The small satellite ‘Galileo Galilei’ (GG) will test the universality of free fall and hence the weak equivalence principle which is the founding pillar of general relativity to 1 part in 1017. It will use proof masses whose atoms differ substantially from one another in their mass energy content, so as to maximize the chance of violation. GG will improve by four orders of magnitude the current best ‘Eöt-Wash’ tests based on slowly rotating torsion balances, which have been able to reach their thermal noise level. In GG, the expected violation signal is a relative displacement between the proof masses of ≃ 0.6 pm caused by a differential acceleration aGG ≃ 8 × 10−17 ms−2 pointing to the center of mass of the Earth as the satellite orbits around it at νGG ≃ 1.7 × 10−4 Hz. GG will fly an innovative acceleration sensor based on rapidly rotating macroscopic test masses weakly coupled in 2D which up-converts the signal to νspin ≃ 1 Hz, a value well above the frequency of natural oscillations of the masses relative to each other νd = 1/Td ≃ 1/(540 s). The sensor is unique in that it ensures high rotation frequency, low thermal noise and no attenuation of the signal strength (Pegna et al 2011 Phys. Rev. Lett. 107 200801). A readout based on a very low noise laser interferometry gauge developed at Jet Propulsion Laboratory (≃ 1 pm Hz−1/2 at 1 Hz demonstrated) allows the short integration time to be fully exploited. A full scale sensor with the same degrees of freedom and the same dynamical features as the one to fly in GG has been setup on ground (GGG). The proof masses of GGG are affected by acceleration and tilt noise acting on the rotating shaft because of ball bearings and terrain microseismicity (both absent in space). Overall, by means of appropriate 2D flexure joints, these noise sources have been reduced by a factor almost 105 down to a differential acceleration between the proof masses of ≃ 7 × 10−11 m s−2 (at 1.7 × 10−4 Hz up-converted by rotation to ≃ 0.2 Hz). The corresponding noise in the relative displacements of the proof masses, read by co-rotating capacitance bridges, is ≃ 180 pm, which is 300 times larger than the target in space. GGG error budget shows that it can reach a differential acceleration sensitivity aGGGgoal ≃ 8 × 10−16 m s−2, not limited by thermal noise. This value is only a factor 10 larger than what GG must reach in space to meet its target, and slightly smaller than the acceleration noise of the torsion balance. It can be achieved partly by means of weaker joints and an optimized mechanical design—so as to improve the attenuation factor—and partly by replacing the current ball bearings with much less noisy air bearings (also used in torsion balance tests) so as to reduce input noise. A laser gauge readout with noise level rlaser-ro ≃ 30 pm Hz−1/2 at 0.2÷3 Hz will be implemented.

`Galileo Galilei' (GG) is a proposal for a small, low-orbit satellite devoted to testing the equivalence principle (EP) of Galileo, Newton and Einstein. The GG report on the phase A study recently carried out with funding from ASI (Agenzia Spaziale Italiana) concluded that GG can test the equivalence principle to 1 part in 1017 at room temperature. The main novelty is to modulate the expected differential signal of an EP violation at the spin rate of the spacecraft (2 Hz). Compared with other experiments, the modulation frequency is increased by more than a factor of 104, thus reducing 1/f (low-frequency) electronic and mechanical noise. The challenge for an EP test in space is to improve over the sensitivity of ground-based experiments (about 1 part in 1012) by many orders of magnitude, so as to deeply probe a so far totally unexplored field; doing that with more than one pair of bodies is an unnecessary complication. For this reason GG is now proposed with a single pair of test masses. At present the best and most reliable laboratory-controlled tests of the equivalence principle have been achieved by the `Eöt-Wash' group with small test cylinders arranged on a torsion balance placed on a turntable which provides the modulation of the signal (a 1-2 h rotation period). The torsion balance is not a suitable instrument in space. We have designed and built the GGG (`GG on the Ground') prototype. It is made of coaxial test cylinders weakly coupled (via mechanical suspensions) and quickly rotating (6 Hz achieved so far); in addition, it is well suited to be flown in space - where the driving signal is about three orders of magnitude stronger and the absence of weight is very helpful - inside the coaxial, co-rotating GG cylindrical spacecraft. The GGG apparatus is now operational. Preliminary measurement data indicate that weakly coupled, fast-spinning macroscopic rotors can be a suitable instrument to detect small differential effects. Rotation (up to 6 Hz so far) is stabilized by a small passive oil damper. A finer active damper, using small capacitance sensors and actuators as in the design of the space experiment, is in preparation. The current sensitivity of the GGG system is of 10-9 m s-2/√Hz at about 300 s, which can be improved because horizontal seismic noise is rejected very well; perturbing effects of terrain tilts (due to microseismicity and tides) will be reduced by adding a passive cardanic suspension. As for the capacitance read-out, the current sensitivity (5 pm displacements in 1 s integration time at room temperature) is adequate to make GGG competitive with the torsion balance. Because of the stronger signal and weaker coupling of the test rotors in space, this sensitivity is also adequate for GG to reach its target accuracy (10-17). Information, references, research papers and photographs of the apparatus are available on the Web (http://tycho.dm.unipi.it/nobili).

Mechanical oscillators can be sensitive to very small forces. Low frequency effects are up-converted to higher frequency by rotating the oscillator. We show that for 2-dimensional oscillators rotating at frequency much higher than the signal the thermal noise force due to internal losses and competing with it is abated as the square root of the rotation frequency. We also show that rotation at frequency much higher than the natural one is possible if the oscillator has 2 degrees of freedom, and describe how this property applies also to torsion balances. In addition, in the 2D oscillator the signal is up-converted above resonance without being attenuated as in the 1D case, thus relaxing requirements on the read out. This work indicates that proof masses weakly coupled in 2D and rapidly rotating can play a major role in very small force physics experiments.

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