According to the Weak Equivalence Principle, all bodies should fall at the same rate in a gravitational field. The MICROSCOPE satellite, launched in April 2016, aims to test its validity at the 10 −15 precision level, by measuring the force required to maintain two test masses (of titanium and platinum alloys) exactly in the same orbit. A non-vanishing result would correspond to a violation of the Equivalence Principle, or to the discovery of a new long-range force. Analysis of the first data gives δ(Ti, Pt) = [−1±9(stat)±9(syst)]×10−15 (1σ statistical uncertainty) for the titanium-platinum Eötvös parameter characterizing the relative difference in their free-fall accelerations.

This paper focuses on the dedicated accelerometers developed for the MICROSCOPE mission taking into account the specific range of acceleration to be measured on board the satellite. Considering one micro-g and even less as the full range of the instrument with an objective of one femto-g resolution, that leads to a customized concept and a high-performance electronics for the sensing and servo-actuations of the accelerometer test-masses. This range and performance directed the payload development plan. In addition to a very accurate geometrical sensor core, a high performance electronics architecture provides the measurement of the weak electrostatic forces and torques applied to the test-masses. A set of capacitive detectors delivers the position and the attitude of the test-mass with respect to a very steady gold-coated cage made in silica. The voltages applied on the electrodes surrounding each test-mass are finely controlled to generate the adequate electrical field and so the electrostatic pressures on the test-mass. This field maintains the test-mass motionless with respect to the instrument structure. Digital control laws are implemented in order to enable instrument operation flexibility and a weak position detector noise. These electronics provide both the scientific data for MICROSCOPE’s test of the weak equivalence principle and the input for the satellite drag-free and attitude control system.

The need for high-quality aspheres is rapidly growing, necessitating increased accuracy in their measurement. A reliable uncertainty assessment of asphere form measurement techniques is difficult due to their complexity. In order to explore the accuracy of current asphere form measurement techniques, an interlaboratory comparison was carried out in which four aspheres were measured by eight laboratories using tactile measurements, optical point measurements, and optical areal measurements. Altogether, 12 different devices were employed. The measurement results were analysed after subtracting the design topography and subsequently a best-fit sphere from the measurements. The surface reduced in this way was compared to a reference topography that was obtained by taking the pointwise median across the ensemble of reduced topographies on a Cartesian grid. The deviations of the reduced topographies from the reference topography were analysed in terms of several characteristics including peak-to-valley and root-mean-square deviations. Root-mean-square deviations of the reduced topographies from the reference topographies were found to be on the order of some tens of nanometres up to 89 nm, with most of the deviations being smaller than 20 nm. Our results give an indication of the accuracy that can currently be expected in form measurements of aspheres.

The space mission MICROSCOPE dedicated to the test of the equivalence principle (EP) operated from April 25, 2016 until the deactivation of the satellite on October 16, 2018. In this analysis we compare the free-fall accelerations (a A and a B) of two test masses in terms of the Eötvös parameter η ( A,B ) = 2 a A − a B a A + a B . No EP violation has been detected for two test masses, made from platinum and titanium alloys, in a sequence of 19 segments lasting from 13 to 198 h down to the limit of the statistical error which is smaller than 10−14 for η(Ti, Pt). Accumulating data from all segments leads to η(Ti, Pt) = [−1.5 ± 2.3 (stat) ± 1.5 (syst)] × 10−15 showing no EP violation at the level of 2.7 × 10−15 if we combine stochastic and systematic errors quadratically. This represents an improvement of almost two orders of magnitude with respect to the previous best such test performed by the Eöt-Wash group. The reliability of this limit has been verified by comparing the free falls of two test masses of the same composition (platinum) leading to a null Eötvös parameter with a statistical uncertainty of 1.1 × 10−15.

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