A dynamical technique for measuring the gravitational quadrupole coupling of the step and µscope experimental test masses

This paper describes a new method for determining the suitability of 'test masses' for use in exceptionally sensitive spaceborne experiments for testing the equivalence principle, such as STEP and µSCOPE. It is aimed at measuring the size of the gravitational quadrupolar coupling of test masses. Conventional dynamical methods measure principal moments of inertia separately, and then difference them. The technique proposed here measures directly any moment of inertia imbalance of the mass under test, by spinning it at low frequency (a few hertz) about a vertical axis through its centre of mass. Any mass quadrupolar moment then results in a torque on the body about a horizontal axis. In order to quantify the quadrupolar coupling either this torque may be measured directly, or the test mass may be allowed to perform low-frequency oscillations. Some practical limitations of the technique are discussed.