Mass properties measurement for drag-free test masses

Space-borne gravitational wave observatories like the Laser Interferometer Space Antenna (LISA) and those beyond, which may utilize a Modular Gravitational Reference Sensor (MGRS), greatly benefit from precise knowledge of the mass center location and moment of inertia tensor of the test mass prior to launch. The motion of the mass center of a drag-free test mass, which follows a pure geodesic, must be inferred from measurements of the surface. Therefore, knowledge of the mass center is critical for calibration of the cross-coupling between rotational and translational degrees of freedom. Together with the moment of inertia tensor, the mass center can also provide an estimate of the material density inhomogeneity to quadratic order, and the gravitational potential to second order, which improves modeling of self gravitation forces. These benefits, which are independent of the test mass shape, motivate the development of three new techniques for improving mass center and moment of inertia measurements beyond the current state of the art. A static pendulum is proposed to determine the mass center of a cubic test mass to ~ 1 μm by measuring the equilibrium position with the cube in up to 24 different orientations relative to the pendulum platform. Measuring the natural frequency of a dynamic torsion pendulum can determine both the mass center and moment of inertia tensor of arbitrarily shaped objects to ~ 5 μm and 1 part in ~ 104 respectively. The velocity modulation technique for measuring the mass center of a sphere has raised the bar in precision to ~ 150 nm, a factor of 20 improvement over the work presented at the LISA 6th symposium. This new technique involves rolling the sphere down a set of parallel rails to spectrally shift the mass center offset information to the rolling rate frequency, in order to avoid the 1/f noise that typically prevents other techniques from achieving precision below 1 μm.