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.

• Received 1 March 2013

DOI:https://doi.org/10.1103/PhysRevD.89.042005