The aim of this paper is to extend, clarify, and deepen the results of our previous work [D. M. Lucchesi and R. Peron, Phys. Rev. Lett. 105, 231103 (2010)

Through the contributions of Galileo, Newton, and Einstein, we recall the universality of free fall (UFF), the weak equivalence principle (WEP), and the strong equivalence principle (SEP), in order to stress that general relativity requires all test masses to be equally accelerated in a gravitational field; that is, it requires UFF and WEP to hold. The possibility of testing this crucial fact with null, highly sensitive experiments makes these the most powerful tests of the theory. Following Schiff, we derive the gravitational redshift from the WEP and special relativity and show that, as long as clocks are affected by a gravitating body like normal matter, measurement of the redshift is a test of UFF/WEP but cannot compete with direct null tests. A new measurement of the gravitational redshift based on free-falling cold atoms and an absolute gravimeter is not competitive either. Finally, we compare UFF/WEP experiments using macroscopic masses as test bodies in one case and cold atoms in the other. We conclude that there is no difference in the nature of the test and that the merit of any such experiment rests on the accuracy it can achieve and on the physical differences between the elements it can test, macroscopic proof masses being superior in both respects

Recent results of the LARASE research program in terms of model improvements and relativistic measurements are presented. In particular, the results regarding the development of new models for the non-gravitational perturbations that affect the orbit of the LAGEOS and LARES satellites are described and discussed. These are subtle and complex effects that need a deep knowledge of the structure and the physical characteristics of the satellites in order to be correctly accounted for. In the field of gravitational measurements, we present a new measurement of the relativistic Lense-Thirring precession with a $0.5\%$ precision. In this measurement, together with the relativistic effect we also estimated two even zonal harmonics coefficients. The uncertainties of the even zonal harmonics of the gravitational field of the Earth have been responsible, until now, of the larger systematic uncertainty in the error budget of this kind of measurements. For this reason, the role of the errors related to the model used for the gravitational field of the Earth in these measurements is discussed. In particular, emphasis is given to GRACE temporal models, that strongly help to reduce this kind of systematic errors.

A new measurement of the gravitomagnetic field of the Earth is presented. The measurement has been obtained through the careful evaluation of the Lense-Thirring (LT) precession on the combined orbits of three passive geodetic satellites, LAGEOS, LAGEOS II, and LARES, tracked by the Satellite Laser Ranging (SLR) technique. This general relativity precession, also known as frame-dragging, is a manifestation of spacetime curvature generated by mass-currents, a peculiarity of Einstein’s theory of gravitation. The measurement stands out, compared to previous measurements in the same context, for its precision ($\simeq 7.4\times {10}^{-3}$, at a 95% confidence level) and accuracy ($\simeq 16\times {10}^{-3}$), i.e., for a reliable and robust evaluation of the systematic sources of error due to both gravitational and non-gravitational perturbations. To achieve this measurement, we have largely exploited the results of the GRACE (Gravity Recovery And Climate Experiment) mission in order to significantly improve the description of the Earth’s gravitational field, also modeling its dependence on time. In this way, we strongly reduced the systematic errors due to the uncertainty in the knowledge of the Earth even zonal harmonics and, at the same time, avoided a possible bias of the final result and, consequently, of the precision of the measurement, linked to a non-reliable handling of the unmodeled and mismodeled periodic effects.

The integration time required by space experiments to perform high accuracy tests of the universality of free fall and the weak equivalence principle is a crucial issue. It is inversely proportional to the square of the acceleration to be measured, which is extremely small; the duration of the mission is a severe limitation and experiments in space lack repeatability. An exceedingly long integration time can therefore rule out a mission target. We have evaluated the integration time due to thermal noise from gas damping, Johnson noise and eddy currents—which are independent of the signal frequency—and to internal damping, which is known to decrease with increasing frequency. It is found that at low frequencies thermal noise from internal damping dominates. In the “Galileo Galilei” proposed space experiment to test the equivalence principle to ${10}^{-17}$ the rapid rotation of the satellite (1 Hz) up-converts the signal to a frequency region where thermal noise from internal damping is lower than gas damping and only a factor 2 higher than Johnson noise, with a total integration time of 2.4 to 3.5 hours even in a very conservative estimate. With an adequate readout and additional care in reducing systematics the test could be improved by another order of magnitude, close to ${10}^{-18}$, requiring a hundred times longer—still affordable—integration time of 10 to 14.6 days. $\mu \text{SCOPE}$, a similar room temperature mission under construction by the French space agency to be launched in 2015, aims at a ${10}^{-15}$ test with an estimated integration time of 1.4 days. Space tests using cold atoms and atom interferometry have been proposed to be performed on the space station (Q-WEP, to ${10}^{-14}$) and on a dedicated mission (STE-QUEST, to ${10}^{-15}$ like $\mu \text{SCOPE}$). In this case integration is required in order to reduce single shot noise. European Space Agency funded studies report an integration time of several months and a few years respectively. DOI: http://dx.doi.org/10.1103/PhysRevD.89.042005 © 2014 American Physical Society