1. Introduction

The equivalence principle (EP) stated by Galileo, reformulated by Newton and reexamined by Einstein to become the founding principle of General Relativity, can be tested from its most direct consequence: the universality of free fall (UFF), whereby all bodies fall with the same acceleration regardless of their mass and composition . The most accurate EP experiments have been carried out on the ground with test bodies suspended on a torsion balance, finding no violation to about 10¹³ (Adelberger et al., 1990; Su et al., 1994; Baeßler et al., 1999). (See Note added in proof.) Test bodies in low Earth orbit are subject to a driving gravitational (and inertial) acceleration much stronger than on torsion balances on the ground, by about three orders of magnitude. Moreover, the absence of weight is ideal in small force experiments. As a consequence, space missions can potentially improve by several orders of magnitude the current sensitivity in EP tests. Three such experiments are being considered, and the goals are: 10¹⁵ for the French µSCOPE (MICROSCOPE Website: http://www.cnes.fr/activites/programmes/microsatellite/1sommaire_microsatellite.htm and http://www.onera.fr/dmph-en/accelerometre; Touboul et al., 2001), 10¹⁷ for the Italian "GALILEO GALILEI" (GG) ("GALILEO GALILEI" (GG), Phase A Report, 1998; Nobili et al., 1999; "GALILEO GALILEI" (GG) Website: http://eotvos.dm.unipi.it/nobili; Nobili et al., 2001), 10¹⁸ for the American STEP (Worden, 1978; STEP Satellite Test of the Equivalence Principle, 1993; STEP Satellite Test of the Equivalence Principle, 1996; Step Website: http://einstein.stanford.edu/STEP) [however, STEP studies within the European Space Agency are consistent with a goal of 10¹⁷ (STEP Satellite Test of the Equivalence Principle, 1993; STEP Satellite Test of the Equivalence Principle, 1996)]. µSCOPE and GG are room temperature experiments, STEP is cryogenic at very low temperature.

In all the proposed space experiments the test bodies are hollow cylinders one inside the other, with their centers of mass as close as possible for classical differential effects (such as tides) to be reduced. However, in spite of the different arrangement of the test bodies needed in space, the main features of the ground apparata which have so far provided the best sensitivity should be retained. The most relevant of such features is the differential nature of the torsion balance, which makes it ideally insensitive to common mode effects. Its implementation at the end of the 19th century (Eötvös et al., 1922) has provided a major improvement, by about three orders of magnitude, over previous pendulum tests of the EP. However, Eötvös tested the universality of free fall in the field of the Earth, therefore looking for a constant (DC) anomalous acceleration in the North-South direction of the plane of the horizon. Another major improvement (by about three more orders of magnitude) was made possible in the 1960s and 1970s (Roll et al., 1964; Braginsky and Panov, 1972) when a torsion balance was used to search for a deviation from UFF in the field of the Sun, in which case the diurnal rotation of the Earth itself provides a 24-h modulation of the expected signal. Further improvements on the torsion balance, including its rotation faster than the diurnal rotation of the Earth (at 1 h period) and consequent modulation of the signal at higher frequency, have provided the most sensitive tests so far (Adelberger et al., 1990; Su et al., 1994; Baeßler et al., 1999)

It seems therefore appropriate, for an EP experiment in space, that the instrument be designed as a rotating differential accelerometer made of concentric test cylinders, thus leading naturally to a spacecraft of cylindrical symmetry too, and co-rotating with the test cylinders. If the axis of symmetry is the axis of maximum moment of inertia, one-axis rotation provides (passive) spacecraft attitude stabilization. This is how the GG space experiment for testing the EP in the field of the Earth has been designed: the concentric test cylinders spin around the symmetry axis at a rather high frequency (2 Hz with respect to the center of the Earth) and are sensitive to differential effects in the plane perpendicular to the spin/symmetry axis. A cylindrical spacecraft encloses, in a nested configuration, a cylindrical cage with the test cylinders inside, and is stabilized by rotation around the symmetry axis. As shown in Fig. 1, an EP violation in the field of the Earth would generate a signal of constant amplitude (for zero orbital eccentricity) whose direction is always pointing to the center of the Earth, hence changing orientation with the orbital period of the satellite. The read-out, also rotating with the system, will therefore modulate an EP violation signal at its spin frequency.

Fig. 1. Section across the spin/symmetry axis of the GG outer and inner test cylinders (of different composition) as they orbit around the Earth inside a co-rotating, passively stabilized spacecraft (not shown). The centers of mass of the test cylinders are shown to be displaced towards the center of the Earth as in the case of a violation of the equivalence principle in the field of the Earth (indicated by the arrows). The signal is modulated at the spin frequency of the system (2 Hz with respect to the center of the Earth). The figure is not to scale (taken from Nobili et al., 2001).

We have designed and built a differential, rotating accelerometer similar to the one proposed for the GG space experiment. It is a full scale prototype devoted to testing the main features of the proposed instrument, in spite of the fact that the local acceleration of gravity is about eight orders of magnitude bigger than the largest disturbances the accelerometer would be subject to in space (due to the residual air drag and to solar radiation pressure). Here we describe the ground apparatus, show how it is operated and report the results obtained from measurement data so far. To conclude, we discuss the relevance of these results in view of the GG target sensitivity.