a Short-Range Test of the Inverse-Square Law of Gravitation with a Superconducting Torsion Balance

A question of increasing interest in gravitational physics examines the validity of the inverse-square law (ISL) of gravity on small scales. Some theoretical models such as the fat graviton and string theory predict that the effect of the fundamental force at sufficiently small range would deviate from the Newtonian prediction. We aim to measure the force of gravity on a scale of ≈ 15μm using a novel superconducting torsion balance. Two major components of this instrument are 1) the ILIAD interferometer to measure rotation in the balance, and 2) the micropositioning system of the source-mass disk, which relies on capacitance measurements in order to align the instrument precisely. This project focused on these two components: aligning the ILIAD and evaluating performance at low (N2) temperatures and numerically evaluating possible deformation patterns in the test masses and the effects of these on capacitance measurements for the micropositioning system.