Gravitational modelling of the test masses for STEP and LISA

The test masses for the proposed STEP (satellite test of the equivalence principle) experiment can be influenced, adversely, by time-varying gravitational coupling to other masses within the spacecraft. The liquid helium in the spacecraft's Dewar is a severe potential source of this effect, since its influence is at the same frequency as any actual equivalence principal violation. The pairs of STEP test masses must be made differentially immune to this effect, and a measure of this immunity can be quantified in terms of a 'differential acceleration susceptibility', defined as .R; ; '/ D 1az=a. Here 1az and a are the differential-axial and commonmode accelerations, respectively, of the two masses, for a perturbing source at relative position .R; ; '/. This work presents the results of analyses for STEP's test masses having either four or six flats, included to prevent them from rolling in azimuth .'/. Different schemes for minimizing .R; ; '/ are discussed in detail, and it is shown that the gravitational effect of the flats may be balanced between the inner and outer masses, leading to a 'fully-balanced' pair. However, it is concluded that such a scheme is not practical, and the 'susceptibility' may be minimized, alternatively, by choosing six flats rather than four. It is noted that the gravitational theory used here may be applied to six- or four-sided bodies, including cubic test masses-as proposed for LISA.