Differential gravitational coupling between cylindrically-symmetric, concentric test masses and an arbitrary gravitational source: relevance to the STEP experiment

Abstract

The gravitational interaction between a point mass and a finite, hollow, thick-walled cylinder is calculated, the axial force is derived, and the parametric form of the coupling coefficients k_2p is presented. This theory is applied to the test-masses for the Satellite Test of the Equivalence Principle (STEP) experiment, and an equation is derived for the differential gravitational coupling to these masses which is more than 10⁵ times faster to compute than a Monte-Carlo integration of similar accuracy.