‘Galileo Galilei’ (GG): space test of the weak equivalence principle to 10 ⁻¹⁷ and laboratory demonstrations

Abstract

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 10^(17). 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
\ncurrent 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
\nsignal is a relative displacement between the proof masses of ≃ 0.6 pm caused by a differential acceleration a_(GG) ≃ 8 × 10^(−17) ms^(−2) pointing to the center of mass of the Earth as the satellite orbits around it at ν_(GG) ≃ 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 ν_(spin)≃ 1Hz, a value well above the frequency of natural oscillations of the masses relative to each other ν_d = 1/T_d ≃ 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 (≃ 1pm Hz^(−1/2) at 1Hz demonstrated) allows the short integration time to be fully exploited. A full scale sensor with the same degrees of freedom and the
\nsame 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
\n(both absent in space). Overall, by means of appropriate 2D flexure joints, these noise sources have been reduced by a factor almost 10^5 down to a differential acceleration between the proof masses of ≃ 7 × 10^(−11) ms^(−2) (at
\n1.7 × 10^(−4) Hz up-converted by rotation to ≃ 0.2Hz). 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 α_(GGGgoal) 8×10^(−16) ms^(−2), not limited by thermal noise. This value
\nis 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
\nbe 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 r_(laser-ro) ≃ 30 pm Hz^(−1/2) at 0.2 ÷ 3Hz will be implemented.