E. Polacco

Evaluation of a proposed test of the weak equivalence principle using Earth-orbiting bodies in high-speed co-rotation: re-establishing the physical bases

Test masses coupled by weak mechanical suspensions are sensitive to differential forces such as the force due to a possible violation of the equivalence principle (EP). If in addition they are put in rapid rotation, the differential signal is modulated at high frequency, which is beneficial for noise reduction. Galileo Galilei (GG) is a proposed space experiment for testing the equivalence principle to 1 part in 10 17 based on these concepts. A recent paper by Jafry and Weinberger (1998 Class. Quantum Grav.15 481-500) claims that GG can only reach 10 14 . We show that the analysis of this paper is flawed (by several orders of magnitude) because of two misconceptions: one on the physical nature of mechanical damping and the other on active control methods for the stabilization of spinning bodies.

The “Galileo Galilei” (GG) project: Testing the Equivalence Principle in space and on Earth

“GALILEO GALILEI” (GG) is a proposal for a small, low orbit satellite devoted to testing the Equivalence Principle (EP) of Galileo, Newton and Einstein to 1 part in 1017. At the end of 1997 GG has been selected and funded by ASI (Agenzia Spaziale Italiana) for a 1-year Phase A study. The main novelty of GG is that the concentric hollow test cylinders whose relative motion (in the plane perpendicular to the spin axis) would be affected by an EP violation, spin together with the read-out capacitance sensors placed in between them. The nominal spin rate is 2 Hz, and this is the frequency at which the putative EP violation signal is modulated by the sensors. As compared to other experiments the modulation frequency is increased by more than a factor 104, thus reducing 1f (low frequency) electronic and mechanical noise. GG will have FEEP ion thrusters for drag compensation. The required amount of propellant is of a few grams only. The experiment works at room temperature. To demonstrate the feasibility of the space experiment a payload prototype for EP testing on the ground (GGG - GG on the Ground) is under development in the laboratories of Laben. The challenge in this field is to fly an experiment able to improve by many orders of magnitude the current best ground sensitivity (≅10−12). This requires spurious relative motions of the test bodies to be greatly reduced, leaving them essentially motionless. Doing that with more than one pair of bodies appears to be an unnecessary complication. This is why GG is now proposed with a single pair of test masses. Information, research papers and photographs of the ground apparatus are available on the Web (http://tycho.dm.unipi.it/nobili).

A rotating differential accelerometer for testing the equivalence principle in space: results from laboratory tests of a ground prototype

a, a a a b * Abstract We have proposed to test the equivalence principle (EP) in low Earth orbit with a rapidly rotating differential accelerometer (made of weakly coupled concentric test cylinders) whose rotation provides high frequency signal modulation and avoids severe limitations otherwise due to operation at room temperature (PhRvD 63 (2001) 101101). Although the accelerometer has been conceived for best performance in absence of weight, we have designed, built and tested a variant of it at 1-g. Here we report the results of measurements performed so far. Losses measured with the full system in operation yield a quality factor only four times smaller than the value required for the proposed high accuracy EP test in space. Unstable whirl motions, which are known to arise in the system and might be a matter of concern, are found to grow as slowly as predicted and can be stabilized. The capacitance differential read-out (the mechanical parts, electronics and software for data analysis) is in all similar to what is needed in the space experiment. In the instrument described here the coupling of the test masses is 24 000 times stiffer than in the one proposed for flight, which makes it 24 000 times less 22 sensitive to differential displacements. With this stiffness it should detect test masses separations of 1.5 ?10 mm, while so far we have achieved only 1.5 mm, because of large perturbations—due to the motor, the ball bearings, the non-perfect verticality of the system—all of which, however, are absent in space. The effects of these perturbations should be reduced by 100 times in order to perform a better demonstration. Further instrument improvements are underway to fill this gap and also to reduce its stiffness, thus increasing its significance as a prototype of the space experiment.  2002 Elsevier B.V. All rights reserved.

Radiometer effect in the μSCOPE space mission

Abstract Space experiments to test the Equivalence Principle (EP) are affected by a systematic radiometer effect having the same signature as the target signal. In [PhRvD 63 (2001) 101101(R)] we have investigated this effect for the three proposed experiments currently under study by space agencies: μSCOPE, STEP and GG, setting the requirements to be met—on temperature gradients at the level of the test masses—for each experiment to reach its goal. We have now re-examined the radiometer effect in the case of μSCOPE and carried out a quantitative comparative analysis, on this issue, with the proposed heliocentric LISA mission for the detection of gravity waves. We find that, even assuming that the μSCOPE spacecraft and payload be built to meet all the challenging requirements of LISA, temperature gradients along its test masses would still make the radiometer effect larger than the target signal of an EP violation because of flying in the low geocentric orbit required for EP testing. We find no way to separate with certainty the radiometer systematic disturbance from the signal. μSCOPE is designed to fly a second accelerometer whose test masses have the same composition, in order to separate out systematic effects which—not being composition dependent like the signal—must be detected by both accelerometers. We point out that this accelerometer is in fact insensitive to the radiometer effect, just as it is to an EP violation signal, and therefore even having it onboard will not allow this disturbance to be separated out. μSCOPE is under construction and it is scheduled to fly in 2004. If it will detect a signal to the expected level, it will be impossible to establish with certainty whether it is due to the well known classical radiometer effect or else to a violation of the equivalence principle—which would invalidate General Relativity. The option to increase the rotation speed of the spacecraft (now set at about 10−3 Hz) so as to average out the temperature gradients which generate the radiometer effect, is allowed in the GG design, not in that of STEP and μSCOPE.

Proposed noncryogenic, nondrag-free test of the equivalence principle in space

Ever since Galileo scientists have known that all bodies fall with the same acceleration regardless of their mass and composition. Known as the Universality of Free Fall, this is the most direct experimental evidence of the Weak Equivalence Principle, a founding pillar of General Relativity according to which the gravitational (passive) mass m and the inertial g mass m are always in the same positive ratio in all test bodies. A space experiment offers two main advantages: a signal i

Dynamical response of the Galileo Galilei rotor for a Ground test of the Equivalence Principle: theory, simulation and experiment. Part I: the normal modes

Recent theoretical work suggests that violation of the equivalence principle might be revealed in a measurement of the fractional differential acceleration η between two test bodies—of different compositions, falling in the gravitational field of a source mass—if the measurement is made to the level of η≃10−13 or better. This being within the reach of ground based experiments gives them a new impetus. However, while slowly rotating torsion balances in ground laboratories are close to reaching this level, only an experiment performed in a low orbit around the Earth is likely to provide a much better accuracy. We report on the progress made with the “Galileo Galilei on the ground” (GGG) experiment, which aims to compete with torsion balances using an instrument design also capable of being converted into a much higher sensitivity space test. In the present and following articles (Part I and Part II), we demonstrate that the dynamical response of the GGG differential accelerometer set into supercritical rota...